Controlling matter waves in momentum space

NASA Astrophysics Data System (ADS)

Lin, De-Hone

2014-07-01

The transformation design method of momentum for matter waves in a harmonic trap is proposed. As applications, we design (1) a momentum invisibility cloak to control the distribution of a wave function in momentum space, (2) a quantum localization cloak that localizes a matter wave around zero momentum, and (3) the unusual quantum states of momentum space. Comprehension of these momentum cloaks in position space through the Fourier transformation is presented. In contrast to the construct of quantum cloaks in position space, the momentum cloaks presented here can only be reached by controlling the spring parameter of the trap and offering a potential there, without needing to control the effective mass of quantum particles themselves. The presented discussions also provide a possible inspiration to help localize and maintain a quantum state in momentum space by way of controlling the shape of a trap and a supplied potential.

Quantum information processing in phase space: A modular variables approach

NASA Astrophysics Data System (ADS)

Ketterer, A.; Keller, A.; Walborn, S. P.; Coudreau, T.; Milman, P.

2016-08-01

Binary quantum information can be fault-tolerantly encoded in states defined in infinite-dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal operations. The drawback of this encoding is that the corresponding logical states are unphysical, meaning infinitely localized in phase space. We use the modular variables formalism to show that, in a number of protocols relevant for quantum information and for the realization of fundamental tests of quantum mechanics, it is possible to loosen the requirements on the logical subspace without jeopardizing their usefulness or their successful implementation. Such protocols involve measurements of appropriately chosen modular variables that permit the readout of the encoded discrete quantum information from the corresponding logical states. Finally, we demonstrate the experimental feasibility of our approach by applying it to the transverse degrees of freedom of single photons.

Experimental quantum teleportation over a high-loss free-space channel.

PubMed

Ma, Xiao-song; Kropatschek, Sebastian; Naylor, William; Scheidl, Thomas; Kofler, Johannes; Herbst, Thomas; Zeilinger, Anton; Ursin, Rupert

2012-10-08

We present a high-fidelity quantum teleportation experiment over a high-loss free-space channel between two laboratories. We teleported six states of three mutually unbiased bases and obtained an average state fidelity of 0.82(1), well beyond the classical limit of 2/3. With the obtained data, we tomographically reconstructed the process matrices of quantum teleportation. The free-space channel attenuation of 31 dB corresponds to the estimated attenuation regime for a down-link from a low-earth-orbit satellite to a ground station. We also discussed various important technical issues for future experiments, including the dark counts of single-photon detectors, coincidence-window width etc. Our experiment tested the limit of performing quantum teleportation with state-of-the-art resources. It is an important step towards future satellite-based quantum teleportation and paves the way for establishing a worldwide quantum communication network.

Wigner's quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

NASA Astrophysics Data System (ADS)

Kakofengitis, Dimitris; Steuernagel, Ole

2017-09-01

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current J . This current reveals fine details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J's discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

RAPID COMMUNICATIONS: Long-distance quantum teleportation assisted with free-space entanglement distribution

NASA Astrophysics Data System (ADS)

Ren, Ji-Gang; Yang, Bin; Yi, Zhen-Huan; Zhou, Fei; Chen, Kai; Peng, Cheng-Zhi; Pan, Jian-Wei

2009-08-01

Faithful long-distance quantum teleportation necessitates prior entanglement distribution between two communicated locations. The particle carrying on the unknown quantum information is then combined with one particle of the entangled states for Bell-state measurements, which leads to a transfer of the original quantum information onto the other particle of the entangled states. However in most of the implemented teleportation experiments nowadays, the Bell-state measurements are performed even before successful distribution of entanglement. This leads to an instant collapse of the quantum state for the transmitted particle, which is actually a single-particle transmission thereafter. Thus the true distance for quantum teleportation is, in fact, only in a level of meters. In the present experiment we design a novel scheme which has overcome this limit by utilizing fiber as quantum memory. A complete quantum teleportation is achieved upon successful entanglement distribution over 967 meters in public free space. Active feed-forward control techniques are developed for real-time transfer of quantum information. The overall experimental fidelities for teleported states are better than 89.6%, which signify high-quality teleportation.

Optimized decoy state QKD for underwater free space communication

NASA Astrophysics Data System (ADS)

Lopes, Minal; Sarwade, Nisha

Quantum cryptography (QC) is envisioned as a solution for global key distribution through fiber optic, free space and underwater optical communication due to its unconditional security. In view of this, this paper investigates underwater free space quantum key distribution (QKD) model for enhanced transmission distance, secret key rates and security. It is reported that secure underwater free space QKD is feasible in the clearest ocean water with the sifted key rates up to 207kbps. This paper extends this work by testing performance of optimized decoy state QKD protocol with underwater free space communication model. The attenuation of photons, quantum bit error rate and the sifted key generation rate of underwater quantum communication is obtained with vector radiative transfer theory and Monte Carlo method. It is observed from the simulations that optimized decoy state QKD evidently enhances the underwater secret key transmission distance as well as secret key rates.

Quantum-secret-sharing scheme based on local distinguishability of orthogonal multiqudit entangled states

NASA Astrophysics Data System (ADS)

Wang, Jingtao; Li, Lixiang; Peng, Haipeng; Yang, Yixian

2017-02-01

In this study, we propose the concept of judgment space to investigate the quantum-secret-sharing scheme based on local distinguishability (called LOCC-QSS). Because of the proposing of this conception, the property of orthogonal mutiqudit entangled states under restricted local operation and classical communication (LOCC) can be described more clearly. According to these properties, we reveal that, in the previous (k ,n )-threshold LOCC-QSS scheme, there are two required conditions for the selected quantum states to resist the unambiguous attack: (i) their k -level judgment spaces are orthogonal, and (ii) their (k -1 )-level judgment spaces are equal. Practically, if k

Average fidelity between random quantum states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zyczkowski, Karol; Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Aleja Lotnikow 32/44, 02-668 Warsaw; Perimeter Institute, Waterloo, Ontario, N2L 2Y5

2005-03-01

We analyze mean fidelity between random density matrices of size N, generated with respect to various probability measures in the space of mixed quantum states: the Hilbert-Schmidt measure, the Bures (statistical) measure, the measure induced by the partial trace, and the natural measure on the space of pure states. In certain cases explicit probability distributions for the fidelity are derived. The results obtained may be used to gauge the quality of quantum-information-processing schemes.

Transition probability spaces in loop quantum gravity

NASA Astrophysics Data System (ADS)

Guo, Xiao-Kan

2018-03-01

We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-categories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity.

Entropy for quantum pure states and quantum H theorem

NASA Astrophysics Data System (ADS)

Han, Xizhi; Wu, Biao

2015-06-01

We construct a complete set of Wannier functions that are localized at both given positions and momenta. This allows us to introduce the quantum phase space, onto which a quantum pure state can be mapped unitarily. Using its probability distribution in quantum phase space, we define an entropy for a quantum pure state. We prove an inequality regarding the long-time behavior of our entropy's fluctuation. For a typical initial state, this inequality indicates that our entropy can relax dynamically to a maximized value and stay there most of time with small fluctuations. This result echoes the quantum H theorem proved by von Neumann [Zeitschrift für Physik 57, 30 (1929), 10.1007/BF01339852]. Our entropy is different from the standard von Neumann entropy, which is always zero for quantum pure states. According to our definition, a system always has bigger entropy than its subsystem even when the system is described by a pure state. As the construction of the Wannier basis can be implemented numerically, the dynamical evolution of our entropy is illustrated with an example.

Relativistic quantum cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Molotkov, S. N., E-mail: molotkov@issp.ac.ru

2011-03-15

A new protocol of quantum key distribution is proposed to transmit keys through free space. Along with quantum-mechanical restrictions on the discernibility of nonorthogonal quantum states, the protocol uses additional restrictions imposed by special relativity theory. Unlike all existing quantum key distribution protocols, this protocol ensures key secrecy for a not strictly one-photon source of quantum states and an arbitrary length of a quantum communication channel.

Phase space flow of particles in squeezed states

NASA Technical Reports Server (NTRS)

Ceperley, Peter H.

1994-01-01

The manipulation of noise and uncertainty in squeezed states is governed by the wave nature of the quantum mechanical particles in these states. This paper uses a deterministic model of quantum mechanics in which real guiding waves control the flow of localized particles. This model will be used to examine the phase space flow of particles in typical squeezed states.

Wavelets and the squeezed states of quantum optics

NASA Technical Reports Server (NTRS)

Defacio, B.

1992-01-01

Wavelets are new mathematical objects which act as 'designer trigonometric functions.' To obtain a wavelet, the original function space of finite energy signals is generalized to a phase-space, and the translation operator in the original space has a scale change in the new variable adjoined to the translation. Localization properties in the phase-space can be improved and unconditional bases are obtained for a broad class of function and distribution spaces. Operators in phase space are 'almost diagonal' instead of the traditional condition of being diagonal in the original function space. These wavelets are applied to the squeezed states of quantum optics. The scale change required for a quantum wavelet is shown to be a Yuen squeeze operator acting on an arbitrary density operator.

Towards quantum communications in free-space seawater.

PubMed

Ji, Ling; Gao, Jun; Yang, Ai-Lin; Feng, Zhen; Lin, Xiao-Feng; Li, Zhong-Gen; Jin, Xian-Min

2017-08-21

Long-distance quantum channels capable of transferring quantum states faithfully for unconditionally secure quantum communication have been so far confirmed to be feasible in both fiber and free-space air. However, it remains unclear whether seawater, which covers more than 70% of the earth, can also be utilized, leaving global quantum communication incomplete. Here we experimentally demonstrate that polarization quantum states including general qubits of single photon and entangled states can survive well after travelling through seawater. We perform experiments with seawater collected over a range of 36 kilometers in the Yellow Sea. For single photons at 405 nm in a blue-green window, we obtain an average process fidelity above 98%. For entangled photons at 810nm, albeit very high loss, we observe the violation of Bell inequality with 33 standard deviations. Our results confirm the feasibility of a seawater quantum channel, representing the first step towards underwater quantum communication.

Characterizing quantum channels with non-separable states of classical light

NASA Astrophysics Data System (ADS)

Ndagano, Bienvenu; Perez-Garcia, Benjamin; Roux, Filippus S.; McLaren, Melanie; Rosales-Guzman, Carmelo; Zhang, Yingwen; Mouane, Othmane; Hernandez-Aranda, Raul I.; Konrad, Thomas; Forbes, Andrew

2017-04-01

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links that cannot be repaired without performing quantum tomography on the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterize quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled photons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories, and thus enables precise quantum error correction in short- and long-haul optical communication, in both free space and fibre.

Quantum Optics in Phase Space

NASA Astrophysics Data System (ADS)

Schleich, Wolfgang P.

2001-04-01

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khrennikov, Andrei

2010-08-15

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical randommore » fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.« less

Quantum decimation in Hilbert space: Coarse graining without structure

NASA Astrophysics Data System (ADS)

Singh, Ashmeet; Carroll, Sean M.

2018-03-01

We present a technique to coarse grain quantum states in a finite-dimensional Hilbert space. Our method is distinguished from other approaches by not relying on structures such as a preferred factorization of Hilbert space or a preferred set of operators (local or otherwise) in an associated algebra. Rather, we use the data corresponding to a given set of states, either specified independently or constructed from a single state evolving in time. Our technique is based on principle component analysis (PCA), and the resulting coarse-grained quantum states live in a lower-dimensional Hilbert space whose basis is defined using the underlying (isometric embedding) transformation of the set of fine-grained states we wish to coarse grain. Physically, the transformation can be interpreted to be an "entanglement coarse-graining" scheme that retains most of the global, useful entanglement structure of each state, while needing fewer degrees of freedom for its reconstruction. This scheme could be useful for efficiently describing collections of states whose number is much smaller than the dimension of Hilbert space, or a single state evolving over time.

Can a quantum state over time resemble a quantum state at a single time?

NASA Astrophysics Data System (ADS)

Horsman, Dominic; Heunen, Chris; Pusey, Matthew F.; Barrett, Jonathan; Spekkens, Robert W.

2017-09-01

The standard formalism of quantum theory treats space and time in fundamentally different ways. In particular, a composite system at a given time is represented by a joint state, but the formalism does not prescribe a joint state for a composite of systems at different times. If there were a way of defining such a joint state, this would potentially permit a more even-handed treatment of space and time, and would strengthen the existing analogy between quantum states and classical probability distributions. Under the assumption that the joint state over time is an operator on the tensor product of single-time Hilbert spaces, we analyse various proposals for such a joint state, including one due to Leifer and Spekkens, one due to Fitzsimons, Jones and Vedral, and another based on discrete Wigner functions. Finding various problems with each, we identify five criteria for a quantum joint state over time to satisfy if it is to play a role similar to the standard joint state for a composite system: that it is a Hermitian operator on the tensor product of the single-time Hilbert spaces; that it represents probabilistic mixing appropriately; that it has the appropriate classical limit; that it has the appropriate single-time marginals; that composing over multiple time steps is associative. We show that no construction satisfies all these requirements. If Hermiticity is dropped, then there is an essentially unique construction that satisfies the remaining four criteria.

Phase Space Tweezers for Tailoring Cavity Fields by Quantum Zeno Dynamics

NASA Astrophysics Data System (ADS)

Raimond, J. M.; Sayrin, C.; Gleyzes, S.; Dotsenko, I.; Brune, M.; Haroche, S.; Facchi, P.; Pascazio, S.

2010-11-01

We discuss an implementation of quantum Zeno dynamics in a cavity quantum electrodynamics experiment. By performing repeated unitary operations on atoms coupled to the field, we restrict the field evolution in chosen subspaces of the total Hilbert space. This procedure leads to promising methods for tailoring nonclassical states. We propose to realize “tweezers” picking a coherent field at a point in phase space and moving it towards an arbitrary final position without affecting other nonoverlapping coherent components. These effects could be observed with a state-of-the-art apparatus.

Integrability and nonintegrability of quantum systems. II. Dynamics in quantum phase space

NASA Astrophysics Data System (ADS)

Zhang, Wei-Min; Feng, Da Hsuan; Yuan, Jian-Min

1990-12-01

Based on the concepts of integrability and nonintegrability of a quantum system presented in a previous paper [Zhang, Feng, Yuan, and Wang, Phys. Rev. A 40, 438 (1989)], a realization of the dynamics in the quantum phase space is now presented. For a quantum system with dynamical group scrG and in one of its unitary irreducible-representation carrier spaces gerhΛ, the quantum phase space is a 2MΛ-dimensional topological space, where MΛ is the quantum-dynamical degrees of freedom. This quantum phase space is isomorphic to a coset space scrG/scrH via the unitary exponential mapping of the elementary excitation operator subspace of scrg (algebra of scrG), where scrH (⊂scrG) is the maximal stability subgroup of a fixed state in gerhΛ. The phase-space representation of the system is realized on scrG/scrH, and its classical analogy can be obtained naturally. It is also shown that there is consistency between quantum and classical integrability. Finally, a general algorithm for seeking the manifestation of ``quantum chaos'' via the classical analogy is provided. Illustrations of this formulation in several important quantum systems are presented.

A space-efficient quantum computer simulator suitable for high-speed FPGA implementation

NASA Astrophysics Data System (ADS)

Frank, Michael P.; Oniciuc, Liviu; Meyer-Baese, Uwe H.; Chiorescu, Irinel

2009-05-01

Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a function of the number of quantum operations applied. However, this exponential-space requirement can be avoided by using general space-time tradeoffs long known to complexity theorists, which can be appropriately optimized for this particular problem in a way that also illustrates some interesting reformulations of quantum mechanics. In this paper, we describe the design and empirical space/time complexity measurements of a working software prototype of a quantum computer simulator that avoids excessive space requirements. Due to its space-efficiency, this design is well-suited to embedding in single-chip environments, permitting especially fast execution that avoids access latencies to main memory. We plan to prototype our design on a standard FPGA development board.

Device-independent characterizations of a shared quantum state independent of any Bell inequalities

NASA Astrophysics Data System (ADS)

Wei, Zhaohui; Sikora, Jamie

2017-03-01

In a Bell experiment two parties share a quantum state and perform local measurements on their subsystems separately, and the statistics of the measurement outcomes are recorded as a Bell correlation. For any Bell correlation, it turns out that a quantum state with minimal size that is able to produce this correlation can always be pure. In this work, we first exhibit two device-independent characterizations for the pure state that Alice and Bob share using only the correlation data. Specifically, we give two conditions that the Schmidt coefficients must satisfy, which can be tight, and have various applications in quantum tasks. First, one of the characterizations allows us to bound the entanglement between Alice and Bob using Renyi entropies and also to bound the underlying Hilbert space dimension. Second, when the Hilbert space dimension bound is tight, the shared pure quantum state has to be maximally entangled. Third, the second characterization gives a sufficient condition that a Bell correlation cannot be generated by particular quantum states. We also show that our results can be generalized to the case of shared mixed states.

EPR & Klein Paradoxes in Complex Hamiltonian Dynamics and Krein Space Quantization

NASA Astrophysics Data System (ADS)

Payandeh, Farrin

2015-07-01

Negative energy states are applied in Krein space quantization approach to achieve a naturally renormalized theory. For example, this theory by taking the full set of Dirac solutions, could be able to remove the propagator Green function's divergences and automatically without any normal ordering, to vanish the expected value for vacuum state energy. However, since it is a purely mathematical theory, the results are under debate and some efforts are devoted to include more physics in the concept. Whereas Krein quantization is a pure mathematical approach, complex quantum Hamiltonian dynamics is based on strong foundations of Hamilton-Jacobi (H-J) equations and therefore on classical dynamics. Based on complex quantum Hamilton-Jacobi theory, complex spacetime is a natural consequence of including quantum effects in the relativistic mechanics, and is a bridge connecting the causality in special relativity and the non-locality in quantum mechanics, i.e. extending special relativity to the complex domain leads to relativistic quantum mechanics. So that, considering both relativistic and quantum effects, the Klein-Gordon equation could be derived as a special form of the Hamilton-Jacobi equation. Characterizing the complex time involved in an entangled energy state and writing the general form of energy considering quantum potential, two sets of positive and negative energies will be realized. The new states enable us to study the spacetime in a relativistic entangled “space-time” state leading to 12 extra wave functions than the four solutions of Dirac equation for a free particle. Arguing the entanglement of particle and antiparticle leads to a contradiction with experiments. So, in order to correct the results, along with a previous investigation [1], we realize particles and antiparticles as physical entities with positive energy instead of considering antiparticles with negative energy. As an application of modified descriptions for entangled (space-time) states, the original version of EPR paradox can be discussed and the correct answer can be verified based on the strong rooted complex quantum Hamilton-Jacobi theory [2-27] and as another example we can use the negative energy states, to remove the Klein's paradox without the need of any further explanations or justifications like backwardly moving electrons. Finally, comparing the two approaches, we can point out to the existence of a connection between quantum Hamiltonian dynamics, standard quantum field theory, and Krein space quantization [28-43].

Quantum teleportation and entanglement distribution over 100-kilometre free-space channels.

PubMed

Yin, Juan; Ren, Ji-Gang; Lu, He; Cao, Yuan; Yong, Hai-Lin; Wu, Yu-Ping; Liu, Chang; Liao, Sheng-Kai; Zhou, Fei; Jiang, Yan; Cai, Xin-Dong; Xu, Ping; Pan, Ge-Sheng; Jia, Jian-Jun; Huang, Yong-Mei; Yin, Hao; Wang, Jian-Yu; Chen, Yu-Ao; Peng, Cheng-Zhi; Pan, Jian-Wei

2012-08-09

Transferring an unknown quantum state over arbitrary distances is essential for large-scale quantum communication and distributed quantum networks. It can be achieved with the help of long-distance quantum teleportation and entanglement distribution. The latter is also important for fundamental tests of the laws of quantum mechanics. Although quantum teleportation and entanglement distribution over moderate distances have been realized using optical fibre links, the huge photon loss and decoherence in fibres necessitate the use of quantum repeaters for larger distances. However, the practical realization of quantum repeaters remains experimentally challenging. Free-space channels, first used for quantum key distribution, offer a more promising approach because photon loss and decoherence are almost negligible in the atmosphere. Furthermore, by using satellites, ultra-long-distance quantum communication and tests of quantum foundations could be achieved on a global scale. Previous experiments have achieved free-space distribution of entangled photon pairs over distances of 600 metres (ref. 14) and 13 kilometres (ref. 15), and transfer of triggered single photons over a 144-kilometre one-link free-space channel. Most recently, following a modified scheme, free-space quantum teleportation over 16 kilometres was demonstrated with a single pair of entangled photons. Here we report quantum teleportation of independent qubits over a 97-kilometre one-link free-space channel with multi-photon entanglement. An average fidelity of 80.4 ± 0.9 per cent is achieved for six distinct states. Furthermore, we demonstrate entanglement distribution over a two-link channel, in which the entangled photons are separated by 101.8 kilometres. Violation of the Clauser-Horne-Shimony-Holt inequality is observed without the locality loophole. Besides being of fundamental interest, our results represent an important step towards a global quantum network. Moreover, the high-frequency and high-accuracy acquiring, pointing and tracking technique developed in our experiment can be directly used for future satellite-based quantum communication and large-scale tests of quantum foundations.

Satellite-to-ground quantum key distribution.

PubMed

Liao, Sheng-Kai; Cai, Wen-Qi; Liu, Wei-Yue; Zhang, Liang; Li, Yang; Ren, Ji-Gang; Yin, Juan; Shen, Qi; Cao, Yuan; Li, Zheng-Ping; Li, Feng-Zhi; Chen, Xia-Wei; Sun, Li-Hua; Jia, Jian-Jun; Wu, Jin-Cai; Jiang, Xiao-Jun; Wang, Jian-Feng; Huang, Yong-Mei; Wang, Qiang; Zhou, Yi-Lin; Deng, Lei; Xi, Tao; Ma, Lu; Hu, Tai; Zhang, Qiang; Chen, Yu-Ao; Liu, Nai-Le; Wang, Xiang-Bin; Zhu, Zhen-Cai; Lu, Chao-Yang; Shu, Rong; Peng, Cheng-Zhi; Wang, Jian-Yu; Pan, Jian-Wei

2017-09-07

Quantum key distribution (QKD) uses individual light quanta in quantum superposition states to guarantee unconditional communication security between distant parties. However, the distance over which QKD is achievable has been limited to a few hundred kilometres, owing to the channel loss that occurs when using optical fibres or terrestrial free space that exponentially reduces the photon transmission rate. Satellite-based QKD has the potential to help to establish a global-scale quantum network, owing to the negligible photon loss and decoherence experienced in empty space. Here we report the development and launch of a low-Earth-orbit satellite for implementing decoy-state QKD-a form of QKD that uses weak coherent pulses at high channel loss and is secure because photon-number-splitting eavesdropping can be detected. We achieve a kilohertz key rate from the satellite to the ground over a distance of up to 1,200 kilometres. This key rate is around 20 orders of magnitudes greater than that expected using an optical fibre of the same length. The establishment of a reliable and efficient space-to-ground link for quantum-state transmission paves the way to global-scale quantum networks.

Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies

PubMed Central

Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

2014-01-01

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects. PMID:24851858

Relativistic quantum metrology: exploiting relativity to improve quantum measurement technologies.

PubMed

Ahmadi, Mehdi; Bruschi, David Edward; Sabín, Carlos; Adesso, Gerardo; Fuentes, Ivette

2014-05-22

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.

On the physical Hilbert space of loop quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noui, Karim; Perez, Alejandro; Vandersloot, Kevin

2005-02-15

In this paper we present a model of Riemannian loop quantum cosmology with a self-adjoint quantum scalar constraint. The physical Hilbert space is constructed using refined algebraic quantization. When matter is included in the form of a cosmological constant, the model is exactly solvable and we show explicitly that the physical Hilbert space is separable, consisting of a single physical state. We extend the model to the Lorentzian sector and discuss important implications for standard loop quantum cosmology.

BFV quantization on hermitian symmetric spaces

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1995-02-01

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/ H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/ H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.

Entanglement entropy and correlations in loop quantum gravity

NASA Astrophysics Data System (ADS)

Feller, Alexandre; Livine, Etera R.

2018-02-01

Black hole entropy is one of the few windows into the quantum aspects of gravitation, and its study over the years has highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into an analysis of the correlations between the regions of the spin network states defining the quantum state of the geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physics, satisfying an area law for entanglement entropy and having non-trivial correlations. We highlight that entanglement comes from holonomy operators acting on loops crossing the boundary of the region.

Quantum tomography of near-unitary processes in high-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Lysne, Nathan; Sosa Martinez, Hector; Jessen, Poul; Baldwin, Charles; Kalev, Amir; Deutsch, Ivan

2016-05-01

Quantum Tomography (QT) is often considered the ideal tool for experimental debugging of quantum devices, capable of delivering complete information about quantum states (QST) or processes (QPT). In practice, the protocols used for QT are resource intensive and scale poorly with system size. In this situation, a well behaved model system with access to large state spaces (qudits) can serve as a useful platform for examining the tradeoffs between resource cost and accuracy inherent in QT. In past years we have developed one such experimental testbed, consisting of the electron-nuclear spins in the electronic ground state of individual Cs atoms. Our available toolkit includes high fidelity state preparation, complete unitary control, arbitrary orthogonal measurements, and accurate and efficient QST in Hilbert space dimensions up to d = 16. Using these tools, we have recently completed a comprehensive study of QPT in 4, 7 and 16 dimensions. Our results show that QPT of near-unitary processes is quite feasible if one chooses optimal input states and efficient QST on the outputs. We further show that for unitary processes in high dimensional spaces, one can use informationally incomplete QPT to achieve high-fidelity process reconstruction (90% in d = 16) with greatly reduced resource requirements.

Projective limits of state spaces IV. Fractal label sets

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2018-01-01

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski (1977) to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces (see Lanéry (2016) [1] for a concise introduction to this formalism). One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier work by Okołów (2013), a projective state space was introduced for this algebra in Lanéry and Thiemann (2016). However, the non-trivial structure of the holonomy-flux algebra prevents the construction of satisfactory semi-classical states (Lanéry and Thiemann, 2017). Implementing the general procedure just mentioned in the case of a one-dimensional version of this algebra, we show how a discrete subalgebra can be extracted without destroying universality nor diffeomorphism invariance. On this subalgebra, quantum states can then be constructed which are more regular than was possible on the original algebra. In particular, this allows the design of semi-classical states whose semi-classicality is enforced step by step, starting from collective, macroscopic degrees of freedom and going down progressively toward smaller and smaller scales.

Phase space quantum mechanics - Direct

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nasiri, S.; Sobouti, Y.; Taati, F.

2006-09-15

Conventional approach to quantum mechanics in phase space (q,p), is to take the operator based quantum mechanics of Schroedinger, or an equivalent, and assign a c-number function in phase space to it. We propose to begin with a higher level of abstraction, in which the independence and the symmetric role of q and p is maintained throughout, and at once arrive at phase space state functions. Upon reduction to the q- or p-space the proposed formalism gives the conventional quantum mechanics, however, with a definite rule for ordering of factors of noncommuting observables. Further conceptual and practical merits of themore » formalism are demonstrated throughout the text.« less

Distribution of squeezed states through an atmospheric channel.

PubMed

Peuntinger, Christian; Heim, Bettina; Müller, Christian R; Gabriel, Christian; Marquardt, Christoph; Leuchs, Gerd

2014-08-08

Continuous variable quantum states of light are used in quantum information protocols and quantum metrology and known to degrade with loss and added noise. We were able to show the distribution of bright polarization squeezed quantum states of light through an urban free-space channel of 1.6 km length. To measure the squeezed states in this extreme environment, we utilize polarization encoding and a postselection protocol that is taking into account classical side information stemming from the distribution of transmission values. The successful distribution of continuous variable squeezed states is accentuated by a quantum state tomography, allowing for determining the purity of the state.

Quantum paradox of choice: More freedom makes summoning a quantum state harder

NASA Astrophysics Data System (ADS)

Adlam, Emily; Kent, Adrian

2016-06-01

The properties of quantum information in space-time can be investigated by studying operational tasks, such as "summoning," in which an unknown quantum state is supplied at one point and a call is made at another for it to be returned at a third. Hayden and May [arXiv:1210.0913] recently proved necessary and sufficient conditions for guaranteeing successful return of a summoned state for finite sets of call and return points when there is a guarantee of at most one summons. We prove necessary and sufficient conditions when there may be several possible summonses and complying with any one constitutes success, and we demonstrate the existence of an apparent paradox: The extra freedom makes it strictly harder to complete the summoning task. This result has practical applications for distributed quantum computing and cryptography and implications for our understanding of relativistic quantum information and its localization in space-time.

Fermi Blobs and the Symplectic Camel: A Geometric Picture of Quantum States

NASA Astrophysics Data System (ADS)

Gossona, Maurice A. De

We have explained in previous work the correspondence between the standard squeezed coherent states of quantum mechanics, and quantum blobs, which are the smallest phase space units compatible with the uncertainty principle of quantum mechanics and having the symplectic group as a group of symmetries. In this work, we discuss the relation between quantum blobs and a certain level set (which we call "Fermi blob") introduced by Enrico Fermi in 1930. Fermi blobs allows us to extend our previous results not only to the excited states of the generalized harmonic oscillator in n dimensions, but also to arbitrary quadratic Hamiltonians. As is the case for quantum blobs, we can evaluate Fermi blobs using a topological notion, related to the uncertainty principle, the symplectic capacity of a phase space set. The definition of this notion is made possible by Gromov's symplectic non-squeezing theorem, nicknamed the "principle of the symplectic camel".

Entanglement-distillation attack on continuous-variable quantum key distribution in a turbulent atmospheric channel

NASA Astrophysics Data System (ADS)

Guo, Ying; Xie, Cailang; Liao, Qin; Zhao, Wei; Zeng, Guihua; Huang, Duan

2017-08-01

The survival of Gaussian quantum states in a turbulent atmospheric channel is of crucial importance in free-space continuous-variable (CV) quantum key distribution (QKD), in which the transmission coefficient will fluctuate in time, thus resulting in non-Gaussian quantum states. Different from quantum hacking of the imperfections of practical devices, here we propose a different type of attack by exploiting the security loopholes that occur in a real lossy channel. Under a turbulent atmospheric environment, the Gaussian states are inevitably afflicted by decoherence, which would cause a degradation of the transmitted entanglement. Therefore, an eavesdropper can perform an intercept-resend attack by applying an entanglement-distillation operation on the transmitted non-Gaussian mixed states, which allows the eavesdropper to bias the estimation of the parameters and renders the final keys shared between the legitimate parties insecure. Our proposal highlights the practical CV QKD vulnerabilities with free-space quantum channels, including the satellite-to-earth links, ground-to-ground links, and a link from moving objects to ground stations.

Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal

NASA Astrophysics Data System (ADS)

Yannouleas, Constantine; Landman, Uzi

2017-10-01

A constructive theoretical platform for the description of quantum space-time crystals uncovers for N interacting and ring-confined rotating particles the existence of low-lying states with proper space-time crystal behavior. The construction of the corresponding many-body trial wave functions proceeds first via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. The ensuing correlated many-body wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group symmetries of the mean-field crystals. This behavior results in the emergence of sequences of select magic angular momenta Lm. For angular-momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond the mean-field level can be induced by superpositions of such good-Lm many-body stationary states. We show that superposing a pair of adjacent magic angular momenta states leads to formation of special broken-symmetry states exhibiting quantum space-time-crystal behavior. In particular, the corresponding particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such quantum space-time-crystal wave packets is predicted to be favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm-type spectra accessed via an externally applied, natural or synthetic, magnetic field. These results are illustrated here for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons.

Ground-to-satellite quantum teleportation.

PubMed

Ren, Ji-Gang; Xu, Ping; Yong, Hai-Lin; Zhang, Liang; Liao, Sheng-Kai; Yin, Juan; Liu, Wei-Yue; Cai, Wen-Qi; Yang, Meng; Li, Li; Yang, Kui-Xing; Han, Xuan; Yao, Yong-Qiang; Li, Ji; Wu, Hai-Yan; Wan, Song; Liu, Lei; Liu, Ding-Quan; Kuang, Yao-Wu; He, Zhi-Ping; Shang, Peng; Guo, Cheng; Zheng, Ru-Hua; Tian, Kai; Zhu, Zhen-Cai; Liu, Nai-Le; Lu, Chao-Yang; Shu, Rong; Chen, Yu-Ao; Peng, Cheng-Zhi; Wang, Jian-Yu; Pan, Jian-Wei

2017-09-07

An arbitrary unknown quantum state cannot be measured precisely or replicated perfectly. However, quantum teleportation enables unknown quantum states to be transferred reliably from one object to another over long distances, without physical travelling of the object itself. Long-distance teleportation is a fundamental element of protocols such as large-scale quantum networks and distributed quantum computation. But the distances over which transmission was achieved in previous teleportation experiments, which used optical fibres and terrestrial free-space channels, were limited to about 100 kilometres, owing to the photon loss of these channels. To realize a global-scale 'quantum internet' the range of quantum teleportation needs to be greatly extended. A promising way of doing so involves using satellite platforms and space-based links, which can connect two remote points on Earth with greatly reduced channel loss because most of the propagation path of the photons is in empty space. Here we report quantum teleportation of independent single-photon qubits from a ground observatory to a low-Earth-orbit satellite, through an uplink channel, over distances of up to 1,400 kilometres. To optimize the efficiency of the link and to counter the atmospheric turbulence in the uplink, we use a compact ultra-bright source of entangled photons, a narrow beam divergence and high-bandwidth and high-accuracy acquiring, pointing and tracking. We demonstrate successful quantum teleportation of six input states in mutually unbiased bases with an average fidelity of 0.80 ± 0.01, well above the optimal state-estimation fidelity on a single copy of a qubit (the classical limit). Our demonstration of a ground-to-satellite uplink for reliable and ultra-long-distance quantum teleportation is an essential step towards a global-scale quantum internet.

Ground-to-satellite quantum teleportation

NASA Astrophysics Data System (ADS)

Ren, Ji-Gang; Xu, Ping; Yong, Hai-Lin; Zhang, Liang; Liao, Sheng-Kai; Yin, Juan; Liu, Wei-Yue; Cai, Wen-Qi; Yang, Meng; Li, Li; Yang, Kui-Xing; Han, Xuan; Yao, Yong-Qiang; Li, Ji; Wu, Hai-Yan; Wan, Song; Liu, Lei; Liu, Ding-Quan; Kuang, Yao-Wu; He, Zhi-Ping; Shang, Peng; Guo, Cheng; Zheng, Ru-Hua; Tian, Kai; Zhu, Zhen-Cai; Liu, Nai-Le; Lu, Chao-Yang; Shu, Rong; Chen, Yu-Ao; Peng, Cheng-Zhi; Wang, Jian-Yu; Pan, Jian-Wei

2017-09-01

An arbitrary unknown quantum state cannot be measured precisely or replicated perfectly. However, quantum teleportation enables unknown quantum states to be transferred reliably from one object to another over long distances, without physical travelling of the object itself. Long-distance teleportation is a fundamental element of protocols such as large-scale quantum networks and distributed quantum computation. But the distances over which transmission was achieved in previous teleportation experiments, which used optical fibres and terrestrial free-space channels, were limited to about 100 kilometres, owing to the photon loss of these channels. To realize a global-scale ‘quantum internet’ the range of quantum teleportation needs to be greatly extended. A promising way of doing so involves using satellite platforms and space-based links, which can connect two remote points on Earth with greatly reduced channel loss because most of the propagation path of the photons is in empty space. Here we report quantum teleportation of independent single-photon qubits from a ground observatory to a low-Earth-orbit satellite, through an uplink channel, over distances of up to 1,400 kilometres. To optimize the efficiency of the link and to counter the atmospheric turbulence in the uplink, we use a compact ultra-bright source of entangled photons, a narrow beam divergence and high-bandwidth and high-accuracy acquiring, pointing and tracking. We demonstrate successful quantum teleportation of six input states in mutually unbiased bases with an average fidelity of 0.80 ± 0.01, well above the optimal state-estimation fidelity on a single copy of a qubit (the classical limit). Our demonstration of a ground-to-satellite uplink for reliable and ultra-long-distance quantum teleportation is an essential step towards a global-scale quantum internet.

Tasks and premises in quantum state determination

NASA Astrophysics Data System (ADS)

Carmeli, Claudio; Heinosaari, Teiko; Schultz, Jussi; Toigo, Alessandro

2014-02-01

The purpose of quantum tomography is to determine an unknown quantum state from measurement outcome statistics. There are two obvious ways to generalize this setting. First, our task need not be the determination of any possible input state but only some input states, for instance pure states. Second, we may have some prior information, or premise, which guarantees that the input state belongs to some subset of states, for instance the set of states with rank less than half of the dimension of the Hilbert space. We investigate state determination under these two supplemental features, concentrating on the cases where the task and the premise are statements about the rank of the unknown state. We characterize the structure of quantum observables (positive operator valued measures) that are capable of fulfilling these type of determination tasks. After the general treatment we focus on the class of covariant phase space observables, thus providing physically relevant examples of observables both capable and incapable of performing these tasks. In this context, the effect of noise is discussed.

Handy elementary algebraic properties of the geometry of entanglement

NASA Astrophysics Data System (ADS)

Blair, Howard A.; Alsing, Paul M.

2013-05-01

The space of separable states of a quantum system is a hyperbolic surface in a high dimensional linear space, which we call the separation surface, within the exponentially high dimensional linear space containing the quantum states of an n component multipartite quantum system. A vector in the linear space is representable as an n-dimensional hypermatrix with respect to bases of the component linear spaces. A vector will be on the separation surface iff every determinant of every 2-dimensional, 2-by-2 submatrix of the hypermatrix vanishes. This highly rigid constraint can be tested merely in time asymptotically proportional to d, where d is the dimension of the state space of the system due to the extreme interdependence of the 2-by-2 submatrices. The constraint on 2-by-2 determinants entails an elementary closed formformula for a parametric characterization of the entire separation surface with d-1 parameters in the char- acterization. The state of a factor of a partially separable state can be calculated in time asymptotically proportional to the dimension of the state space of the component. If all components of the system have approximately the same dimension, the time complexity of calculating a component state as a function of the parameters is asymptotically pro- portional to the time required to sort the basis. Metric-based entanglement measures of pure states are characterized in terms of the separation hypersurface.

The Butterfly and the Photon:. New Perspectives on Unpredictability, and the Notion of Casual Reality, in Quantum Physics

NASA Astrophysics Data System (ADS)

Palmer, T. N.

2012-12-01

This essay discusses a proposal that draws together the three great revolutionary theories of 20th Century physics: quantum theory, relativity theory and chaos theory. Motivated by the Bohmian notion of implicate order, and what in chaos theory would be described as a strange attractor, the proposal attributes special ontological significance to certain non-computable, dynamically invariant state-space geometries for the universe as a whole. Studying the phenomenon of quantum interference, it is proposed to understand quantum wave-particle duality, and indeed classical electromagnetism, in terms of particles in space time and waves on this state space geometry. Studying the EPR experiment, the acausal constraints that this invariant geometry provides on spatially distant degrees of freedom, provides a way for the underlying dynamics to be consistent with the Bell theorem, yet be relativistically covariant ("nonlocality without nonlocality"). It is suggested that the physical basis for such non-computable geometries lies in properties of gravity with the information irreversibility implied by black hole no-hair theorems being crucial. In conclusion it is proposed that quantum theory may be emergent from an extended theory of gravity which is geometric not only in space time, but also in state space. Such a notion would undermine most current attempts to "quantise gravity".

Sculpting oscillators with light within a nonlinear quantum fluid

NASA Astrophysics Data System (ADS)

Tosi, G.; Christmann, G.; Berloff, N. G.; Tsotsis, P.; Gao, T.; Hatzopoulos, Z.; Savvidis, P. G.; Baumberg, J. J.

2012-03-01

Seeing macroscopic quantum states directly remains an elusive goal. Particles with boson symmetry can condense into quantum fluids, producing rich physical phenomena as well as proven potential for interferometric devices. However, direct imaging of such quantum states is only fleetingly possible in high-vacuum ultracold atomic condensates, and not in superconductors. Recent condensation of solid-state polariton quasiparticles, built from mixing semiconductor excitons with microcavity photons, offers monolithic devices capable of supporting room-temperature quantum states that exhibit superfluid behaviour. Here we use microcavities on a semiconductor chip supporting two-dimensional polariton condensates to directly visualize the formation of a spontaneously oscillating quantum fluid. This system is created on the fly by injecting polaritons at two or more spatially separated pump spots. Although oscillating at tunable THz frequencies, a simple optical microscope can be used to directly image their stable archetypal quantum oscillator wavefunctions in real space. The self-repulsion of polaritons provides a solid-state quasiparticle that is so nonlinear as to modify its own potential. Interference in time and space reveals the condensate wavepackets arise from non-equilibrium solitons. Control of such polariton-condensate wavepackets demonstrates great potential for integrated semiconductor-based condensate devices.

Combined-probability space and certainty or uncertainty relations for a finite-level quantum system

NASA Astrophysics Data System (ADS)

Sehrawat, Arun

2017-08-01

The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys certain quantum constraints, which are triangle inequalities in our case. Such a restricted set of combined vectors, called the combined-probability space, is presented here for a d -level quantum system (qudit). The combined space is a compact convex subset of a Euclidean space, and all its extreme points come from a family of parametric curves. Considering a suitable concave function on the combined space to estimate the uncertainty, we deliver an uncertainty relation by finding its global minimum on the curves for a qudit. If one chooses an appropriate concave (or convex) function, then there is no need to search for the absolute minimum (maximum) over the whole space; it will be on the parametric curves. So these curves are quite useful for establishing an uncertainty (or a certainty) relation for a general pair of settings. We also demonstrate that many known tight certainty or uncertainty relations for a qubit can be obtained with the triangle inequalities.

Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Paz, Juan Pablo; Roncaglia, Augusto Jose; Theoretical Division, LANL, MSB213, Los Alamos, New Mexico 87545

2005-07-15

We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2{sup n}). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2{sup n}) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-spacemore » representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem.« less

Quantum sensing of the phase-space-displacement parameters using a single trapped ion

NASA Astrophysics Data System (ADS)

Ivanov, Peter A.; Vitanov, Nikolay V.

2018-03-01

We introduce a quantum sensing protocol for detecting the parameters characterizing the phase-space displacement by using a single trapped ion as a quantum probe. We show that, thanks to the laser-induced coupling between the ion's internal states and the motion mode, the estimation of the two conjugated parameters describing the displacement can be efficiently performed by a set of measurements of the atomic state populations. Furthermore, we introduce a three-parameter protocol capable of detecting the magnitude, the transverse direction, and the phase of the displacement. We characterize the uncertainty of the two- and three-parameter problems in terms of the Fisher information and show that state projective measurement saturates the fundamental quantum Cramér-Rao bound.

Positive spaces, generalized semi-densities, and quantum interactions

NASA Astrophysics Data System (ADS)

Canarutto, Daniel

2012-03-01

The basics of quantum particle physics on a curved Lorentzian background are expressed in a formulation which has original aspects and exploits some non-standard mathematical notions. In particular, positive spaces and generalized semi-densities (in a distributional sense) are shown to link, in a natural way, discrete multi-particle spaces to distributional bundles of quantum states. The treatment of spinor and boson fields is partly original also from an algebraic point of view and suggests a non-standard approach to quantum interactions. The case of electroweak interactions provides examples.

Exploring the Tomlin-Varadarajan quantum constraints in U (1 )3 loop quantum gravity: Solutions and the Minkowski theorem

NASA Astrophysics Data System (ADS)

Lewandowski, Jerzy; Lin, Chun-Yen

2017-03-01

We explicitly solved the anomaly-free quantum constraints proposed by Tomlin and Varadarajan for the weak Euclidean model of canonical loop quantum gravity, in a large subspace of the model's kinematic Hilbert space, which is the space of the charge network states. In doing so, we first identified the subspace on which each of the constraints acts convergingly, and then by explicitly evaluating such actions we found the complete set of the solutions in the identified subspace. We showed that the space of solutions consists of two classes of states, with the first class having a property that involves the condition known from the Minkowski theorem on polyhedra, and the second class satisfying a weaker form of the spatial diffeomorphism invariance.

Imaging the dynamics of free-electron Landau states

PubMed Central

Schattschneider, P.; Schachinger, Th.; Stöger-Pollach, M.; Löffler, S.; Steiger-Thirsfeld, A.; Bliokh, K. Y.; Nori, Franco

2014-01-01

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions. PMID:25105563

Free-Space Quantum Communication with a Portable Quantum Memory

NASA Astrophysics Data System (ADS)

Namazi, Mehdi; Vallone, Giuseppe; Jordaan, Bertus; Goham, Connor; Shahrokhshahi, Reihaneh; Villoresi, Paolo; Figueroa, Eden

2017-12-01

The realization of an elementary quantum network that is intrinsically secure and operates over long distances requires the interconnection of several quantum modules performing different tasks. In this work, we report the realization of a communication network functioning in a quantum regime, consisting of four different quantum modules: (i) a random polarization qubit generator, (ii) a free-space quantum-communication channel, (iii) an ultralow-noise portable quantum memory, and (iv) a qubit decoder, in a functional elementary quantum network possessing all capabilities needed for quantum-information distribution protocols. We create weak coherent pulses at the single-photon level encoding polarization states |H ⟩ , |V ⟩, |D ⟩, and |A ⟩ in a randomized sequence. The random qubits are sent over a free-space link and coupled into a dual-rail room-temperature quantum memory and after storage and retrieval are analyzed in a four-detector polarization analysis akin to the requirements of the BB84 protocol. We also show ultralow noise and fully portable operation, paving the way towards memory-assisted all-environment free-space quantum cryptographic networks.

Corrigendum: First principles calculation of field emission from nanostructures using time-dependent density functional theory: A simplified approach

NASA Astrophysics Data System (ADS)

Tawfik, Sherif A.; El-Sheikh, S. M.; Salem, N. M.

2016-09-01

Recently we have become aware that the description of the quantum wave functions in Sec. 2.1 is incorrect. In the published version of the paper, we have stated that the states are expanded in terms of plane waves. However, the correct description of the quantum states in the context of the real space implementation (using the Octopus code) is that states are represented by discrete points in a real space grid.

ψ -ontology result without the Cartesian product assumption

NASA Astrophysics Data System (ADS)

Myrvold, Wayne C.

2018-05-01

We introduce a weakening of the preparation independence postulate of Pusey et al. [Nat. Phys. 8, 475 (2012), 10.1038/nphys2309] that does not presuppose that the space of ontic states resulting from a product-state preparation can be represented by the Cartesian product of subsystem state spaces. On the basis of this weakened assumption, it is shown that, in any model that reproduces the quantum probabilities, any pair of pure quantum states |ψ >,|ϕ > with <ϕ |ψ > ≤1 /√{2 } must be ontologically distinct.

Mathematics of Quantization and Quantum Fields

NASA Astrophysics Data System (ADS)

Dereziński, Jan; Gérard, Christian

2013-03-01

Preface; 1. Vector spaces; 2. Operators in Hilbert spaces; 3. Tensor algebras; 4. Analysis in L2(Rd); 5. Measures; 6. Algebras; 7. Anti-symmetric calculus; 8. Canonical commutation relations; 9. CCR on Fock spaces; 10. Symplectic invariance of CCR in finite dimensions; 11. Symplectic invariance of the CCR on Fock spaces; 12. Canonical anti-commutation relations; 13. CAR on Fock spaces; 14. Orthogonal invariance of CAR algebras; 15. Clifford relations; 16. Orthogonal invariance of the CAR on Fock spaces; 17. Quasi-free states; 18. Dynamics of quantum fields; 19. Quantum fields on space-time; 20. Diagrammatics; 21. Euclidean approach for bosons; 22. Interacting bosonic fields; Subject index; Symbols index.

Continuous-time quantum random walks require discrete space

NASA Astrophysics Data System (ADS)

Manouchehri, K.; Wang, J. B.

2007-11-01

Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the case of continuous-time quantum random walks, such peculiar dynamics can arise from simple evolution operators closely resembling the quantum free-wave propagator. We investigate the divergence of quantum walk dynamics from the free-wave evolution and show that, in order for continuous-time quantum walks to display their characteristic propagation, the state space must be discrete. This behavior rules out many continuous quantum systems as possible candidates for implementing continuous-time quantum random walks.

Demonstration of a quantum controlled-NOT gate in the telecommunications band.

PubMed

Chen, Jun; Altepeter, Joseph B; Medic, Milja; Lee, Kim Fook; Gokden, Burc; Hadfield, Robert H; Nam, Sae Woo; Kumar, Prem

2008-04-04

We present the first quantum controlled-not (cnot) gate realized using a fiber-based indistinguishable photon-pair source in the 1.55 microm telecommunications band. Using this free-space cnot gate, all four Bell states are produced and fully characterized by performing quantum-state tomography, demonstrating the gate's unambiguous entangling capability and high fidelity. Telecom-band operation makes this cnot gate particularly suitable for quantum-information-processing tasks that are at the interface of quantum communication and linear optical quantum computing.

The Deleuzian Concept of Structure and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Christiaens, Wim A.

2014-03-01

Gilles Deleuze wanted a philosophy of nature in a pre-kantian almost archaic sense. A central concept in his philosophy is `multiplicity'. Although the concept is philosophical through and through, it has roots in the mathematical notion of manifold, specifically the state spaces for dynamical systems exhibiting non-linear behaviour. Deleuze was attracted to such mathematical structures because he believed they indicated a break with the dogmatic image of thought (the kind of thought that constrains itself into producing representations of reality conceived as particular things with strict borders, behaving and interacting according to invariant covering laws within space). However, even though it is true that a phase space representation of a physical entity is not a typical materialist picture of reality, it derives from a normal Euclidean representation, and can in principle be reduced to it. We want to argue that the real break happens with the quantum state space, and that Deleuze's typical description of a multiplicity fits even better with the quantum state space.

Computing the Entropy of Kerr-Newman Black Hole Without Brick Walls Method

NASA Astrophysics Data System (ADS)

Zhang, Li-Chun; Wu, Yue-Qin; Li, Huai-Fan; Ren, Zhao

By using the entanglement entropy method, the statistical entropy of the Bose and Fermi fields in a thin film is calculated and the Bekenstein-Hawking entropy of Kerr-Newman black hole is obtained. Here, the Bose and Fermi fields are entangled with the quantum states in Kerr-Newman black hole and are outside of the horizon. The divergence of brick-wall model is avoided without any cutoff by the new equation of state density obtained with the generalized uncertainty principle. The calculation implies that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole. The black hole entropy is a quantum effect. It is an intrinsic characteristic of space-time. The ultraviolet cutoff in the brick-wall model is unreasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the calculation, the constant λ introduced in the generalized uncertainty principle is related to polar angle θ in an axisymmetric space-time.

Hardware-efficient Bell state preparation using Quantum Zeno Dynamics in superconducting circuits

NASA Astrophysics Data System (ADS)

Flurin, Emmanuel; Blok, Machiel; Hacohen-Gourgy, Shay; Martin, Leigh S.; Livingston, William P.; Dove, Allison; Siddiqi, Irfan

By preforming a continuous joint measurement on a two qubit system, we restrict the qubit evolution to a chosen subspace of the total Hilbert space. This extension of the quantum Zeno effect, called Quantum Zeno Dynamics, has already been explored in various physical systems such as superconducting cavities, single rydberg atoms, atomic ensembles and Bose Einstein condensates. In this experiment, two superconducting qubits are strongly dispersively coupled to a high-Q cavity (χ >> κ) allowing for the doubly excited state | 11 〉 to be selectively monitored. The Quantum Zeno Dynamics in the complementary subspace enables us to coherently prepare a Bell state. As opposed to dissipation engineering schemes, we emphasize that our protocol is deterministic, does not rely direct coupling between qubits and functions only using single qubit controls and cavity readout. Such Quantum Zeno Dynamics can be generalized to larger Hilbert space enabling deterministic generation of many-body entangled states, and thus realizes a decoherence-free subspace allowing alternative noise-protection schemes.

Quantum Correlation Properties in Composite Parity-Conserved Matrix Product States

NASA Astrophysics Data System (ADS)

Zhu, Jing-Min

2016-09-01

We give a new thought for constructing long-range quantum correlation in quantum many-body systems. Our proposed composite parity-conserved matrix product state has long-range quantum correlation only for two spin blocks where their spin-block length larger than 1 compared to any subsystem only having short-range quantum correlation, and we investigate quantum correlation properties of two spin blocks varying with environment parameter and spacing spin number. We also find that the geometry quantum discords of two nearest-neighbor spin blocks and two next-nearest-neighbor spin blocks become smaller and for other conditions the geometry quantum discord becomes larger than that in any subcomponent, i.e., the increase or the production of the long-range quantum correlation is at the cost of reducing the short-range quantum correlation compared to the corresponding classical correlation and total correlation having no any characteristic of regulation. For nearest-neighbor and next-nearest-neighbor all the correlations take their maximal values at the same points, while for other conditions no whether for spacing same spin number or for different spacing spin numbers all the correlations taking their maximal values are respectively at different points which are very close. We believe that our work is helpful to comprehensively and deeply understand the organization and structure of quantum correlation especially for long-range quantum correlation of quantum many-body systems; and further helpful for the classification, the depiction and the measure of quantum correlation of quantum many-body systems.

Quantum-like model of brain's functioning: decision making from decoherence.

PubMed

Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu; Basieva, Irina; Khrennikov, Andrei

2011-07-21

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex. Copyright © 2011 Elsevier Ltd. All rights reserved.

Irreversibility and entanglement spectrum statistics in quantum circuits

NASA Astrophysics Data System (ADS)

Shaffer, Daniel; Chamon, Claudio; Hamma, Alioscia; Mucciolo, Eduardo R.

2014-12-01

We show that in a quantum system evolving unitarily under a stochastic quantum circuit the notions of irreversibility, universality of computation, and entanglement are closely related. As the state evolves from an initial product state, it gets asymptotically maximally entangled. We define irreversibility as the failure of searching for a disentangling circuit using a Metropolis-like algorithm. We show that irreversibility corresponds to Wigner-Dyson statistics in the level spacing of the entanglement eigenvalues, and that this is obtained from a quantum circuit made from a set of universal gates for quantum computation. If, on the other hand, the system is evolved with a non-universal set of gates, the statistics of the entanglement level spacing deviates from Wigner-Dyson and the disentangling algorithm succeeds. These results open a new way to characterize irreversibility in quantum systems.

Investigating Quantum Modulation States

DTIC Science & Technology

2016-03-01

Coherent state quantum data encryption is highly interoperable with current classical optical infrastructure in both fiber and free space optical networks...hub’s field of regard has a transmit/receive module that are endpoints of the Lyot filter stage tree within the hub’s backend electro-optics control... mobile airborne and space-borne networking. Just like any laser communication technology, QC links are affected by several sources of distortions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osovski, Shmuel; Moiseyev, Nimrod

The recent pioneering experiments of the [Nature 412, 52 (2001)] and [Science, 293, 274 (2001)] groups have demonstrated the dynamical tunneling of cold atoms interacting with standing electromagnetic waves. It has been shown [Phys. Rev. Lett. 89, 253201 (2002)], that the tunneling oscillations observed in these experiments correspondingly stems from two- and three-Floquet quantum state mechanism and can be controlled by varying the experimental parameters. The question where are the fingerprints of the classical chaotic dynamics in a quantum dynamical process which is controlled by 2 or 3 quantum states remains open. Our calculations show that although the effective ({Dirac_h}/2{pi})more » associated with the two experiments is large, and the quantum system is far from its semiclassical limit, the quantum Floquet-Bloch quasienergy states still can be classified as regular and chaotic states. In both experiments the quantum and the classical phase-space entropies are quite similar, although the classical phase space is a mixed regular-chaotic space. It is also shown that as the wave packet which is initially localized at one of the two inner regular islands oscillates between them through the chaotic sea, it accumulates a random phase which causes the decay of the amplitude of the oscillating mean momentum, , as measured in both experiments. The extremely high sensitivity of the rate of decay of the oscillations of to the very small changes in the population of different Floquet-Bloch states, is another type of fingerprint of chaos in quantum dynamics that presumably was measured in the NIST and AUSTIN experiments for the first time.« less

Iterative tailoring of optical quantum states with homodyne measurements.

PubMed

Etesse, Jean; Kanseri, Bhaskar; Tualle-Brouri, Rosa

2014-12-01

As they can travel long distances, free space optical quantum states are good candidates for carrying information in quantum information technology protocols. These states, however, are often complex to produce and require protocols whose success probability drops quickly with an increase of the mean photon number. Here we propose a new protocol for the generation and growth of arbitrary states, based on one by one coherent adjunctions of the simple state superposition α|0〉 + β|1〉. Due to the nature of the protocol, which allows for the use of quantum memories, it can lead to high performances.

Controlling quantum interference in phase space with amplitude.

PubMed

Xue, Yinghong; Li, Tingyu; Kasai, Katsuyuki; Okada-Shudo, Yoshiko; Watanabe, Masayoshi; Zhang, Yun

2017-05-23

We experimentally show a quantum interference in phase space by interrogating photon number probabilities (n = 2, 3, and 4) of a displaced squeezed state, which is generated by an optical parametric amplifier and whose displacement is controlled by amplitude of injected coherent light. It is found that the probabilities exhibit oscillations of interference effect depending upon the amplitude of the controlling light field. This phenomenon is attributed to quantum interference in phase space and indicates the capability of controlling quantum interference using amplitude. This remarkably contrasts with the oscillations of interference effects being usually controlled by relative phase in classical optics.

Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

NASA Astrophysics Data System (ADS)

Neukart, Florian; Von Dollen, David; Seidel, Christian; Compostella, Gabriele

2017-12-01

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed n sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.

Quantum storage of orbital angular momentum entanglement in cold atomic ensembles

NASA Astrophysics Data System (ADS)

Shi, Bao-Sen; Ding, Dong-Sheng; Zhang, Wei

2018-02-01

Electromagnetic waves have both spin momentum and orbital angular momentum (OAM). Light carrying OAM has broad applications in micro-particle manipulation, high-precision optical metrology, and potential high-capacity optical communications. In the concept of quantum information, a photon encoded with information in its OAM degree of freedom enables quantum networks to carry much more information and increase their channel capacity greatly compared with those of current technology because of the inherent infinite dimensions for OAM. Quantum memories are indispensable to construct quantum networks. Storing OAM states has attracted considerable attention recently, and many important advances in this direction have been achieved during the past few years. Here we review recent experimental realizations of quantum memories using OAM states, including OAM qubits and qutrits at true single photon level, OAM states entangled in a two-dimensional or a high-dimensional space, hyperentanglement and hybrid entanglement consisting of OAM and other degree of freedom in a physical system. We believe that all achievements described here are very helpful to study quantum information encoded in a high-dimensional space.

Joining the quantum state of two photons into one

NASA Astrophysics Data System (ADS)

Vitelli, Chiara; Spagnolo, Nicolò; Aparo, Lorenzo; Sciarrino, Fabio; Santamato, Enrico; Marrucci, Lorenzo

2013-07-01

Photons are the ideal carriers of quantum information for communication. Each photon can have a single or multiple qubits encoded in its internal quantum state, as defined by optical degrees of freedom such as polarization, wavelength, transverse modes and so on. However, as photons do not interact, multiplexing and demultiplexing the quantum information across photons has not been possible hitherto. Here, we introduce and demonstrate experimentally a physical process, named `quantum joining', in which the two-dimensional quantum states (qubits) of two input photons are combined into a single output photon, within a four-dimensional Hilbert space. The inverse process is also proposed, in which the four-dimensional quantum state of a single photon is split into two photons, each carrying a qubit. Both processes can be iterated, and hence provide a flexible quantum interconnect to bridge multiparticle protocols of quantum information with multidegree-of-freedom ones, with possible applications in future quantum networking.

Quantum entanglement in time

NASA Astrophysics Data System (ADS)

Nowakowski, Marcin

2017-05-01

In this paper we present a concept of quantum entanglement in time in a context of entangled consistent histories. These considerations are supported by presentation of necessary tools closely related to those acting on a space of spatial multipartite quantum states. We show that in similarity to monogamy of quantum entanglement in space, quantum entanglement in time is also endowed with this property for a particular history. Basing on these observations, we discuss further bounding of temporal correlations and derive analytically the Tsirelson bound implied by entangled histories for the Leggett-Garg inequalities.

QIPS: quantum information and quantum physics in space

NASA Astrophysics Data System (ADS)

Schmitt-Manderbach, Tobias; Scheidl, Thomas; Ursin, Rupert; Tiefenbacher, Felix; Weier, Henning; Fürst, Martin; Jennewein, T.; Perdigues, J.; Sodnik, Z.; Rarity, J.; Zeilinger, Anton; Weinfurter, Harald

2017-11-01

The aim of the QIPS project (financed by ESA) is to explore quantum phenomena and to demonstrate quantum communication over long distances. Based on the current state-of-the-art a first study investigating the feasibility of space based quantum communication has to establish goals for mid-term and long-term missions, but also has to test the feasibility of key issues in a long distance ground-to-ground experiment. We have therefore designed a proof-of-concept demonstration for establishing single photon links over a distance of 144 km between the Canary Islands of La Palma and Tenerife to evaluate main limitations for future space experiments. Here we report on the progress of this project and present first measurements of crucial parameters of the optical free space link.

Survey on nonlocal games and operator space theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palazuelos, Carlos, E-mail: cpalazue@mat.ucm.es; Vidick, Thomas, E-mail: vidick@cms.caltech.edu

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify themore » nonlocality of different classes of entangled states.« less

Generalized Ehrenfest Relations, Deformation Quantization, and the Geometry of Inter-model Reduction

NASA Astrophysics Data System (ADS)

Rosaler, Joshua

2018-03-01

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \\hbar → 0, and, on the other, a certain generalization of Ehrenfest's Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models.

Quantum state engineering using one-dimensional discrete-time quantum walks

NASA Astrophysics Data System (ADS)

Innocenti, Luca; Majury, Helena; Giordani, Taira; Spagnolo, Nicolò; Sciarrino, Fabio; Paternostro, Mauro; Ferraro, Alessandro

2017-12-01

Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.

Coherent states for the quantum complete rigid rotor

NASA Astrophysics Data System (ADS)

Fontanari, Daniele; Sadovskií, Dmitrií A.

2018-07-01

Motivated by the possibility to describe orientations of quantum triaxial rigid rotors, such as molecules, with respect to both internal (body-fixed) and external (laboratory) frames, we go through the theory of coherent states and design the appropriate family of coherent states on T∗ SO(3) , the classical phase space of the freely rotating rigid body (the Euler top). We pay particular attention to the resolution of identity property in order to establish the explicit relation between the parameters of the coherent states and classical phase-space variables, actions and angles.

A Back-to-Front Derivation: The Equal Spacing of Quantum Levels Is a Proof of Simple Harmonic Oscillator Physics

ERIC Educational Resources Information Center

Andrews, David L.; Romero, Luciana C. Davila

2009-01-01

The dynamical behaviour of simple harmonic motion can be found in numerous natural phenomena. Within the quantum realm of atomic, molecular and optical systems, two main features are associated with harmonic oscillations: a finite ground-state energy and equally spaced quantum energy levels. Here it is shown that there is in fact a one-to-one…

Duality constructions from quantum state manifolds

NASA Astrophysics Data System (ADS)

Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.

2015-11-01

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

NASA Astrophysics Data System (ADS)

Cao, ChunJun; Carroll, Sean M.

2018-04-01

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

Quantum teleportation over 143 kilometres using active feed-forward.

PubMed

Ma, Xiao-Song; Herbst, Thomas; Scheidl, Thomas; Wang, Daqing; Kropatschek, Sebastian; Naylor, William; Wittmann, Bernhard; Mech, Alexandra; Kofler, Johannes; Anisimova, Elena; Makarov, Vadim; Jennewein, Thomas; Ursin, Rupert; Zeilinger, Anton

2012-09-13

The quantum internet is predicted to be the next-generation information processing platform, promising secure communication and an exponential speed-up in distributed computation. The distribution of single qubits over large distances via quantum teleportation is a key ingredient for realizing such a global platform. By using quantum teleportation, unknown quantum states can be transferred over arbitrary distances to a party whose location is unknown. Since the first experimental demonstrations of quantum teleportation of independent external qubits, an internal qubit and squeezed states, researchers have progressively extended the communication distance. Usually this occurs without active feed-forward of the classical Bell-state measurement result, which is an essential ingredient in future applications such as communication between quantum computers. The benchmark for a global quantum internet is quantum teleportation of independent qubits over a free-space link whose attenuation corresponds to the path between a satellite and a ground station. Here we report such an experiment, using active feed-forward in real time. The experiment uses two free-space optical links, quantum and classical, over 143 kilometres between the two Canary Islands of La Palma and Tenerife. To achieve this, we combine advanced techniques involving a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors and entanglement-assisted clock synchronization. The average teleported state fidelity is well beyond the classical limit of two-thirds. Furthermore, we confirm the quality of the quantum teleportation procedure without feed-forward by complete quantum process tomography. Our experiment verifies the maturity and applicability of such technologies in real-world scenarios, in particular for future satellite-based quantum teleportation.

Quantum walks and wavepacket dynamics on a lattice with twisted photons.

PubMed

Cardano, Filippo; Massa, Francesco; Qassim, Hammam; Karimi, Ebrahim; Slussarenko, Sergei; Paparo, Domenico; de Lisio, Corrado; Sciarrino, Fabio; Santamato, Enrico; Boyd, Robert W; Marrucci, Lorenzo

2015-03-01

The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.

Quantum walks and wavepacket dynamics on a lattice with twisted photons

PubMed Central

Cardano, Filippo; Massa, Francesco; Qassim, Hammam; Karimi, Ebrahim; Slussarenko, Sergei; Paparo, Domenico; de Lisio, Corrado; Sciarrino, Fabio; Santamato, Enrico; Boyd, Robert W.; Marrucci, Lorenzo

2015-01-01

The “quantum walk” has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations. PMID:26601157

Real-space imaging of fractional quantum Hall liquids

NASA Astrophysics Data System (ADS)

Hayakawa, Junichiro; Muraki, Koji; Yusa, Go

2013-01-01

Electrons in semiconductors usually behave like a gas--as independent particles. However, when confined to two dimensions under a perpendicular magnetic field at low temperatures, they condense into an incompressible quantum liquid. This phenomenon, known as the fractional quantum Hall (FQH) effect, is a quantum-mechanical manifestation of the macroscopic behaviour of correlated electrons that arises when the Landau-level filling factor is a rational fraction. However, the diverse microscopic interactions responsible for its emergence have been hidden by its universality and macroscopic nature. Here, we report real-space imaging of FQH liquids, achieved with polarization-sensitive scanning optical microscopy using trions (charged excitons) as a local probe for electron spin polarization. When the FQH ground state is spin-polarized, the triplet/singlet intensity map exhibits a spatial pattern that mirrors the intrinsic disorder potential, which is interpreted as a mapping of compressible and incompressible electron liquids. In contrast, when FQH ground states with different spin polarization coexist, domain structures with spontaneous quasi-long-range order emerge, which can be reproduced remarkably well from the disorder patterns using a two-dimensional random-field Ising model. Our results constitute the first reported real-space observation of quantum liquids in a class of broken symmetry state known as the quantum Hall ferromagnet.

Transferring arbitrary d-dimensional quantum states of a superconducting transmon qudit in circuit QED.

PubMed

Liu, Tong; Su, Qi-Ping; Yang, Jin-Hu; Zhang, Yu; Xiong, Shao-Jie; Liu, Jin-Ming; Yang, Chui-Ping

2017-08-01

A qudit (d-level quantum system) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary d-dimensional quantum states (known or unknown) between two superconducting transmon qudits coupled to a single cavity. The state transfer can be performed by employing resonant interactions only. In addition, quantum states can be deterministically transferred without measurement. Numerical simulations show that high-fidelity transfer of quantum states between two superconducting transmon qudits (d ≤ 5) is feasible with current circuit QED technology. This proposal is quite general and can be applied to accomplish the same task with natural or artificial atoms of a ladder-type level structure coupled to a cavity or resonator.

Simple procedure for phase-space measurement and entanglement validation

NASA Astrophysics Data System (ADS)

Rundle, R. P.; Mills, P. W.; Tilma, Todd; Samson, J. H.; Everitt, M. J.

2017-08-01

It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasiprobability distribution (Wigner function) [Phys. Rev. Lett. 117, 180401 (2016), 10.1103/PhysRevLett.117.180401]. Such functions take the form of expectation values of an observable that has a direct analogy to displaced parity operators. In this work we give a procedure for the measurement of the Wigner function that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five-qubit quantum processor to demonstrate that we can measure and generate the Wigner functions of two different Bell states as well as the five-qubit Greenberger-Horne-Zeilinger state. Because Wigner functions for spin systems are not unique, we define, compare, and contrast two distinct examples. We show how the use of these Wigner functions leads to an optimal method for quantum state analysis especially in the situation where specific characteristic features are of particular interest (such as for spin Schrödinger cat states). Furthermore we show that this analysis leads to straightforward, and potentially very efficient, entanglement test and state characterization methods.

On observation of position in quantum theory

NASA Astrophysics Data System (ADS)

Kryukov, A.

2018-05-01

Newtonian and Schrödinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a "concentration" near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of a state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space.

Quantum Entanglement and the Topological Order of Fractional Hall States

NASA Astrophysics Data System (ADS)

Rezayi, Edward

2015-03-01

Fractional quantum Hall states or, more generally, topological phases of matter defy Landau classification based on order parameter and broken symmetry. Instead they have been characterized by their topological order. Quantum information concepts, such as quantum entanglement, appear to provide the most efficient method of detecting topological order solely from the knowledge of the ground state wave function. This talk will focus on real-space bi-partitioning of quantum Hall states and will present both exact diagonalization and quantum Monte Carlo studies of topological entanglement entropy in various geometries. Results on the torus for non-contractible cuts are quite rich and, through the use of minimum entropy states, yield the modular S-matrix and hence uniquely determine the topological order, as shown in recent literature. Concrete examples of minimum entropy states from known quantum Hall wave functions and their corresponding quantum numbers, used in exact diagonalizations, will be given. In collaboration with Clare Abreu and Raul Herrera. Supported by DOE Grant DE-SC0002140.

Experimental Trapped-ion Quantum Simulation of the Kibble-Zurek dynamics in momentum space

PubMed Central

Cui, Jin-Ming; Huang, Yun-Feng; Wang, Zhao; Cao, Dong-Yang; Wang, Jian; Lv, Wei-Min; Luo, Le; del Campo, Adolfo; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can

2016-01-01

The Kibble-Zurek mechanism is the paradigm to account for the nonadiabatic dynamics of a system across a continuous phase transition. Its study in the quantum regime is hindered by the requisite of ground state cooling. We report the experimental quantum simulation of critical dynamics in the transverse-field Ising model by a set of Landau-Zener crossings in pseudo-momentum space, that can be probed with high accuracy using a single trapped ion. We test the Kibble-Zurek mechanism in the quantum regime in the momentum space and find the measured scaling of excitations is in accordance with the theoretical prediction. PMID:27633087

Polarization tracking system for free-space optical communication, including quantum communication

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nordholt, Jane Elizabeth; Newell, Raymond Thorson; Peterson, Charles Glen

Quantum communication transmitters include beacon lasers that transmit a beacon optical signal in a predetermined state of polarization such as one of the states of polarization of a quantum communication basis. Changes in the beacon polarization are detected at a receiver, and a retarder is adjusted so that the states of polarization in a received quantum communication optical signal are matched to basis polarizations. The beacon and QC signals can be at different wavelengths so that the beacon does not interfere with detection and decoding of the QC optical signal.

Deterministic transfer of an unknown qutrit state assisted by the low-Q microwave resonators

NASA Astrophysics Data System (ADS)

Liu, Tong; Zhang, Yang; Yu, Chang-Shui; Zhang, Wei-Ning

2017-05-01

Qutrits (i.e., three-level quantum systems) can be used to achieve many quantum information and communication tasks due to their large Hilbert spaces. In this work, we propose a scheme to transfer an unknown quantum state between two flux qutrits coupled to two superconducting coplanar waveguide resonators. The quantum state transfer can be deterministically achieved without measurements. Because resonator photons are virtually excited during the operation time, the decoherences caused by the resonator decay and the unwanted inter-resonator crosstalk are greatly suppressed. Moreover, our approach can be adapted to other solid-state qutrits coupled to circuit resonators. Numerical simulations show that the high-fidelity transfer of quantum state between the two qutrits is feasible with current circuit QED technology.

Efficient transfer of an arbitrary qutrit state in circuit quantum electrodynamics.

PubMed

Liu, Tong; Xiong, Shao-Jie; Cao, Xiao-Zhi; Su, Qi-Ping; Yang, Chui-Ping

2015-12-01

Compared with a qubit, a qutrit (i.e., three-level quantum system) has a larger Hilbert space and thus can be used to encode more information in quantum information processing and communication. Here, we propose a method to transfer an arbitrary quantum state between two flux qutrits coupled to two resonators. This scheme is simple because it only requires two basic operations. The state-transfer operation can be performed fast because only resonant interactions are used. Numerical simulations show that the high-fidelity transfer of quantum states between the two qutrits is feasible with current circuit-QED technology. This scheme is quite general and can be applied to accomplish the same task for other solid-state qutrits coupled to resonators.

Loop quantum cosmology with self-dual variables

NASA Astrophysics Data System (ADS)

Wilson-Ewing, Edward

2015-12-01

Using the complex-valued self-dual connection variables, the loop quantum cosmology of a closed Friedmann space-time coupled to a massless scalar field is studied. It is shown how the reality conditions can be imposed in the quantum theory by choosing a particular inner product for the kinematical Hilbert space. While holonomies of the self-dual Ashtekar connection are not well defined in the kinematical Hilbert space, it is possible to introduce a family of generalized holonomylike operators of which some are well defined; these operators in turn are used in the definition of the Hamiltonian constraint operator where the scalar field can be used as a relational clock. The resulting quantum theory is closely related, although not identical, to standard loop quantum cosmology constructed from the Ashtekar-Barbero variables with a real Immirzi parameter. Effective Friedmann equations are derived which provide a good approximation to the full quantum dynamics for sharply peaked states whose volume remains much larger than the Planck volume, and they show that for these states quantum gravity effects resolve the big-bang and big-crunch singularities and replace them by a nonsingular bounce. Finally, the loop quantization in self-dual variables of a flat Friedmann space-time is recovered in the limit of zero spatial curvature and is identical to the standard loop quantization in terms of the real-valued Ashtekar-Barbero variables.

Computing quantum discord is NP-complete

NASA Astrophysics Data System (ADS)

Huang, Yichen

2014-03-01

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some entanglement measures (namely entanglement cost, entanglement of formation, relative entropy of entanglement, squashed entanglement, classical squashed entanglement, conditional entanglement of mutual information, and broadcast regularization of mutual information) and constrained Holevo capacity are NP-hard/NP-complete to compute. These complexity-theoretic results are directly applicable in common randomness distillation, quantum state merging, entanglement distillation, superdense coding, and quantum teleportation; they may offer significant insights into quantum information processing. Moreover, we prove the NP-completeness of two typical problems: linear optimization over classical states and detecting classical states in a convex set, providing evidence that working with classical states is generically computationally intractable.

Generalized Steering Robustness of Bipartite Quantum States

NASA Astrophysics Data System (ADS)

Zheng, Chunming; Guo, Zhihua; Cao, Huaixin

2018-06-01

EPR steering is a kind of quantum correlation that is intermediate between entanglement and Bell nonlocality. In this paper, by recalling the definitions of unsteerability and steerability, some properties of them are given, e.g, it is proved that a local quantum channel transforms every unsteerable state into an unsteerable state. Second, a way of quantifying quantum steering, which we called the generalized steering robustness (GSR), is introduced and some interesting properties are established, including: (1) GSR of a state vanishes if and only if the state is unsteerable; (2) a local quantum channel does not increase GSR of any state; (3) GSR is invariant under each local unitary operation; (4) as a function on the state space, GSR is convex and lower-semi continuous. Lastly, by using the majorization between the reduced states of two pure states, GSR of the two pure states are compared, and it is proved that every maximally entangled state has the maximal GSR.

Classical and Quantum-Mechanical State Reconstruction

ERIC Educational Resources Information Center

Khanna, F. C.; Mello, P. A.; Revzen, M.

2012-01-01

The aim of this paper is to present the subject of state reconstruction in classical and in quantum physics, a subject that deals with the experimentally acquired information that allows the determination of the physical state of a system. Our first purpose is to explain a method for retrieving a classical state in phase space, similar to that…

Conditions for monogamy of quantum correlations in multipartite systems

NASA Astrophysics Data System (ADS)

Kumar, Asutosh

2016-09-01

Monogamy of quantum correlations is a vibrant area of research because of its potential applications in several areas in quantum information ranging from quantum cryptography to co-operative phenomena in many-body physics. In this paper, we investigate conditions under which monogamy is preserved for functions of quantum correlation measures. We prove that a monogamous measure remains monogamous on raising its power, and a non-monogamous measure remains non-monogamous on lowering its power. We also prove that monogamy of a convex quantum correlation measure for arbitrary multipartite pure quantum state leads to its monogamy for mixed states in the same Hilbert space. Monogamy of squared negativity for mixed states and that of entanglement of formation follow as corollaries of our results.

Probing quantum state space: does one have to learn everything to learn something?

PubMed

Carmeli, Claudio; Heinosaari, Teiko; Schultz, Jussi; Toigo, Alessandro

2017-05-01

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task.

Probing quantum state space: does one have to learn everything to learn something?

PubMed Central

Carmeli, Claudio; Schultz, Jussi; Toigo, Alessandro

2017-01-01

Determining the state of a quantum system is a consuming procedure. For this reason, whenever one is interested only in some particular property of a state, it would be desirable to design a measurement set-up that reveals this property with as little effort as possible. Here, we investigate whether, in order to successfully complete a given task of this kind, one needs an informationally complete measurement, or if something less demanding would suffice. The first alternative means that in order to complete the task, one needs a measurement which fully determines the state. We formulate the task as a membership problem related to a partitioning of the quantum state space and, in doing so, connect it to the geometry of the state space. For a general membership problem, we prove various sufficient criteria that force informational completeness, and we explicitly treat several physically relevant examples. For the specific cases that do not require informational completeness, we also determine bounds on the minimal number of measurement outcomes needed to ensure success in the task. PMID:28588404

Spin squeezing as an indicator of quantum chaos in the Dicke model.

PubMed

Song, Lijun; Yan, Dong; Ma, Jian; Wang, Xiaoguang

2009-04-01

We study spin squeezing, an intrinsic quantum property, in the Dicke model without the rotating-wave approximation. We show that the spin squeezing can reveal the underlying chaotic and regular structures in phase space given by a Poincaré section, namely, it acts as an indicator of quantum chaos. Spin squeezing vanishes after a very short time for an initial coherent state centered in a chaotic region, whereas it persists over a longer time for the coherent state centered in a regular region of the phase space. We also study the distribution of the mean spin directions when quantum dynamics takes place. Finally, we discuss relations among spin squeezing, bosonic quadrature squeezing, and two-qubit entanglement in the dynamical processes.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dehesa, J.S.; Martinez-Finkelshtein, A.; Sorokin, V.N.

The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x{sup 2k} with k is a member of N and x is a member of R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremalmore » case k{yields}{infinity} (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states.« less

Dynamics of Entropy in Quantum-like Model of Decision Making

NASA Astrophysics Data System (ADS)

Basieva, Irina; Khrennikov, Andrei; Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu

2011-03-01

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)

Relativistic and noise effects on multiplayer Prisoners' dilemma with entangling initial states

NASA Astrophysics Data System (ADS)

Goudarzi, H.; Rashidi, S. S.

2017-11-01

Three-players Prisoners' dilemma (Alice, Bob and Colin) is studied in the presence of a single collective environment effect as a noise. The environmental effect is coupled with final states by a particular form of Kraus operators K_0 and K_1 through amplitude damping channel. We introduce the decoherence parameter 0≤p≤1 to the corresponding noise matrices, in order to controling the rate of environment influence on payoff of each players. Also, we consider the Unruh effect on the payoff of player, who is located at a noninertial frame. We suppose that two players (Bob and Colin) are in Rindler region I from Minkowski space-time, and move with same uniform acceleration (r_b=r_c) and frequency mode. The game is begun with the classical strategies cooperation ( C) and defection ( D) accessible to each player. Furthermore, the players are allowed to access the quantum strategic space ( Q and M). The quantum entanglement is coupled with initial classical states by the parameter γ \\in [0,π /2]. Using entangled initial states by exerting an unitary operator \\hat{J} as entangling gate, the quantum game (competition between Prisoners, as a three-qubit system) is started by choosing the strategies from classical or quantum strategic space. Arbitrarily chosen strategy by each player can lead to achieving profiles, which can be considered as Nash equilibrium or Pareto optimal. It is shown that in the presence of noise effect, choosing quantum strategy Q results in a winning payoff against the classical strategy D and, for example, the strategy profile ( Q, D, C) is Pareto optimal. We find that the unfair miracle move of Eisert from quantum strategic space is an effective strategy for accelerated players in decoherence mode (p=1) of the game.

Measurement-based quantum teleportation on finite AKLT chains

NASA Astrophysics Data System (ADS)

Fujii, Akihiko; Feder, David

In the measurement-based model of quantum computation, universal quantum operations are effected by making repeated local measurements on resource states which contain suitable entanglement. Resource states include two-dimensional cluster states and the ground state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the honeycomb lattice. Recent studies suggest that measurements on one-dimensional systems in the Haldane phase teleport perfect single-qubit gates in the correlation space, protected by the underlying symmetry. As laboratory realizations of symmetry-protected states will necessarily be finite, we investigate the potential for quantum gate teleportation in finite chains of a bilinear-biquadratic Hamiltonian which is a generalization of the AKLT model representing the full Haldane phase.

Open quantum dots—probing the quantum to classical transition

NASA Astrophysics Data System (ADS)

Ferry, D. K.; Burke, A. M.; Akis, R.; Brunner, R.; Day, T. E.; Meisels, R.; Kuchar, F.; Bird, J. P.; Bennett, B. R.

2011-04-01

Quantum dots provide a natural system in which to study both quantum and classical features of transport. As a closed testbed, they provide a natural system with a very rich set of eigenstates. When coupled to the environment through a pair of quantum point contacts, each of which passes several modes, the original quantum environment evolves into a set of decoherent and coherent states, which classically would compose a mixed phase space. The manner of this breakup is governed strongly by Zurek's decoherence theory, and the remaining coherent states possess all the properties of his pointer states. These states are naturally studied via traditional magnetotransport at low temperatures. More recently, we have used scanning gate (conductance) microscopy to probe the nature of the coherent states, and have shown that families of states exist through the spectrum in a manner consistent with quantum Darwinism. In this review, we discuss the nature of the various states, how they are formed, and the signatures that appear in magnetotransport and general conductance studies.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

Description of quantum states using in free space optic communication

NASA Astrophysics Data System (ADS)

Kučera, Petr

2017-11-01

In the article we concentrate our attention on the quantum description of states which are prepared by light sources. The main goal of the article is the determination of density matrix of background radiation source. It is shown that these matrix elements satisfy Geometric distribution in the number state representation.

Behavior of the maximum likelihood in quantum state tomography

NASA Astrophysics Data System (ADS)

Scholten, Travis L.; Blume-Kohout, Robin

2018-02-01

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.

Behavior of the maximum likelihood in quantum state tomography

DOE PAGES

Blume-Kohout, Robin J; Scholten, Travis L.

2018-02-22

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) shouldmore » not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.« less

Behavior of the maximum likelihood in quantum state tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blume-Kohout, Robin J; Scholten, Travis L.

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) shouldmore » not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.« less

Investigations of quantum pendulum dynamics in a spin-1 BEC

NASA Astrophysics Data System (ADS)

Hoang, Thai; Gerving, Corey; Land, Ben; Anquez, Martin; Hamley, Chris; Chapman, Michael

2013-05-01

We investigate the quantum spin dynamics of a spin-1 BEC initialized to an unstable critical point of the dynamical phase space. The subsequent evolution of the collective states of the system is analogous to an inverted simple pendulum in the quantum limit and yields non-classical states with quantum correlations. For short evolution times in the low depletion limit, we observe squeezed states and for longer times beyond the low depletion limit we observe highly non-Gaussian distributions. C.D. Hamley, C.S. Gerving, T.M. Hoang, E.M. Bookjans, and M.S. Chapman, ``Spin-Nematic Squeezed Vacuum in a Quantum Gas,'' Nature Physics 8, 305-308 (2012).

Tensor network states in time-bin quantum optics

NASA Astrophysics Data System (ADS)

Lubasch, Michael; Valido, Antonio A.; Renema, Jelmer J.; Kolthammer, W. Steven; Jaksch, Dieter; Kim, M. S.; Walmsley, Ian; García-Patrón, Raúl

2018-06-01

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bianchi, Eugenio; Speziale, Simone; Dona, Pietro

Intertwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in R{sup 3}: A polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: We give formulas for the edge lengths, the volume, and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner withmore » the state of a quantum polyhedron, thus generalizing the notion of the quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spin foams with nonsimplicial graphs.« less

The quantum holonomy-diffeomorphism algebra and quantum gravity

NASA Astrophysics Data System (ADS)

Aastrup, Johannes; Grimstrup, Jesper Møller

2016-03-01

We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we show that semiclassical states exist on the holonomy-diffeomorphism part of the algebra but that these states cannot be extended to the full algebra. Via a Dirac-type operator we derive a certain class of unbounded operators that act in the GNS construction of the semiclassical states. These unbounded operators are the type of operators, which we have previously shown to entail the spatial three-dimensional Dirac operator and Dirac-Hamiltonian in a semiclassical limit. Finally, we show that the structure of the Hamilton constraint emerges from a Yang-Mills-type operator over the space of SU(2)-connections.

Resonance and decay phenomena lead to quantum mechanical time asymmetry

NASA Astrophysics Data System (ADS)

Bohm, A.; Bui, H. V.

2013-04-01

The states (Schrödinger picture) and observables (Heisenberg picture) in the standard quantum theory evolve symmetrically in time, given by the unitary group with time extending over -∞ < t < +∞. This time evolution is a mathematical consequence of the Hilbert space boundary condition for the dynamical differential equations. However, this unitary group evolution violates causality. Moreover, it does not solve an old puzzle of Wigner: How does one describe excited states of atoms which decay exponentially, and how is their lifetime τ related to the Lorentzian width Γ? These question can be answered if one replaces the Hilbert space boundary condition by new, Hardy space boundary conditions. These Hardy space boundary conditions allow for a distinction between states (prepared by a preparation apparatus) and observables (detected by a registration apparatus). The new Hardy space quantum theory is time asymmetric, i.e, the time evolution is given by the semigroup with t0 <= t < +∞, which predicts a finite "beginning of time" t0, where t0 is the ensemble of time at which each individual system has been prepared. The Hardy space axiom also leads to the new prediction: the width Γ and the lifetime τ are exactly related by τ = hslash/Γ.

Lorentz quantum mechanics

NASA Astrophysics Data System (ADS)

Zhang, Qi; Wu, Biao

2018-01-01

We present a theoretical framework for the dynamics of bosonic Bogoliubov quasiparticles. We call it Lorentz quantum mechanics because the dynamics is a continuous complex Lorentz transformation in complex Minkowski space. In contrast, in usual quantum mechanics, the dynamics is the unitary transformation in Hilbert space. In our Lorentz quantum mechanics, three types of state exist: space-like, light-like and time-like. Fundamental aspects are explored in parallel to the usual quantum mechanics, such as a matrix form of a Lorentz transformation, and the construction of Pauli-like matrices for spinors. We also investigate the adiabatic evolution in these mechanics, as well as the associated Berry curvature and Chern number. Three typical physical systems, where bosonic Bogoliubov quasi-particles and their Lorentz quantum dynamics can arise, are presented. They are a one-dimensional fermion gas, Bose-Einstein condensate (or superfluid), and one-dimensional antiferromagnet.

Testing the Dimension of Hilbert Spaces

NASA Astrophysics Data System (ADS)

Brunner, Nicolas; Pironio, Stefano; Acin, Antonio; Gisin, Nicolas; Méthot, André Allan; Scarani, Valerio

2008-05-01

Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describe such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and quantum information applications.

Group field theories for all loop quantum gravity

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Ryan, James P.; Thürigen, Johannes

2015-02-01

Group field theories represent a second quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs of arbitrary valence. On the other hand, group field theories have usually been defined in a simplicial context, thus dealing with a restricted set of graphs. In this paper, we generalize the combinatorics of group field theories to cover all the loop quantum gravity state space. As an explicit example, we describe the group field theory formulation of the KKL spin foam model, as well as a particular modified version. We show that the use of tensor model tools allows for the most effective construction. In order to clarify the mathematical basis of our construction and of the formalisms with which we deal, we also give an exhaustive description of the combinatorial structures entering spin foam models and group field theories, both at the level of the boundary states and of the quantum amplitudes.

Proof-of-principle test of coherent-state continuous variable quantum key distribution through turbulent atmosphere (Conference Presentation)

NASA Astrophysics Data System (ADS)

Derkach, Ivan D.; Peuntinger, Christian; Ruppert, László; Heim, Bettina; Gunthner, Kevin; Usenko, Vladyslav C.; Elser, Dominique; Marquardt, Christoph; Filip, Radim; Leuchs, Gerd

2016-10-01

Continuous-variable quantum key distribution is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis. Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks. It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied. We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations. The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

NASA Technical Reports Server (NTRS)

Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.

1989-01-01

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

On a two-pass scheme without a faraday mirror for free-space relativistic quantum cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kravtsov, K. S.; Radchenko, I. V.; Korol'kov, A. V.

2013-05-15

The stability of destructive interference independent of the input polarization and the state of a quantum communication channel in fiber optic systems used in quantum cryptography plays a principal role in providing the security of communicated keys. A novel optical scheme is proposed that can be used both in relativistic quantum cryptography for communicating keys in open space and for communicating them over fiber optic lines. The scheme ensures stability of destructive interference and admits simple automatic balancing of a fiber interferometer.

Large scale exact quantum dynamics calculations: Ten thousand quantum states of acetonitrile

NASA Astrophysics Data System (ADS)

Halverson, Thomas; Poirier, Bill

2015-03-01

'Exact' quantum dynamics (EQD) calculations of the vibrational spectrum of acetonitrile (CH3CN) are performed, using two different methods: (1) phase-space-truncated momentum-symmetrized Gaussian basis and (2) correlated truncated harmonic oscillator basis. In both cases, a simple classical phase space picture is used to optimize the selection of individual basis functions-leading to drastic reductions in basis size, in comparison with existing methods. Massive parallelization is also employed. Together, these tools-implemented into a single, easy-to-use computer code-enable a calculation of tens of thousands of vibrational states of CH3CN to an accuracy of 0.001-10 cm-1.

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

NASA Astrophysics Data System (ADS)

Perl, Y.; Band, Y. B.; Boukobza, E.

2017-05-01

We analyze a resonant single-atom two-photon quantum optical amplifier both dynamically and thermodynamically. A detailed thermodynamic analysis shows that the nonlinear amplifier is thermodynamically equivalent to the linear amplifier. However, by calculating the Wigner quasiprobability distribution for various initial field states, we show that unique quantum features in optical phase space, absent in the linear amplifier, are retained for extended times, despite the fact that dissipation tends to wash out dynamical features observed at early evolution times. These features are related to the discrete nature of the two-photon matter-field interaction and fingerprint the initial field state at thermodynamic times.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

NASA Astrophysics Data System (ADS)

Peise, J.; Kruse, I.; Lange, K.; Lücke, B.; Pezzè, L.; Arlt, J.; Ertmer, W.; Hammerer, K.; Santos, L.; Smerzi, A.; Klempt, C.

2016-03-01

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, as shown successfully with light fields. Here, we report on the production of massive particles which meet the EPR criterion for continuous phase/amplitude variables. The created quantum state of ultracold atoms shows an EPR parameter of 0.18(3), which is 2.4 standard deviations below the threshold of 1/4. Our state presents a resource for tests of quantum nonlocality with massive particles and a wide variety of applications in the field of continuous-variable quantum information and metrology.

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

NASA Astrophysics Data System (ADS)

Srinivasan, K.; Raghavan, G.

2018-03-01

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.

The enhancement of quantum entanglement under an open Dirac system with the Hawking effect in Schwarzschild space-time

NASA Astrophysics Data System (ADS)

Sun, Wen-Yang; Wang, Dong; Fang, Bao-Long; Shi, Jia-Dong; Ye, Liu

2018-06-01

In this letter, we mainly investigate how to enhance the damaged quantum entanglement under an open Dirac system with the Hawking effect within Schwarzschild space-time. We consider that particle A held by Alice undergoes generalized amplitude damping noise in a flat space-time, and that another particle B by Bob entangled with A is under a Schwarzschild space-time. Subsequently, we put forward a physical scheme to recover the damaged quantum entanglement by prior weak measurement on subsystem A before the interaction with the decoherence noise followed by post-measurement filtering operation. The results indicate that our scheme can effectively recover the damaged quantum entanglement affected by the Hawking effect and the noisy channel. Thus, our work might be beneficial to understand the dynamic behavior of the quantum state and recover the damaged quantum entanglement with open Dirac systems under the Hawking effect in the background of a Schwarzschild black hole.

Geometric descriptions of entangled states by auxiliary varieties

NASA Astrophysics Data System (ADS)

Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-01

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n + 1), for n ⩾ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.

Geometrical Phases in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Christian, Joy Julius

In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a truly quantum regime, and allows, for the first time, the measurements of such phases associated with arbitrary non-cyclic evolutions of entangled linear-momentum photon -states. This non-classical manifestation of the geometrical phases is due to the entangled character of linear-momentum photon-states of two correlated photons produced by parametric down-conversion in non-linear crystals. Finally, the non-local aspect of the geometrical phase is contrasted with the fundamental non-locality of quantum mechanics due to the entangled character of quantum states.

Coherent Oscillations inside a Quantum Manifold Stabilized by Dissipation

NASA Astrophysics Data System (ADS)

Touzard, S.; Grimm, A.; Leghtas, Z.; Mundhada, S. O.; Reinhold, P.; Axline, C.; Reagor, M.; Chou, K.; Blumoff, J.; Sliwa, K. M.; Shankar, S.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.

2018-04-01

Manipulating the state of a logical quantum bit (qubit) usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schrödinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits.

Phase space dynamics and control of the quantum particles associated to hypergraph states

NASA Astrophysics Data System (ADS)

Berec, Vesna

2015-05-01

As today's nanotechnology focus becomes primarily oriented toward production and manipulation of materials at the subatomic level, allowing the performance and complexity of interconnects where the device density accepts more than hundreds devices on a single chip, the manipulation of semiconductor nanostructures at the subatomic level sets its prime tasks on preserving and adequate transmission of information encoded in specified (quantum) states. The presented study employs the quantum communication protocol based on the hypergraph network model where the numerical solutions of equations of motion of quantum particles are associated to vertices (assembled with device chip), which follow specific controllable paths in the phase space. We address these findings towards ultimate quest for prediction and selective control of quantum particle trajectories. In addition, presented protocols could represent valuable tool for reducing background noise and uncertainty in low-dimensional and operationally meaningful, scalable complex systems.

Discrete-time Quantum Walks via Interchange Framework and Memory in Quantum Evolution

NASA Astrophysics Data System (ADS)

Dimcovic, Zlatko

One of the newer and rapidly developing approaches in quantum computing is based on "quantum walks," which are quantum processes on discrete space that evolve in either discrete or continuous time and are characterized by mixing of components at each step. The idea emerged in analogy with the classical random walks and stochastic techniques, but these unitary processes are very different even as they have intriguing similarities. This thesis is concerned with study of discrete-time quantum walks. The original motivation from classical Markov chains required for discrete-time quantum walks that one adds an auxiliary Hilbert space, unrelated to the one in which the system evolves, in order to be able to mix components in that space and then take the evolution steps accordingly (based on the state in that space). This additional, "coin," space is very often an internal degree of freedom like spin. We have introduced a general framework for construction of discrete-time quantum walks in a close analogy with the classical random walks with memory that is rather different from the standard "coin" approach. In this method there is no need to bring in a different degree of freedom, while the full state of the system is still described in the direct product of spaces (of states). The state can be thought of as an arrow pointing from the previous to the current site in the evolution, representing the one-step memory. The next step is then controlled by a single local operator assigned to each site in the space, acting quite like a scattering operator. This allows us to probe and solve some problems of interest that have not had successful approaches with "coined" walks. We construct and solve a walk on the binary tree, a structure of great interest but until our result without an explicit discrete time quantum walk, due to difficulties in managing coin spaces necessary in the standard approach. Beyond algorithmic interests, the model based on memory allows one to explore effects of history on the quantum evolution and the subtle emergence of classical features as "memory" is explicitly kept for additional steps. We construct and solve a walk with an additional correlation step, finding interesting new features. On the other hand, the fact that the evolution is driven entirely by a local operator, not involving additional spaces, enables us to choose the Fourier transform as an operator completely controlling the evolution. This in turn allows us to combine the quantum walk approach with Fourier transform based techniques, something decidedly not possible in classical computational physics. We are developing a formalism for building networks manageable by walks constructed with this framework, based on the surprising efficiency of our framework in discovering internals of a simple network that we so far solved. Finally, in line with our expectation that the field of quantum walks can take cues from the rich history of development of the classical stochastic techniques, we establish starting points for the work on non-Abelian quantum walks, with a particular quantum-walk analog of the classical "card shuffling," the walk on the permutation group. In summary, this thesis presents a new framework for construction of discrete time quantum walks, employing and exploring memoried nature of unitary evolution. It is applied to fully solving the problems of: A walk on the binary tree and exploration of the quantum-to-classical transition with increased correlation length (history). It is then used for simple network discovery, and to lay the groundwork for analysis of complex networks, based on combined power of efficient exploration of the Hilbert space (as a walk mixing components) and Fourier transformation (since we can choose this for the evolution operator). We hope to establish this as a general technique as its power would be unmatched by any approaches available in the classical computing. We also looked at the promising and challenging prospect of walks on non-Abelian structures by setting up the problem of "quantum card shuffling," a quantum walk on the permutation group. Relation to other work is thoroughly discussed throughout, along with examination of the context of our work and overviews of our current and future work.

Two-Step Deterministic Remote Preparation of an Arbitrary Quantum State

NASA Astrophysics Data System (ADS)

Wang, Mei-Yu; Yan, Feng-Li

2010-11-01

We present a two-step deterministic remote state preparation protocol for an arbitrary quhit with the aid of a three-particle Greenberger—Horne—Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.

Dimension of quantum phase space measured by photon correlations

NASA Astrophysics Data System (ADS)

Leuchs, Gerd; Glauber, Roy J.; Schleich, Wolfgang P.

2015-06-01

We show that the different values 1, 2 and 3 of the normalized second-order correlation function {g}(2)(0) corresponding to a coherent state, a thermal state and a highly squeezed vacuum originate from the different dimensionality of these states in phase space. In particular, we derive an exact expression for {g}(2)(0) in terms of the ratio of the moments of the classical energy evaluated with the Wigner function of the quantum state of interest and corrections proportional to the reciprocal of powers of the average number of photons. In this way we establish a direct link between {g}(2)(0) and the shape of the state in phase space. Moreover, we illuminate this connection by demonstrating that in the semi-classical limit the familiar photon statistics of a thermal state arise from an area in phase space weighted by a two-dimensional Gaussian, whereas those of a highly squeezed state are governed by a line-integral of a one-dimensional Gaussian. We dedicate this article to Margarita and Vladimir Man’ko on the occasion of their birthdays. The topic of our contribution is deeply rooted in and motivated by their love for non-classical light, quantum mechanical phase space distribution functions and orthogonal polynomials. Indeed, through their articles, talks and most importantly by many stimulating discussions and intensive collaborations with us they have contributed much to our understanding of physics. Happy birthday to you both!

Optical Spectroscopy Of Charged Quantum Dot Molecules

NASA Astrophysics Data System (ADS)

Scheibner, M.; Bracker, A. S.; Stinaff, E. A.; Doty, M. F.; Gammon, D.; Ponomarev, I. V.; Reinecke, T. L.; Korenev, V. L.

2007-04-01

Coupling between two closely spaced quantum dots is observed by means of photoluminescence spectroscopy. Hole coupling is realized by rational crystal growth and heterostructure design. We identify molecular resonances of different excitonic charge states, including the important case of a doubly charged quantum dot molecule.

Sufficient condition for a quantum state to be genuinely quantum non-Gaussian

NASA Astrophysics Data System (ADS)

Happ, L.; Efremov, M. A.; Nha, H.; Schleich, W. P.

2018-02-01

We show that the expectation value of the operator \\hat{{ \\mathcal O }}\\equiv \\exp (-c{\\hat{x}}2)+\\exp (-c{\\hat{p}}2) defined by the position and momentum operators \\hat{x} and \\hat{p} with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.

Compensated Crystal Assemblies for Type-II Entangled Photon Generation in Quantum Cluster States

DTIC Science & Technology

2010-03-01

in quantum computational architectures that operate by principles entirely distinct from any based on classical physics. In contrast with other...of the SPDC spectral function, to enable applications in regions that have not been accessible with other methods. Quantum Information and Computation ...Eliminating frequency and space-time correlations in multi-photon states, PRA 64, 063815, 2001 [2]A. Zeilinger et.al. Experimental One-way computing

A Generalized Quantum Theory

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2014-09-01

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lueders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate - the non-existence of third-order interference (third-order interference and its impossibility in quantum mechanics were discovered by R. Sorkin in 1994). This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed.

Electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Yun

The discovery of quantum Hall e ect has motivated the use of topology instead of broken symmetry to classify the states of matter. Quantum spin Hall e ect has been proposed to have a separation of spin currents as an analogue of the charge currents separation in quantum Hall e ect, leading us to the era of topological insulators. Three-dimensional analogue of the Dirac state in graphene has brought us the three-dimensional Dirac states. Materials with three-dimensional Dirac states could potentially be the parent compounds for Weyl semimetals and topological insulators when time-reversal or space inversion symmetry is broken. Inmore » addition to the single Dirac point linking the two dispersion cones in the Dirac/Weyl semimetals, Dirac points can form a line in the momentum space, resulting in a topological node line semimetal. These fascinating novel topological quantum materials could provide us platforms for studying the relativistic physics in condensed matter systems and potentially lead to design of new electronic devices that run faster and consume less power than traditional, silicon based transistors. In this thesis, we present the electronic properties of novel topological quantum materials studied by angle-resolved photoemission spectroscopy (ARPES).« less

Large numbers hypothesis. IV - The cosmological constant and quantum physics

NASA Technical Reports Server (NTRS)

Adams, P. J.

1983-01-01

In standard physics quantum field theory is based on a flat vacuum space-time. This quantum field theory predicts a nonzero cosmological constant. Hence the gravitational field equations do not admit a flat vacuum space-time. This dilemma is resolved using the units covariant gravitational field equations. This paper shows that the field equations admit a flat vacuum space-time with nonzero cosmological constant if and only if the canonical LNH is valid. This allows an interpretation of the LNH phenomena in terms of a time-dependent vacuum state. If this is correct then the cosmological constant must be positive.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

Time-reversal-symmetric single-photon wave packets for free-space quantum communication.

PubMed

Trautmann, N; Alber, G; Agarwal, G S; Leuchs, G

2015-05-01

Readout and retrieval processes are proposed for efficient, high-fidelity quantum state transfer between a matter qubit, encoded in the level structure of a single atom or ion, and a photonic qubit, encoded in a time-reversal-symmetric single-photon wave packet. They are based on controlling spontaneous photon emission and absorption of a matter qubit on demand in free space by stimulated Raman adiabatic passage. As these processes do not involve mode selection by high-finesse cavities or photon transport through optical fibers, they offer interesting perspectives as basic building blocks for free-space quantum-communication protocols.

Measurement and control of a Coulomb-blockaded parafermion box

NASA Astrophysics Data System (ADS)

Snizhko, Kyrylo; Egger, Reinhold; Gefen, Yuval

2018-02-01

Parafermionic zero modes are fractional topologically protected quasiparticles expected to arise in various platforms. We show that Coulomb charging effects define a parafermion box with unique access options via fractional edge states and/or quantum antidots. Basic protocols for the detection, manipulation, and control of parafermionic quantum states are formulated. With those tools, one may directly observe the dimension of the zero-mode Hilbert space, prove the degeneracy of this space, and perform on-demand digital operations satisfying a parafermionic algebra.

Optimal secure quantum teleportation of coherent states of light

NASA Astrophysics Data System (ADS)

Liuzzo-Scorpo, Pietro; Adesso, Gerardo

2017-08-01

We investigate quantum teleportation of ensembles of coherent states of light with a Gaussian distributed displacement in phase space. Recently, the following general question has been addressed in [P. Liuzzo-Scorpo et al., arXiv:1705.03017]: Given a limited amount of entanglement and mean energy available as resources, what is the maximal fidelity that can be achieved on average in the teleportation of such an alphabet of states? Here, we consider a variation of this question, where Einstein-Podolsky-Rosen steering is used as a resource rather than plain entanglement. We provide a solution by means of an optimisation within the space of Gaussian quantum channels, which allows for an intuitive visualisation of the problem. We first show that not all channels are accessible with a finite degree of steering, and then prove that practical schemes relying on asymmetric two-mode Gaussian states enable one to reach the maximal fidelity at the border with the inaccessible region. Our results provide a rigorous quantitative assessment of steering as a resource for secure quantum teleportation beyond the so-called no-cloning threshold. The schemes we propose can be readily implemented experimentally by a conventional Braunstein-Kimble continuous variable teleportation protocol involving homodyne detections and corrective displacements with an optimally tuned gain. These protocols can be integrated as elementary building blocks in quantum networks, for reliable storage and transmission of quantum optical states.

Information Theoretic Characterization of Physical Theories with Projective State Space

NASA Astrophysics Data System (ADS)

Zaopo, Marco

2015-08-01

Probabilistic theories are a natural framework to investigate the foundations of quantum theory and possible alternative or deeper theories. In a generic probabilistic theory, states of a physical system are represented as vectors of outcomes probabilities and state spaces are convex cones. In this picture the physics of a given theory is related to the geometric shape of the cone of states. In quantum theory, for instance, the shape of the cone of states corresponds to a projective space over complex numbers. In this paper we investigate geometric constraints on the state space of a generic theory imposed by the following information theoretic requirements: every non completely mixed state of a system is perfectly distinguishable from some other state in a single shot measurement; information capacity of physical systems is conserved under making mixtures of states. These assumptions guarantee that a generic physical system satisfies a natural principle asserting that the more a state of the system is mixed the less information can be stored in the system using that state as logical value. We show that all theories satisfying the above assumptions are such that the shape of their cones of states is that of a projective space over a generic field of numbers. Remarkably, these theories constitute generalizations of quantum theory where superposition principle holds with coefficients pertaining to a generic field of numbers in place of complex numbers. If the field of numbers is trivial and contains only one element we obtain classical theory. This result tells that superposition principle is quite common among probabilistic theories while its absence gives evidence of either classical theory or an implausible theory.

The sudden death and sudden birth of quantum discord.

PubMed

Xia, Wei; Hou, Jin-Xing; Wang, Xiao-Hui; Liu, Si-Yuan

2018-03-28

The interaction of quantum system and its environment brings out abundant quantum phenomenons. The sudden death of quantum resources, including entanglement, quantum discord and coherence, have been studied from the perspective of quantum breaking channels (QBC). QBC of quantum resources reveal the common features of quantum resources. The definition of QBC implies the relationship between quantum resources. However, sudden death of quantum resources can also appear under some other quantum channels. We consider the dynamics of Bell-diagonal states under a stochastic dephasing noise along the z-direction, and the sudden death and sudden birth of quantum discord are investigated. Next we explain this phenomenon from the geometric structure of quantum discord. According to the above results, the states with sudden death and sudden birth can be filtered in three-parameter space. Then we provide two necessary conditions to judge which kind of noise channels can make Bell-diagonal states sudden death and sudden birth. Moreover, the relation between quantum discord and coherence indicates that the sudden death and sudden birth of quantum discord implies the sudden death and sudden birth of coherence in an optimal basis.

Hybrid annealing: Coupling a quantum simulator to a classical computer

NASA Astrophysics Data System (ADS)

Graß, Tobias; Lewenstein, Maciej

2017-05-01

Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.

Base norms and discrimination of generalized quantum channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jenčová, A.

2014-02-15

We introduce and study norms in the space of hermitian matrices, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels, and networks. We further introduce generalized quantum decision problems and show that the maximal average payoffs of decision procedures are again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum channels exists, such that the input state is maximally entangled.

Magnonic qudit and algebraic Bethe Ansatz

NASA Astrophysics Data System (ADS)

Lulek, B.; Lulek, T.

2010-03-01

A magnonic qudit is proposed as the memory unit of a register of a quantum computer. It is the N-dimensional space, extracted from the 2N-dimensional space of all quantum states of the magnetic Heisenberg ring of N spins 1/2, as the space of all states of a single magnon. Three bases: positional, momentum, and that of Weyl duality are described, together with appropriate Fourier and Kostka transforms. It is demonstrated how exact Bethe Ansatz (BA) eigenfunctions, classified in terms of rigged string configurations, can be coded using a collection of magnonic qudits. To this aim, the algebraic BA is invoked, such that a single magnonic qudit is prepared in a state corresponding to a magnon in one of the states provided by spectral parameters emerging from the corresponding BA equations.

Neural-Network Quantum States, String-Bond States, and Chiral Topological States

NASA Astrophysics Data System (ADS)

Glasser, Ivan; Pancotti, Nicola; August, Moritz; Rodriguez, Ivan D.; Cirac, J. Ignacio

2018-01-01

Neural-network quantum states have recently been introduced as an Ansatz for describing the wave function of quantum many-body systems. We show that there are strong connections between neural-network quantum states in the form of restricted Boltzmann machines and some classes of tensor-network states in arbitrary dimensions. In particular, we demonstrate that short-range restricted Boltzmann machines are entangled plaquette states, while fully connected restricted Boltzmann machines are string-bond states with a nonlocal geometry and low bond dimension. These results shed light on the underlying architecture of restricted Boltzmann machines and their efficiency at representing many-body quantum states. String-bond states also provide a generic way of enhancing the power of neural-network quantum states and a natural generalization to systems with larger local Hilbert space. We compare the advantages and drawbacks of these different classes of states and present a method to combine them together. This allows us to benefit from both the entanglement structure of tensor networks and the efficiency of neural-network quantum states into a single Ansatz capable of targeting the wave function of strongly correlated systems. While it remains a challenge to describe states with chiral topological order using traditional tensor networks, we show that, because of their nonlocal geometry, neural-network quantum states and their string-bond-state extension can describe a lattice fractional quantum Hall state exactly. In addition, we provide numerical evidence that neural-network quantum states can approximate a chiral spin liquid with better accuracy than entangled plaquette states and local string-bond states. Our results demonstrate the efficiency of neural networks to describe complex quantum wave functions and pave the way towards the use of string-bond states as a tool in more traditional machine-learning applications.

Baryon spectrum from superconformal quantum mechanics and its light-front holographic embedding

DOE PAGES

de Teramond, Guy F.; Dosch, Hans Gunter; Brodsky, Stanley J.

2015-02-27

We describe the observed light-baryon spectrum by extending superconformal quantum mechanics to the light front and its embedding in AdS space. This procedure uniquely determines the confinement potential for arbitrary half-integer spin. To this end, we show that fermionic wave equations in AdS space are dual to light-front supersymmetric quantum-mechanical bound-state equations in physical space-time. The specific breaking of conformal invariance explains hadronic properties common to light mesons and baryons, such as the observed mass pattern in the radial and orbital excitations, from the spectrum generating algebra. Lastly, the holographic embedding in AdS also explains distinctive and systematic features, suchmore » as the spin-J degeneracy for states with the same orbital angular momentum, observed in the light-baryon spectrum.« less

Quantum origin of quantum jumps: Breaking of unitary symmetry induced by information transfer in the transition from quantum to classical

NASA Astrophysics Data System (ADS)

Zurek, Wojciech Hubert

2007-11-01

Measurements transfer information about a system to the apparatus and then, further on, to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible unperturbed outcomes to an orthogonal subset of all possible states of the system, thus breaking the unitary symmetry of its Hilbert space implied by the quantum superposition principle. Preferred outcome states emerge as a result. They provide a framework for “wave-packet collapse,” designating terminal points of quantum jumps and defining the measured observable by specifying its eigenstates. In quantum Darwinism, they are the progenitors of multiple copies spread throughout the environment—the fittest quantum states that not only survive decoherence, but subvert the environment into carrying information about them—into becoming a witness.

Quantum-correlated two-photon transitions to excitons in semiconductor quantum wells.

PubMed

Salazar, L J; Guzmán, D A; Rodríguez, F J; Quiroga, L

2012-02-13

The dependence of the excitonic two-photon absorption on the quantum correlations (entanglement) of exciting biphotons by a semiconductor quantum well is studied. We show that entangled photon absorption can display very unusual features depending on space-time-polarization biphoton parameters and absorber density of states for both bound exciton states as well as for unbound electron-hole pairs. We report on the connection between biphoton entanglement, as quantified by the Schmidt number, and absorption by a semiconductor quantum well. Comparison between frequency-anti-correlated, unentangled and frequency-correlated biphoton absorption is addressed. We found that exciton oscillator strengths are highly increased when photons arrive almost simultaneously in an entangled state. Two-photon-absorption becomes a highly sensitive probe of photon quantum correlations when narrow semiconductor quantum wells are used as two-photon absorbers.

Exactly solvable quantum cosmologies from two killing field reductions of general relativity

NASA Astrophysics Data System (ADS)

Husain, Viqar; Smolin, Lee

1989-11-01

An exact and, possibly, general solution to the quantum constraints is given for the sector of general relativity containing cosmological solutions with two space-like, commuting, Killing fields. The dynamics of these model space-times, which are known as Gowdy space-times, is formulated in terms of Ashtekar's new variables. The quantization is done by using the recently introduced self-dual and loop representations. On the classical phase space we find four explicit physical observables, or constants of motion, which generate a GL(2) symmetry group on the space of solutions. In the loop representations we find that a complete description of the physical state space, consisting of the simultaneous solutions to all of the constraints, is given in terms of the equivalence classes, under Diff(S1), of a pair of densities on the circle. These play the same role that the link classes play in the loop representation solution to the full 3+1 theory. An infinite dimensional algebra of physical observables is found on the physical state space, which is a GL(2) loop algebra. In addition, by freezing the local degrees of freedom of the model, we find a finite dimensional quantum system which describes a set of degenerate quantum cosmologies on T3 in which the length of one of the S1's has gone to zero, while the area of the remaining S1×S1 is quantized in units of the Planck area. The quantum kinematics of this sector of the model is identical to that of a one-plaquette SU(2) lattice gauge theory.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nielsen, Michael A.; School of Information Technology and Electrical Engineering, University of Queensland, Brisbane, Queensland 4072; Dawson, Christopher M.

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which showmore » that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.« less

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

Non-monotonicity of Trace Distance Under Tensor Products

NASA Astrophysics Data System (ADS)

Maziero, Jonas

2015-10-01

The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article, we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not show up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states.

Excitonic quantum interference in a quantum dot chain with rings.

PubMed

Hong, Suc-Kyoung; Nam, Seog Woo; Yeon, Kyu-Hwang

2008-04-16

We demonstrate excitonic quantum interference in a closely spaced quantum dot chain with nanorings. In the resonant dipole-dipole interaction model with direct diagonalization method, we have found a peculiar feature that the excitation of specified quantum dots in the chain is completely inhibited, depending on the orientational configuration of the transition dipole moments and specified initial preparation of the excitation. In practice, these excited states facilitating quantum interference can provide a conceptual basis for quantum interference devices of excitonic hopping.

New Constructions of Orthogonal Product Basis Quantum States

NASA Astrophysics Data System (ADS)

Zuo, Huijuan; Liu, Shuxia; Yang, Yinghui

2018-02-01

An orthogonal basis B9 for the Hilbert space C 3 × C 3 was presented by Bennett et al. (Phys. Rev. A 59, 1070, 1999) which was illustrated in a visual figure in their report. The character of the construction is that each base vector is a product state, thus any distinguishing operator cannot create entanglement. In this paper, we mainly focus on some new constructions of orthogonal product basis quantum states in the high-dimensional quantum systems. Especially, as for the quantum system of (2m + 1) ⊗ (2m + 1), where m ∈ Z and m ≥ 2, we have provided the direct construction in mathematical method.

Slowing Quantum Decoherence by Squeezing in Phase Space

NASA Astrophysics Data System (ADS)

Le Jeannic, H.; Cavaillès, A.; Huang, K.; Filip, R.; Laurat, J.

2018-02-01

Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.

Size-dependent energy levels of InSb quantum dots measured by scanning tunneling spectroscopy.

PubMed

Wang, Tuo; Vaxenburg, Roman; Liu, Wenyong; Rupich, Sara M; Lifshitz, Efrat; Efros, Alexander L; Talapin, Dmitri V; Sibener, S J

2015-01-27

The electronic structure of single InSb quantum dots (QDs) with diameters between 3 and 7 nm was investigated using atomic force microscopy (AFM) and scanning tunneling spectroscopy (STS). In this size regime, InSb QDs show strong quantum confinement effects which lead to discrete energy levels on both valence and conduction band states. Decrease of the QD size increases the measured band gap and the spacing between energy levels. Multiplets of equally spaced resonance peaks are observed in the tunneling spectra. There, multiplets originate from degeneracy lifting induced by QD charging. The tunneling spectra of InSb QDs are qualitatively different from those observed in the STS of other III-V materials, for example, InAs QDs, with similar band gap energy. Theoretical calculations suggest the electron tunneling occurs through the states connected with L-valley of InSb QDs rather than through states of the Γ-valley. This observation calls for better understanding of the role of indirect valleys in strongly quantum-confined III-V nanomaterials.

Entanglement for All Quantum States

ERIC Educational Resources Information Center

de la Torre, A. C.; Goyeneche, D.; Leitao, L.

2010-01-01

It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical…

ADHM and the 4d quantum Hall effect

NASA Astrophysics Data System (ADS)

Barns-Graham, Alec; Dorey, Nick; Lohitsiri, Nakarin; Tong, David; Turner, Carl

2018-04-01

Yang-Mills instantons are solitonic particles in d = 4 + 1 dimensional gauge theories. We construct and analyse the quantum Hall states that arise when these particles are restricted to the lowest Landau level. We describe the ground state wavefunctions for both Abelian and non-Abelian quantum Hall states. Although our model is purely bosonic, we show that the excitations of this 4d quantum Hall state are governed by the Nekrasov partition function of a certain five dimensional supersymmetric gauge theory with Chern-Simons term. The partition function can also be interpreted as a variant of the Hilbert series of the instanton moduli space, counting holomorphic sections rather than holomorphic functions. It is known that the Hilbert series of the instanton moduli space can be rewritten using mirror symmetry of 3d gauge theories in terms of Coulomb branch variables. We generalise this approach to include the effect of a five dimensional Chern-Simons term. We demonstrate that the resulting Coulomb branch formula coincides with the corresponding Higgs branch Molien integral which, in turn, reproduces the standard formula for the Nekrasov partition function.

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Extremality of Gaussian quantum states.

PubMed

Wolf, Michael M; Giedke, Geza; Cirac, J Ignacio

2006-03-03

We investigate Gaussian quantum states in view of their exceptional role within the space of all continuous variables states. A general method for deriving extremality results is provided and applied to entanglement measures, secret key distillation and the classical capacity of bosonic quantum channels. We prove that for every given covariance matrix the distillable secret key rate and the entanglement, if measured appropriately, are minimized by Gaussian states. This result leads to a clearer picture of the validity of frequently made Gaussian approximations. Moreover, it implies that Gaussian encodings are optimal for the transmission of classical information through bosonic channels, if the capacity is additive.

Enhancing multi-step quantum state tomography by PhaseLift

NASA Astrophysics Data System (ADS)

Lu, Yiping; Zhao, Qing

2017-09-01

Multi-photon system has been studied by many groups, however the biggest challenge faced is the number of copies of an unknown state are limited and far from detecting quantum entanglement. The difficulty to prepare copies of the state is even more serious for the quantum state tomography. One possible way to solve this problem is to use adaptive quantum state tomography, which means to get a preliminary density matrix in the first step and revise it in the second step. In order to improve the performance of adaptive quantum state tomography, we develop a new distribution scheme of samples and extend it to three steps, that is to correct it once again based on the density matrix obtained in the traditional adaptive quantum state tomography. Our numerical results show that the mean square error of the reconstructed density matrix by our new method is improved to the level from 10-4 to 10-9 for several tested states. In addition, PhaseLift is also applied to reduce the required storage space of measurement operator.

Geometry of discrete quantum computing

NASA Astrophysics Data System (ADS)

Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung

2013-05-01

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.

Dirac δ -function potential in quasiposition representation of a minimal-length scenario

NASA Astrophysics Data System (ADS)

Gusson, M. F.; Gonçalves, A. Oakes O.; Francisco, R. O.; Furtado, R. G.; Fabris, J. C.; Nogueira, J. A.

2018-03-01

A minimal-length scenario can be considered as an effective description of quantum gravity effects. In quantum mechanics the introduction of a minimal length can be accomplished through a generalization of Heisenberg's uncertainty principle. In this scenario, state eigenvectors of the position operator are no longer physical states and the representation in momentum space or a representation in a quasiposition space must be used. In this work, we solve the Schroedinger equation with a Dirac δ -function potential in quasiposition space. We calculate the bound state energy and the coefficients of reflection and transmission for the scattering states. We show that leading corrections are of order of the minimal length ({ O}(√{β })) and the coefficients of reflection and transmission are no longer the same for the Dirac delta well and barrier as in ordinary quantum mechanics. Furthermore, assuming that the equivalence of the 1s state energy of the hydrogen atom and the bound state energy of the Dirac {{δ }}-function potential in the one-dimensional case is kept in a minimal-length scenario, we also find that the leading correction term for the ground state energy of the hydrogen atom is of the order of the minimal length and Δx_{\\min } ≤ 10^{-25} m.

The Biharmonic Oscillator and Asymmetric Linear Potentials: From Classical Trajectories to Momentum-Space Probability Densities in the Extreme Quantum Limit

ERIC Educational Resources Information Center

Ruckle, L. J.; Belloni, M.; Robinett, R. W.

2012-01-01

The biharmonic oscillator and the asymmetric linear well are two confining power-law-type potentials for which complete bound-state solutions are possible in both classical and quantum mechanics. We examine these problems in detail, beginning with studies of their trajectories in position and momentum space, evaluation of the classical probability…

Phase-space foundations of electron holography

NASA Astrophysics Data System (ADS)

Lubk, A.; Röder, F.

2015-09-01

We present a unified formalism for describing various forms of electron holography in quantum mechanical phase space including their extensions to quantum-state reconstructions. The phase-space perspective allows for taking into account partial coherence as well as the quantum mechanical detection process typically hampering the unique reconstruction of a wave function. We elaborate on the limitations imposed by the electron optical elements of the transmission electron microscope as well as the scattering at the target. The results provide the basis for vastly extending the scope of electron holographic techniques towards analyzing partially coherent signals such as inelastically scattered electrons or electron pulses used in ultrafast transmission electron microscopy.

Generic isolated horizons in loop quantum gravity

NASA Astrophysics Data System (ADS)

Beetle, Christopher; Engle, Jonathan

2010-12-01

Isolated horizons model equilibrium states of classical black holes. A detailed quantization, starting from a classical phase space restricted to spherically symmetric horizons, exists in the literature and has since been extended to axisymmetry. This paper extends the quantum theory to horizons of arbitrary shape. Surprisingly, the Hilbert space obtained by quantizing the full phase space of all generic horizons with a fixed area is identical to that originally found in spherical symmetry. The entropy of a large horizon remains one-quarter its area, with the Barbero-Immirzi parameter retaining its value from symmetric analyses. These results suggest a reinterpretation of the intrinsic quantum geometry of the horizon surface.

Quantumness and the role of locality on quantum correlations

NASA Astrophysics Data System (ADS)

Bellomo, G.; Plastino, A.; Plastino, A. R.

2016-06-01

Quantum correlations in a physical system are usually studied with respect to a unique and fixed decomposition of the system into subsystems, without fully exploiting the rich structure of the state space. Here, we show several examples in which the consideration of different ways to decompose a physical system enhances the quantum resources and accounts for a more flexible definition of quantumness measures. Furthermore, we give a different perspective regarding how to reassess the fact that local operations play a key role in general quantumness measures that go beyond entanglement—as discordlike ones. We propose a family of measures to quantify the maximum quantumness of a given state. For the discord-based case, we present some analytical results for 2 ×d -dimensional states. Applying our definition to low-dimensional bipartite states, we show that different behaviors can be reported for separable and entangled states vis-à-vis those corresponding to the usual measures of quantum correlations. We show that there is a close link between our proposal and the criterion to witness quantum correlations based on the rank of the correlation matrix, proposed by Dakić, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010), 10.1103/PhysRevLett.105.190502].

Nonunitary quantum computation in the ground space of local Hamiltonians

NASA Astrophysics Data System (ADS)

Usher, Naïri; Hoban, Matty J.; Browne, Dan E.

2017-09-01

A central result in the study of quantum Hamiltonian complexity is that the k -local Hamiltonian problem is quantum-Merlin-Arthur-complete. In that problem, we must decide if the lowest eigenvalue of a Hamiltonian is bounded below some value, or above another, promised one of these is true. Given the ground state of the Hamiltonian, a quantum computer can determine this question, even if the ground state itself may not be efficiently quantum preparable. Kitaev's proof of QMA-completeness encodes a unitary quantum circuit in QMA into the ground space of a Hamiltonian. However, we now have quantum computing models based on measurement instead of unitary evolution; furthermore, we can use postselected measurement as an additional computational tool. In this work, we generalize Kitaev's construction to allow for nonunitary evolution including postselection. Furthermore, we consider a type of postselection under which the construction is consistent, which we call tame postselection. We consider the computational complexity consequences of this construction and then consider how the probability of an event upon which we are postselecting affects the gap between the ground-state energy and the energy of the first excited state of its corresponding Hamiltonian. We provide numerical evidence that the two are not immediately related by giving a family of circuits where the probability of an event upon which we postselect is exponentially small, but the gap in the energy levels of the Hamiltonian decreases as a polynomial.

Practical recipes for the model order reduction, dynamical simulation and compressive sampling of large-scale open quantum systems

NASA Astrophysics Data System (ADS)

Sidles, John A.; Garbini, Joseph L.; Harrell, Lee E.; Hero, Alfred O.; Jacky, Jonathan P.; Malcomb, Joseph R.; Norman, Anthony G.; Williamson, Austin M.

2009-06-01

Practical recipes are presented for simulating high-temperature and nonequilibrium quantum spin systems that are continuously measured and controlled. The notion of a spin system is broadly conceived, in order to encompass macroscopic test masses as the limiting case of large-j spins. The simulation technique has three stages: first the deliberate introduction of noise into the simulation, then the conversion of that noise into an equivalent continuous measurement and control process, and finally, projection of the trajectory onto state-space manifolds having reduced dimensionality and possessing a Kähler potential of multilinear algebraic form. These state-spaces can be regarded as ruled algebraic varieties upon which a projective quantum model order reduction (MOR) is performed. The Riemannian sectional curvature of ruled Kählerian varieties is analyzed, and proved to be non-positive upon all sections that contain a rule. These manifolds are shown to contain Slater determinants as a special case and their identity with Grassmannian varieties is demonstrated. The resulting simulation formalism is used to construct a positive P-representation for the thermal density matrix. Single-spin detection by magnetic resonance force microscopy (MRFM) is simulated, and the data statistics are shown to be those of a random telegraph signal with additive white noise. Larger-scale spin-dust models are simulated, having no spatial symmetry and no spatial ordering; the high-fidelity projection of numerically computed quantum trajectories onto low dimensionality Kähler state-space manifolds is demonstrated. The reconstruction of quantum trajectories from sparse random projections is demonstrated, the onset of Donoho-Stodden breakdown at the Candès-Tao sparsity limit is observed, a deterministic construction for sampling matrices is given and methods for quantum state optimization by Dantzig selection are given.

Effects of a scalar scaling field on quantum mechanics

DOE PAGES

Benioff, Paul

2016-04-18

This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at eachmore » location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blume-Kohout, Robin J; Scholten, Travis L.

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) shouldmore » not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.« less

Geometric descriptions of entangled states by auxiliary varieties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-15

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete themore » approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.« less

Loop-quantum-gravity vertex amplitude.

PubMed

Engle, Jonathan; Pereira, Roberto; Rovelli, Carlo

2007-10-19

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one and it yields an SO(4)-covariant vertex amplitude for Euclidean loop gravity.

Dynamical generation of noiseless quantum subsystems

PubMed

Viola; Knill; Lloyd

2000-10-16

We combine dynamical decoupling and universal control methods for open quantum systems with coding procedures. By exploiting a general algebraic approach, we show how appropriate encodings of quantum states result in obtaining universal control over dynamically generated noise-protected subsystems with limited control resources. In particular, we provide a constructive scheme based on two-body Hamiltonians for performing universal quantum computation over large noiseless spaces which can be engineered in the presence of arbitrary linear quantum noise.

Momentum-Space Entanglement and Loschmidt Echo in Luttinger Liquids after a Quantum Quench.

PubMed

Dóra, Balázs; Lundgren, Rex; Selover, Mark; Pollmann, Frank

2016-07-01

Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e., the overlap of the disentangled and final wave functions of the system. The second largest eigenvalue is the overlap of the first excited state of the disentangled system with zero total momentum and the final wave function. The entanglement gap is universal both in equilibrium and after a quantum quench. The momentum-space entanglement entropy is always extensive and saturates fast to a time independent value after the quench, in sharp contrast to a spatial bipartitioning.

Satisfying the Einstein–Podolsky–Rosen criterion with massive particles

PubMed Central

Peise, J.; Kruse, I.; Lange, K.; Lücke, B.; Pezzè, L.; Arlt, J.; Ertmer, W.; Hammerer, K.; Santos, L.; Smerzi, A.; Klempt, C.

2015-01-01

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology. PMID:26612105

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles.

PubMed

Peise, J; Kruse, I; Lange, K; Lücke, B; Pezzè, L; Arlt, J; Ertmer, W; Hammerer, K; Santos, L; Smerzi, A; Klempt, C

2015-11-27

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

Satisfying the Einstein-Podolsky-Rosen criterion with massive particles

NASA Astrophysics Data System (ADS)

Peise, J.; Kruse, I.; Lange, K.; Lücke, B.; Pezzè, L.; Arlt, J.; Ertmer, W.; Hammerer, K.; Santos, L.; Smerzi, A.; Klempt, C.

2015-11-01

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology.

Quantum trajectory phase transitions in the micromaser.

PubMed

Garrahan, Juan P; Armour, Andrew D; Lesanovsky, Igor

2011-08-01

We study the dynamics of the single-atom maser, or micromaser, by means of the recently introduced method of thermodynamics of quantum jump trajectories. We find that the dynamics of the micromaser displays multiple space-time phase transitions, i.e., phase transitions in ensembles of quantum jump trajectories. This rich dynamical phase structure becomes apparent when trajectories are classified by dynamical observables that quantify dynamical activity, such as the number of atoms that have changed state while traversing the cavity. The space-time transitions can be either first order or continuous, and are controlled not just by standard parameters of the micromaser but also by nonequilibrium "counting" fields. We discuss how the dynamical phase behavior relates to the better known stationary-state properties of the micromaser.

Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit

NASA Technical Reports Server (NTRS)

Elgradechi, Amine M.

1993-01-01

Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.

Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

NASA Astrophysics Data System (ADS)

Junge, M.; Palazuelos, C.; Pérez-García, D.; Villanueva, I.; Wolf, M. M.

2010-12-01

In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order {Ω left(sqrt{n}/log^2n right)} when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative L p embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise.

Quantum-metric contribution to the pair mass in spin-orbit-coupled Fermi superfluids

NASA Astrophysics Data System (ADS)

Iskin, M.

2018-03-01

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum-metric contribution accounts for a sizable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-Bose-Einstein condensate crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables.

Bond Length Dependence on Quantum States as Shown by Spectroscopy

ERIC Educational Resources Information Center

Lim, Kieran F.

2005-01-01

A discussion on how a spreadsheet simulation of linear-molecular spectra could be used to explore the dependence of rotational band spacing and contours on average bond lengths in the initial and final quantum states is presented. The simulation of hydrogen chloride IR, iodine UV-vis, and nitrogen UV-vis spectra clearly show whether the average…

Quantum supersymmetric Bianchi IX cosmology

NASA Astrophysics Data System (ADS)

Damour, Thibault; Spindel, Philippe

2014-11-01

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle effect" between small-volume universes and large-volume ones, and to a possible reduction of the continuous spectrum to a discrete spectrum of quantum states looking like excited versions of the Planckian-size universes described by the discrete states at fermionic levels NF=0 and 1.

Time Asymmetric Quantum Mechanics

NASA Astrophysics Data System (ADS)

Bohm, Arno R.; Gadella, Manuel; Kielanowski, Piotr

2011-09-01

The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t0≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics.

Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm.

PubMed

Godfrin, C; Ferhat, A; Ballou, R; Klyatskaya, S; Ruben, M; Wernsdorfer, W; Balestro, F

2017-11-03

Quantum algorithms use the principles of quantum mechanics, such as, for example, quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimization, simulation, and solving large systems of linear equations. Here, we implement Grover's quantum algorithm, proposed to find an element in an unsorted list, using a single nuclear 3/2 spin carried by a Tb ion sitting in a single molecular magnet transistor. The coherent manipulation of this multilevel quantum system (qudit) is achieved by means of electric fields only. Grover's search algorithm is implemented by constructing a quantum database via a multilevel Hadamard gate. The Grover sequence then allows us to select each state. The presented method is of universal character and can be implemented in any multilevel quantum system with nonequal spaced energy levels, opening the way to novel quantum search algorithms.

Operating Quantum States in Single Magnetic Molecules: Implementation of Grover's Quantum Algorithm

NASA Astrophysics Data System (ADS)

Godfrin, C.; Ferhat, A.; Ballou, R.; Klyatskaya, S.; Ruben, M.; Wernsdorfer, W.; Balestro, F.

2017-11-01

Quantum algorithms use the principles of quantum mechanics, such as, for example, quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimization, simulation, and solving large systems of linear equations. Here, we implement Grover's quantum algorithm, proposed to find an element in an unsorted list, using a single nuclear 3 /2 spin carried by a Tb ion sitting in a single molecular magnet transistor. The coherent manipulation of this multilevel quantum system (qudit) is achieved by means of electric fields only. Grover's search algorithm is implemented by constructing a quantum database via a multilevel Hadamard gate. The Grover sequence then allows us to select each state. The presented method is of universal character and can be implemented in any multilevel quantum system with nonequal spaced energy levels, opening the way to novel quantum search algorithms.

Experimental realization of non-Abelian non-adiabatic geometric gates.

PubMed

Abdumalikov, A A; Fink, J M; Juliusson, K; Pechal, M; Berger, S; Wallraff, A; Filipp, S

2013-04-25

The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies--the effect of which depends on the order of two consecutive paths--can be obtained. They are important, for example, for the creation of synthetic gauge fields in cold atomic gases or the description of non-Abelian anyon statistics. Moreover, there are proposals to exploit non-Abelian holonomic gates for the purposes of noise-resilient quantum computation. In contrast to Abelian geometric operations, non-Abelian ones have been observed only in nuclear quadrupole resonance experiments with a large number of spins, and without full characterization of the geometric process and its non-commutative nature. Here we realize non-Abelian non-adiabatic holonomic quantum operations on a single, superconducting, artificial three-level atom by applying a well-controlled, two-tone microwave drive. Using quantum process tomography, we determine fidelities of the resulting non-commuting gates that exceed 95 per cent. We show that two different quantum gates, originating from two distinct paths in Hilbert space, yield non-equivalent transformations when applied in different orders. This provides evidence for the non-Abelian character of the implemented holonomic quantum operations. In combination with a non-trivial two-quantum-bit gate, our method suggests a way to universal holonomic quantum computing.

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Investigation of the spinfoam path integral with quantum cuboid intertwiners

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Steinhaus, Sebastian

2016-05-01

In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.

Quantum control of quasi-collision states: A protocol for hybrid fusion

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2018-04-01

When confined to small regions quantum systems exhibit electronic and structural properties different from their free space behavior. These properties are of interest, for example, for molecular insertion, hydrogen storage and the exploration of new pathways for chemical and nuclear reactions. Here, a confined three-body problem is studied, with emphasis on the study of the “quantum scars” associated to dynamical collisions. For the particular case of nuclear reactions, it is proposed that a molecular cage might simply be used as a confining device with the collision states accessed by quantum control techniques.

Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.

PubMed

Adesso, Gerardo; Girolami, Davide; Serafini, Alessio

2012-11-09

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.

Quantum information processing by a continuous Maxwell demon

NASA Astrophysics Data System (ADS)

Stevens, Josey; Deffner, Sebastian

Quantum computing is believed to be fundamentally superior to classical computing; however quantifying the specific thermodynamic advantage has been elusive. Experimentally motivated, we generalize previous minimal models of discrete demons to continuous state space. Analyzing our model allows one to quantify the thermodynamic resources necessary to process quantum information. By further invoking the semi-classical limit we compare the quantum demon with its classical analogue. Finally, this model also serves as a starting point to study open quantum systems.

Experimental optimal maximum-confidence discrimination and optimal unambiguous discrimination of two mixed single-photon states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steudle, Gesine A.; Knauer, Sebastian; Herzog, Ulrike

2011-05-15

We present an experimental implementation of optimum measurements for quantum state discrimination. Optimum maximum-confidence discrimination and optimum unambiguous discrimination of two mixed single-photon polarization states were performed. For the latter the states of rank 2 in a four-dimensional Hilbert space are prepared using both path and polarization encoding. Linear optics and single photons from a true single-photon source based on a semiconductor quantum dot are utilized.

Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions

DTIC Science & Technology

1998-05-01

in Hilbert space and almost always precludes the exis- tence of “large” Schrödinger-cat-like states except on extremely short time scales. A...Hamiltonian Hideal operate on the Hilbert space formed by the ↓l and ↑l states of the L qubits. In practice, for the case of trapped ions, the...auxiliary state (Sec. 3.3). If decoherence mechanisms cause other states to be populated, the Hilbert space must be expanded. Although more streamlined

Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.

The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.; Müller, Markus P.; Dahlsten, Oscar C. O.

2017-12-01

The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.

The complex and quaternionic quantum bit from relativity of simultaneity on an interferometer.

PubMed

Garner, Andrew J P; Müller, Markus P; Dahlsten, Oscar C O

2017-12-01

The patterns of fringes produced by an interferometer have long been important testbeds for our best contemporary theories of physics. Historically, interference has been used to contrast quantum mechanics with classical physics, but recently experiments have been performed that test quantum theory against even more exotic alternatives. A physically motivated family of theories are those where the state space of a two-level system is given by a sphere of arbitrary dimension. This includes classical bits, and real, complex and quaternionic quantum theory. In this paper, we consider relativity of simultaneity (i.e. that observers may disagree about the order of events at different locations) as applied to a two-armed interferometer, and show that this forbids most interference phenomena more complicated than those of complex quantum theory. If interference must depend on some relational property of the setting (such as path difference), then relativity of simultaneity will limit state spaces to standard complex quantum theory, or a subspace thereof. If this relational assumption is relaxed, we find one additional theory compatible with relativity of simultaneity: quaternionic quantum theory. Our results have consequences for current laboratory interference experiments: they have to be designed carefully to avoid rendering beyond-quantum effects invisible by relativity of simultaneity.

Quantum mechanics: why complex Hilbert space?

NASA Astrophysics Data System (ADS)

Cassinelli, G.; Lahti, P.

2017-10-01

We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field. This article is part of the themed issue `Second quantum revolution: foundational questions'.

Quantum corrections in thermal states of fermions on anti-de Sitter space-time

NASA Astrophysics Data System (ADS)

Ambruş, Victor E.; Winstanley, Elizabeth

2017-12-01

We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.

Quantum storage of entangled telecom-wavelength photons in an erbium-doped optical fibre

NASA Astrophysics Data System (ADS)

Saglamyurek, Erhan; Jin, Jeongwan; Verma, Varun B.; Shaw, Matthew D.; Marsili, Francesco; Nam, Sae Woo; Oblak, Daniel; Tittel, Wolfgang

2015-02-01

The realization of a future quantum Internet requires the processing and storage of quantum information at local nodes and interconnecting distant nodes using free-space and fibre-optic links. Quantum memories for light are key elements of such quantum networks. However, to date, neither an atomic quantum memory for non-classical states of light operating at a wavelength compatible with standard telecom fibre infrastructure, nor a fibre-based implementation of a quantum memory, has been reported. Here, we demonstrate the storage and faithful recall of the state of a 1,532 nm wavelength photon entangled with a 795 nm photon, in an ensemble of cryogenically cooled erbium ions doped into a 20-m-long silica fibre, using a photon-echo quantum memory protocol. Despite its currently limited efficiency and storage time, our broadband light-matter interface brings fibre-based quantum networks one step closer to reality.

Exciton absorption of entangled photons in semiconductor quantum wells

NASA Astrophysics Data System (ADS)

Rodriguez, Ferney; Guzman, David; Salazar, Luis; Quiroga, Luis; Condensed Matter Physics Group Team

2013-03-01

The dependence of the excitonic two-photon absorption on the quantum correlations (entanglement) of exciting biphotons by a semiconductor quantum well is studied. We show that entangled photon absorption can display very unusual features depending on space-time-polarization biphoton parameters and absorber density of states for both bound exciton states as well as for unbound electron-hole pairs. We report on the connection between biphoton entanglement, as quantified by the Schmidt number, and absorption by a semiconductor quantum well. Comparison between frequency-anti-correlated, unentangled and frequency-correlated biphoton absorption is addressed. We found that exciton oscillator strengths are highly increased when photons arrive almost simultaneously in an entangled state. Two-photon-absorption becomes a highly sensitive probe of photon quantum correlations when narrow semiconductor quantum wells are used as two-photon absorbers. Research funds from Facultad de Ciencias, Universidad de los Andes

Experimental Satellite Quantum Communications

NASA Astrophysics Data System (ADS)

Vallone, Giuseppe; Bacco, Davide; Dequal, Daniele; Gaiarin, Simone; Luceri, Vincenza; Bianco, Giuseppe; Villoresi, Paolo

2015-07-01

Quantum communication (QC), namely, the faithful transmission of generic quantum states, is a key ingredient of quantum information science. Here we demonstrate QC with polarization encoding from space to ground by exploiting satellite corner cube retroreflectors as quantum transmitters in orbit and the Matera Laser Ranging Observatory of the Italian Space Agency in Matera, Italy, as a quantum receiver. The quantum bit error ratio (QBER) has been kept steadily low to a level suitable for several quantum information protocols, as the violation of Bell inequalities or quantum key distribution (QKD). Indeed, by taking data from different satellites, we demonstrate an average value of QBER =4.6 % for a total link duration of 85 s. The mean photon number per pulse μsat leaving the satellites was estimated to be of the order of one. In addition, we propose a fully operational satellite QKD system by exploiting our communication scheme with orbiting retroreflectors equipped with a modulator, a very compact payload. Our scheme paves the way toward the implementation of a QC worldwide network leveraging existing receivers.

Experimental realization of universal geometric quantum gates with solid-state spins.

PubMed

Zu, C; Wang, W-B; He, L; Zhang, W-G; Dai, C-Y; Wang, F; Duan, L-M

2014-10-02

Experimental realization of a universal set of quantum logic gates is the central requirement for the implementation of a quantum computer. In an 'all-geometric' approach to quantum computation, the quantum gates are implemented using Berry phases and their non-Abelian extensions, holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilience features. On the experimental side, geometric phases and holonomies have been observed in thermal ensembles of liquid molecules using nuclear magnetic resonance; however, such systems are known to be non-scalable for the purposes of quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting quantum bits and quantum dots, and a recent experiment has realized geometric single-bit gates in a superconducting system. Here we report the experimental realization of a universal set of geometric quantum gates using the solid-state spins of diamond nitrogen-vacancy centres. These diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system.

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

The Strange (Hi)story of Particles and Waves

NASA Astrophysics Data System (ADS)

Zeh, H. Dieter

2016-03-01

This is an attempt of a non-technical but conceptually consistent presentation of quantum theory in a historical context. While the first part is written for a general readership, Section 5 may appear a bit provocative to some quantum physicists. I argue that the single-particle wave functions of quantum mechanics have to be correctly interpreted as field modes that are "occupied once" (i.e. first excited states of the corresponding quantum oscillators in the case of boson fields). Multiple excitations lead to apparent many-particle wave functions, while the quantum states proper are defined by wave function(al)s on the "configuration" space of fundamental fields, or on another, as yet elusive, fundamental local basis.

From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''

NASA Astrophysics Data System (ADS)

Bergeron, H.

2001-09-01

Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence principle). Moreover spins for particles are naturally generated, including an approximation of their interaction with magnetic fields. We also recover by this approach the semi-classical formalism developed by E. Prugovečki [Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)].

Prefixed-threshold real-time selection method in free-space quantum key distribution

NASA Astrophysics Data System (ADS)

Wang, Wenyuan; Xu, Feihu; Lo, Hoi-Kwong

2018-03-01

Free-space quantum key distribution allows two parties to share a random key with unconditional security, between ground stations, between mobile platforms, and even in satellite-ground quantum communications. Atmospheric turbulence causes fluctuations in transmittance, which further affect the quantum bit error rate and the secure key rate. Previous postselection methods to combat atmospheric turbulence require a threshold value determined after all quantum transmission. In contrast, here we propose a method where we predetermine the optimal threshold value even before quantum transmission. Therefore, the receiver can discard useless data immediately, thus greatly reducing data storage requirements and computing resources. Furthermore, our method can be applied to a variety of protocols, including, for example, not only single-photon BB84 but also asymptotic and finite-size decoy-state BB84, which can greatly increase its practicality.

Nonclassicality of Photon-Added Displaced Thermal State via Quantum Phase-Space Distributions

NASA Astrophysics Data System (ADS)

Zhang, Ran; Meng, Xiang-Guo; Du, Chuan-Xun; Wang, Ji-Suo

2018-02-01

We introduce a new kind of nonclassical mixed state generated by adding arbitrary photons to a displaced thermal state, i.e., the photon-added displaced thermal state (PADTS), and obtain the normalization factor, which is simply related to two-variable Hermite polynomials. We also discuss the nonclassicality of the PADTS by considering quantum phase-space distributions. The results indicate that the value of the photon count statistics is maximum when the number of detected photons is equal to the number of added photons, and that the photon-added operation has a similar modulation effect with increasing displacement. Moreover, the negative volume of the Wigner function for the PADTS takes a maximal value for a specific photon-added number.

Quantum work in the Bohmian framework

NASA Astrophysics Data System (ADS)

Sampaio, R.; Suomela, S.; Ala-Nissila, T.; Anders, J.; Philbin, T. G.

2018-01-01

At nonzero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for example, is characterized by the ensemble of system trajectories in phase space and, by including the probabilities for various trajectories to occur, a work distribution can be constructed. However, without phase-space trajectories, the task of constructing a work probability distribution in the quantum regime has proven elusive. Here we use quantum trajectories in phase space and define fluctuating work as power integrated along the trajectories, in complete analogy to classical statistical physics. The resulting work probability distribution is valid for any quantum evolution, including cases with coherences in the energy basis. We demonstrate the quantum work probability distribution and its properties with an exactly solvable example of a driven quantum harmonic oscillator. An important feature of the work distribution is its dependence on the initial statistical mixture of pure states, which is reflected in higher moments of the work. The proposed approach introduces a fundamentally different perspective on quantum thermodynamics, allowing full thermodynamic characterization of the dynamics of quantum systems, including the measurement process.

A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vignat, C.; Lamberti, P. W.

2009-10-15

Recently, Carinena, et al. [Ann. Phys. 322, 434 (2007)] introduced a new family of orthogonal polynomials that appear in the wave functions of the quantum harmonic oscillator in two-dimensional constant curvature spaces. They are a generalization of the Hermite polynomials and will be called curved Hermite polynomials in the following. We show that these polynomials are naturally related to the relativistic Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)], and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between the solutions of the quantum harmonic oscillator on negative curvature spaces and on positivemore » curvature spaces. At last, we show a maximum entropy property for the ground states of these oscillators.« less

Integrated generation of complex optical quantum states and their coherent control

NASA Astrophysics Data System (ADS)

Roztocki, Piotr; Kues, Michael; Reimer, Christian; Romero Cortés, Luis; Sciara, Stefania; Wetzel, Benjamin; Zhang, Yanbing; Cino, Alfonso; Chu, Sai T.; Little, Brent E.; Moss, David J.; Caspani, Lucia; Azaña, José; Morandotti, Roberto

2018-01-01

Complex optical quantum states based on entangled photons are essential for investigations of fundamental physics and are the heart of applications in quantum information science. Recently, integrated photonics has become a leading platform for the compact, cost-efficient, and stable generation and processing of optical quantum states. However, onchip sources are currently limited to basic two-dimensional (qubit) two-photon states, whereas scaling the state complexity requires access to states composed of several (<2) photons and/or exhibiting high photon dimensionality. Here we show that the use of integrated frequency combs (on-chip light sources with a broad spectrum of evenly-spaced frequency modes) based on high-Q nonlinear microring resonators can provide solutions for such scalable complex quantum state sources. In particular, by using spontaneous four-wave mixing within the resonators, we demonstrate the generation of bi- and multi-photon entangled qubit states over a broad comb of channels spanning the S, C, and L telecommunications bands, and control these states coherently to perform quantum interference measurements and state tomography. Furthermore, we demonstrate the on-chip generation of entangled high-dimensional (quDit) states, where the photons are created in a coherent superposition of multiple pure frequency modes. Specifically, we confirm the realization of a quantum system with at least one hundred dimensions. Moreover, using off-the-shelf telecommunications components, we introduce a platform for the coherent manipulation and control of frequencyentangled quDit states. Our results suggest that microcavity-based entangled photon state generation and the coherent control of states using accessible telecommunications infrastructure introduce a powerful and scalable platform for quantum information science.

Quantum Teleportation and Grover's Algorithm Without the Wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

2017-02-01

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover's search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead of Hilbert spaces and wavefunctions.

A quantum extension to inspection game

NASA Astrophysics Data System (ADS)

Deng, Xinyang; Deng, Yong; Liu, Qi; Chang, Shuhua; Wang, Zhen

2016-06-01

Quantum game theory is a new interdisciplinary field between game theory and system engineering research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement between players. Our results show that the quantum inspection game has various Nash equilibria depending on the initial quantum state of the game. It is also shown that quantization can respectively help each player to increase his own payoff, yet fails to bring Pareto improvement for the collective payoff in the quantum inspection game.

Exponential energy growth due to slow parameter oscillations in quantum mechanical systems.

PubMed

Turaev, Dmitry

2016-05-01

It is shown that a periodic emergence and destruction of an additional quantum number leads to an exponential growth of energy of a quantum mechanical system subjected to a slow periodic variation of parameters. The main example is given by systems (e.g., quantum billiards and quantum graphs) with periodically divided configuration space. In special cases, the process can also lead to a long period of cooling that precedes the acceleration, and to the desertion of the states with a particular value of the quantum number.

Exchange interaction and the tunneling induced transparency in coupled quantum dots

NASA Astrophysics Data System (ADS)

Borges, Halyne; Alcalde, Augusto; Ulloa, Sergio

2014-03-01

Stacked semiconductor quantum dots coupled by tunneling are unique ``quantum molecule'' where it is possible to create a multilevel structure of excitonic states. This structure allows the investigation of quantum interference processes and their control via electric external fields. In this work, we investigate the optical response of a quantum molecule coherently driven by a polarized laser, considering the splitting in excitonic levels caused by isotropic and anisotropic exchange interactions. In our model we consider interdot transitions mediated by the the hole tunneling between states with the same total spin and, between bright and dark exciton states. Using realistic experimental parameters, we demonstrate that the excitonic states coupled by tunneling exhibit an enriched and controllable optical response. Our results show that through the appropriate control of the external electric field and light polarization, the tunneling coupling establishes an efficient destructive quantum interference path that creates a transparency window in the absorption spectra, whenever states of appropriate symmetry are mixed by the hole tunneling. We explore the relevant parameters space that would allows with the experiments. CAPES, INCT-IQ and MWN/CIAM-NSF.

Constraining the loop quantum gravity parameter space from phenomenology

NASA Astrophysics Data System (ADS)

Brahma, Suddhasattwa; Ronco, Michele

2018-03-01

Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG) theories, in deriving falsifiable modified dispersion relations (MDRs) for particles on a deformed Minkowski space-time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG) (such as the regularization scheme used or the representation of the gauge group) are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches.

Quantum autoencoders for efficient compression of quantum data

NASA Astrophysics Data System (ADS)

Romero, Jonathan; Olson, Jonathan P.; Aspuru-Guzik, Alan

2017-12-01

Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x, to map x to a lower dimensional point y such that x can likely be recovered from y. The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.

Fractional charge and inter-Landau-level states at points of singular curvature.

PubMed

Biswas, Rudro R; Son, Dam Thanh

2016-08-02

The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

Quantum Control of Open Systems and Dense Atomic Ensembles

NASA Astrophysics Data System (ADS)

DiLoreto, Christopher

Controlling the dynamics of open quantum systems; i.e. quantum systems that decohere because of interactions with the environment, is an active area of research with many applications in quantum optics and quantum computation. My thesis expands the scope of this inquiry by seeking to control open systems in proximity to an additional system. The latter could be a classical system such as metal nanoparticles, or a quantum system such as a cluster of similar atoms. By modelling the interactions between the systems, we are able to expand the accessible state space of the quantum system in question. For a single, three-level quantum system, I examine isolated systems that have only normal spontaneous emission. I then show that intensity-intensity correlation spectra, which depend directly on the density matrix of the system, can be used detect whether transitions share a common energy level. This detection is possible due to the presence of quantum interference effects between two transitions if they are connected. This effect allows one to asses energy level structure diagrams in complex atoms/molecules. By placing an open quantum system near a nanoparticle dimer, I show that the spontaneous emission rate of the system can be changed "on demand" by changing the polarization of an incident, driving field. In a three-level, Lambda system, this allows a qubit to both retain high qubit fidelity when it is operating, and to be rapidly initialized to a pure state once it is rendered unusable by decoherence. This type of behaviour is not possible in a single open quantum system; therefore adding a classical system nearby extends the overall control space of the quantum system. An open quantum system near identical neighbours in a dense ensemble is another example of how the accessible state space can be expanded. I show that a dense ensemble of atoms rapidly becomes disordered with states that are not directly excited by an incident field becoming significantly populated. This effect motivates the need for using multi-directional basis sets in theoretical analysis of dense quantum systems. My results demonstrate the shortcomings of short-pulse techniques used in many recent studies. Based on my numerical studies, I hypothesize that the dense ensemble can be modelled by an effective single quantum system that has a decoherence rate that changes over time. My effective single particle model provides a way in which computational time can be reduced, and also a model in which the underlying physical processes involved in the system's evolution are much easier to understand. I then use this model to provide an elegant theoretical explanation for an unusual experimental result called "transverse optical magnetism''. My effective single particle model's predictions match very well with experimental data.

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

Analysis of limiting information characteristics of quantum-cryptography protocols

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sych, D V; Grishanin, Boris A; Zadkov, Viktor N

2005-01-31

The problem of increasing the critical error rate of quantum-cryptography protocols by varying a set of letters in a quantum alphabet for space of a fixed dimensionality is studied. Quantum alphabets forming regular polyhedra on the Bloch sphere and the continual alphabet equally including all the quantum states are considered. It is shown that, in the absence of basis reconciliation, a protocol with the tetrahedral alphabet has the highest critical error rate among the protocols considered, while after the basis reconciliation, a protocol with the continual alphabet possesses the highest critical error rate. (quantum optics and quantum computation)

Projective loop quantum gravity. II. Searching for semi-classical states

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2017-05-01

In the first paper of this series, an extension of the Ashtekar-Lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by Kijowski. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (also known as holonomies and fluxes). While this is the first step toward the construction of states semi-classical with respect to a full set of observables, one uncovers a deeper issue, which we analyse in the present article in the case of real-valued holonomies. Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomy and flux observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself. A way out would be to suitably restrict the algebra of observables: we take the first step in this direction in a companion paper.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

NASA Astrophysics Data System (ADS)

Bernardini, A. E.; Leal, P.; Bertolami, O.

2018-02-01

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

Probability Distributions for Random Quantum Operations

NASA Astrophysics Data System (ADS)

Schultz, Kevin

Motivated by uncertainty quantification and inference of quantum information systems, in this work we draw connections between the notions of random quantum states and operations in quantum information with probability distributions commonly encountered in the field of orientation statistics. This approach identifies natural sample spaces and probability distributions upon these spaces that can be used in the analysis, simulation, and inference of quantum information systems. The theory of exponential families on Stiefel manifolds provides the appropriate generalization to the classical case. Furthermore, this viewpoint motivates a number of additional questions into the convex geometry of quantum operations relative to both the differential geometry of Stiefel manifolds as well as the information geometry of exponential families defined upon them. In particular, we draw on results from convex geometry to characterize which quantum operations can be represented as the average of a random quantum operation. This project was supported by the Intelligence Advanced Research Projects Activity via Department of Interior National Business Center Contract Number 2012-12050800010.

Quantum mechanics: why complex Hilbert space?

PubMed

Cassinelli, G; Lahti, P

2017-11-13

We outline a programme for an axiomatic reconstruction of quantum mechanics based on the statistical duality of states and effects that combines the use of a theorem of Solér with the idea of symmetry. We also discuss arguments favouring the choice of the complex field.This article is part of the themed issue 'Second quantum revolution: foundational questions'. © 2017 The Author(s).

Optical reading of field-effect transistors by phase-space absorption quenching in a single InGaAs quantum well conducting channel

NASA Astrophysics Data System (ADS)

Chemla, D. S.; Bar-Joseph, I.; Klingshirn, C.; Miller, D. A. B.; Kuo, J. M.

1987-03-01

Absorption switching in a semiconductor quantum well by electrically varying the charge density in the quantum well conducting channel of a selectively doped heterostructure transistor is reported for the first time. The phase-space absorption quenching (PAQ) is observed at room temperature in an InGaAs/InAlAs grown on InP FET, and it shows large absorption coefficient changes with relatively broad spectral bandwidth. This PAQ is large enough to be used for direct optical determination of the logic state of the FET.

Geometry of quantum dynamics in infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Grabowski, Janusz; Kuś, Marek; Marmo, Giuseppe; Shulman, Tatiana

2018-04-01

We develop a geometric approach to quantum mechanics based on the concept of the Tulczyjew triple. Our approach is genuinely infinite-dimensional, i.e. we do not restrict considerations to finite-dimensional Hilbert spaces, contrary to many other works on the geometry of quantum mechanics, and include a Lagrangian formalism in which self-adjoint (Schrödinger) operators are obtained as Lagrangian submanifolds associated with the Lagrangian. As a byproduct we also obtain results concerning coadjoint orbits of the unitary group in infinite dimensions, embedding of pure states in the unitary group, and self-adjoint extensions of symmetric relations.

What is an integrable quench?

NASA Astrophysics Data System (ADS)

Piroli, Lorenzo; Pozsgay, Balázs; Vernier, Eric

2017-12-01

Inspired by classical results in integrable boundary quantum field theory, we propose a definition of integrable initial states for quantum quenches in lattice models. They are defined as the states which are annihilated by all local conserved charges that are odd under space reflection. We show that this class includes the states which can be related to integrable boundary conditions in an appropriate rotated channel, in loose analogy with the picture in quantum field theory. Furthermore, we provide an efficient method to test integrability of given initial states. We revisit the recent literature of global quenches in several models and show that, in all of the cases where closed-form analytical results could be obtained, the initial state is integrable according to our definition. In the prototypical example of the XXZ spin-s chains we show that integrable states include two-site product states but also larger families of matrix product states with arbitrary bond dimension. We argue that our results could be practically useful for the study of quantum quenches in generic integrable models.

Quantum fluctuating geometries and the information paradox

NASA Astrophysics Data System (ADS)

Eyheralde, Rodrigo; Campiglia, Miguel; Gambini, Rodolfo; Pullin, Jorge

2017-12-01

We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking’s original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering a back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell. More work will be needed to determine whether all the information can be recovered. The calculations show that non-trivial quantum effects can occur in regions of low curvature when horizons are involved, as is proposed in the firewall scenario, for instance.

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Cosmological evolution as squeezing: a toy model for group field cosmology

NASA Astrophysics Data System (ADS)

Adjei, Eugene; Gielen, Steffen; Wieland, Wolfgang

2018-05-01

We present a simple model of quantum cosmology based on the group field theory (GFT) approach to quantum gravity. The model is formulated on a subspace of the GFT Fock space for the quanta of geometry, with a fixed volume per quantum. In this Hilbert space, cosmological expansion corresponds to the generation of new quanta. Our main insight is that the evolution of a flat Friedmann–Lemaître–Robertson–Walker universe with a massless scalar field can be described on this Hilbert space as squeezing, familiar from quantum optics. As in GFT cosmology, we find that the three-volume satisfies an effective Friedmann equation similar to the one of loop quantum cosmology, connecting the classical contracting and expanding solutions by a quantum bounce. The only free parameter in the model is identified with Newton’s constant. We also comment on the possible topological interpretation of our squeezed states. This paper can serve as an introduction into the main ideas of GFT cosmology without requiring the full GFT formalism; our results can also motivate new developments in GFT and its cosmological application.

Observation of photonic states dynamics in 3-D integrated Fourier circuits

NASA Astrophysics Data System (ADS)

Flamini, Fulvio; Viggianiello, Niko; Giordani, Taira; Bentivegna, Marco; Spagnolo, Nicolò; Crespi, Andrea; Corrielli, Giacomo; Osellame, Roberto; Martin-Delgado, Miguel Angel; Sciarrino, Fabio

2018-07-01

Entanglement is a fundamental resource at the basis of quantum-enhanced performances in several applications, such as quantum algorithms and quantum metrology. In these contexts, Fourier interferometers implement a relevant class of unitary evolutions which can be embedded in a large variety of protocols. For instance, in the single-particle regime it can be adopted to implement the quantum Fourier transform, while in the multi-particle scenario it can be employed to generate quantum states possessing useful entanglement for quantum phase estimation purposes, or as a tool to verify genuine multi-photon interference. In this article, we study experimentally the dynamics of single-photon and two-photon input states during the evolution provided by a 8-mode Fourier transformation, implemented by exploiting a three-dimensional architecture enabled by the femtosecond laser micromachining technology. In such a way, we fabricated three devices to study the evolution after each step of the decomposition. We observe that the probability distributions obey a step-by-step majorization relationship, where the quantum state occupies a progressively larger portion of the Hilbert space. Such behaviour can be related to the majorization principle, which has been conjectured as a necessary condition for quantum speedup.

Macroscopic features of quantum fluctuations in large-N qubit systems

NASA Astrophysics Data System (ADS)

Klimov, Andrei B.; Muñoz, Carlos

2014-05-01

We introduce a discrete Q function of an N-qubit system projected into the space of symmetric measurements as a tool for analyzing general properties of quantum systems in the macroscopic limit. For known states the projected Q function helps to visualize the results of collective measurements, and for unknown states it can be approximately reconstructed by measuring the lowest moments of the collective variables.

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

2016-06-15

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems,more » which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).« less

Nonrelativistic Quantum Mechanics with Fundamental Environment

NASA Astrophysics Data System (ADS)

Gevorkyan, Ashot S.

2011-03-01

Spontaneous transitions between bound states of an atomic system, "Lamb Shift" of energy levels and many other phenomena in real nonrelativistic quantum systems are connected within the influence of the quantum vacuum fluctuations ( fundamental environment (FE)) which are impossible to consider in the limits of standard quantum-mechanical approaches. The joint system "quantum system (QS) + FE" is described in the framework of the stochastic differential equation (SDE) of Langevin-Schrödinger (L-Sch) type, and is defined on the extended space R 3 ⊗ R { ξ}, where R 3 and R { ξ} are the Euclidean and functional spaces, respectively. The density matrix for single QS in FE is defined. The entropy of QS entangled with FE is defined and investigated in detail. It is proved that as a result of interaction of QS with environment there arise structures of various topologies which are a new quantum property of the system.

Cosmological implications of quantum entanglement in the multiverse

NASA Astrophysics Data System (ADS)

Kanno, Sugumi

2015-12-01

We explore the cosmological implications of quantum entanglement between two causally disconnected universes in the multiverse. We first consider two causally separated de Sitter spaces with a state which is initially entangled. We derive the reduced density matrix of our universe and compute the spectrum of vacuum fluctuations. We then consider the same system with an initially non-entangled state. We find that due to quantum interference scale dependent modulations may enter the spectrum for the case of initially non-entangled state. This gives rise to the possibility that the existence of causally disconnected universes may be experimentally tested by analyzing correlators in detail.

Dual Vector Spaces and Physical Singularities

NASA Astrophysics Data System (ADS)

Rowlands, Peter

Though we often refer to 3-D vector space as constructed from points, there is no mechanism from within its definition for doing this. In particular, space, on its own, cannot accommodate the singularities that we call fundamental particles. This requires a commutative combination of space as we know it with another 3-D vector space, which is dual to the first (in a physical sense). The combination of the two spaces generates a nilpotent quantum mechanics/quantum field theory, which incorporates exact supersymmetry and ultimately removes the anomalies due to self-interaction. Among the many natural consequences of the dual space formalism are half-integral spin for fermions, zitterbewegung, Berry phase and a zero norm Berwald-Moor metric for fermionic states.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rosales-Zarate, Laura E. C.; Drummond, P. D.

We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. Themore » preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.« less

Quantum entanglement and spin control in silicon nanocrystal.

PubMed

Berec, Vesna

2012-01-01

Selective coherence control and electrically mediated exchange coupling of single electron spin between triplet and singlet states using numerically derived optimal control of proton pulses is demonstrated. We obtained spatial confinement below size of the Bohr radius for proton spin chain FWHM. Precise manipulation of individual spins and polarization of electron spin states are analyzed via proton induced emission and controlled population of energy shells in pure (29)Si nanocrystal. Entangled quantum states of channeled proton trajectories are mapped in transverse and angular phase space of (29)Si <100> axial channel alignment in order to avoid transversal excitations. Proton density and proton energy as impact parameter functions are characterized in single particle density matrix via discretization of diagonal and nearest off-diagonal elements. We combined high field and low densities (1 MeV/92 nm) to create inseparable quantum state by superimposing the hyperpolarizationed proton spin chain with electron spin of (29)Si. Quantum discretization of density of states (DOS) was performed by the Monte Carlo simulation method using numerical solutions of proton equations of motion. Distribution of gaussian coherent states is obtained by continuous modulation of individual spin phase and amplitude. Obtained results allow precise engineering and faithful mapping of spin states. This would provide the effective quantum key distribution (QKD) and transmission of quantum information over remote distances between quantum memory centers for scalable quantum communication network. Furthermore, obtained results give insights in application of channeled protons subatomic microscopy as a complete versatile scanning-probe system capable of both quantum engineering of charged particle states and characterization of quantum states below diffraction limit linear and in-depth resolution.PACS NUMBERS: 03.65.Ud, 03.67.Bg, 61.85.+p, 67.30.hj.

Unified quantum no-go theorems and transforming of quantum pure states in a restricted set

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2017-12-01

The linear superposition principle in quantum mechanics is essential for several no-go theorems such as the no-cloning theorem, the no-deleting theorem and the no-superposing theorem. In this paper, we investigate general quantum transformations forbidden or permitted by the superposition principle for various goals. First, we prove a no-encoding theorem that forbids linearly superposing of an unknown pure state and a fixed pure state in Hilbert space of a finite dimension. The new theorem is further extended for multiple copies of an unknown state as input states. These generalized results of the no-encoding theorem include the no-cloning theorem, the no-deleting theorem and the no-superposing theorem as special cases. Second, we provide a unified scheme for presenting perfect and imperfect quantum tasks (cloning and deleting) in a one-shot manner. This scheme may lead to fruitful results that are completely characterized with the linear independence of the representative vectors of input pure states. The upper bounds of the efficiency are also proved. Third, we generalize a recent superposing scheme of unknown states with a fixed overlap into new schemes when multiple copies of an unknown state are as input states.

Revealing nonclassicality beyond Gaussian states via a single marginal distribution

PubMed Central

Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul

2017-01-01

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential—a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis–independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement. PMID:28077456

Revealing nonclassicality beyond Gaussian states via a single marginal distribution.

PubMed

Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul

2017-01-31

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.

A Possible Operational Motivation for the Orthocomplementation in Quantum Structures

NASA Astrophysics Data System (ADS)

D'Hooghe, Bart

2010-11-01

In the foundations of quantum mechanics Gleason’s theorem dictates the uniqueness of the state transition probability via the inner product of the corresponding state vectors in Hilbert space, independent of which measurement context induces this transition. We argue that the state transition probability should not be regarded as a secondary concept which can be derived from the structure on the set of states and properties, but instead should be regarded as a primitive concept for which measurement context is crucial. Accordingly, we adopt an operational approach to quantum mechanics in which a physical entity is defined by the structure of its set of states, set of properties and the possible (measurement) contexts which can be applied to this entity. We put forward some elementary definitions to derive an operational theory from this State-COntext-Property (SCOP) formalism. We show that if the SCOP satisfies a Gleason-like condition, namely that the state transition probability is independent of which measurement context induces the change of state, then the lattice of properties is orthocomplemented, which is one of the ‘quantum axioms’ used in the Piron-Solèr representation theorem for quantum systems. In this sense we obtain a possible physical meaning for the orthocomplementation widely used in quantum structures.

Flexible resources for quantum metrology

NASA Astrophysics Data System (ADS)

Friis, Nicolai; Orsucci, Davide; Skotiniotis, Michalis; Sekatski, Pavel; Dunjko, Vedran; Briegel, Hans J.; Dür, Wolfgang

2017-06-01

Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilising entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantum probe states and measurements, which vary drastically for different metrological scenarios, is usually not taken into account. We show that for a wide range of tasks in metrology, 2D cluster states (a particular family of states useful for measurement-based quantum computation) can serve as flexible resources that allow one to efficiently prepare any required state for sensing, and perform appropriate (entangled) measurements using only single qubit operations. Crucially, the overhead in the number of qubits is less than quadratic, thus preserving the quantum scaling advantage. This is ensured by using a compression to a logarithmically sized space that contains all relevant information for sensing. We specifically demonstrate how our method can be used to obtain optimal scaling for phase and frequency estimation in local estimation problems, as well as for the Bayesian equivalents with Gaussian priors of varying widths. Furthermore, we show that in the paradigmatic case of local phase estimation 1D cluster states are sufficient for optimal state preparation and measurement.

Remote preparation of a qudit using maximally entangled states of qubits

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yu Changshui; Song Heshan; Wang Yahong

2006-02-15

Known quantum pure states of a qudit can be remotely prepared onto a group of particles of qubits exactly or probabilistically with the aid of two-level Einstein-Podolsky-Rosen states. We present a protocol for such kind of remote state preparation. We are mainly focused on the remote preparation of the ensembles of equatorial states and those of states in real Hilbert space. In particular, a kind of states of qudits in real Hilbert space have been shown to be remotely prepared in faith without the limitation of the input space dimension.

Quantum theory of the classical: quantum jumps, Born's Rule and objective classical reality via quantum Darwinism.

PubMed

Zurek, Wojciech Hubert

2018-07-13

The emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. In this paper, I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the environment. I begin with the derivation of preferred sets of states that help to define what exists-our everyday classical reality. They emerge as a result of the breaking of the unitary symmetry of the Hilbert space which happens when the unitarity of quantum evolutions encounters nonlinearities inherent in the process of amplification-of replicating information. This derivation is accomplished without the usual tools of decoherence, and accounts for the appearance of quantum jumps and the emergence of preferred pointer states consistent with those obtained via environment-induced superselection, or einselection The pointer states obtained in this way determine what can happen-define events-without appealing to Born's Rule for probabilities. Therefore, p k =| ψ k | 2 can now be deduced from the entanglement-assisted invariance, or envariance -a symmetry of entangled quantum states. With probabilities at hand, one also gains new insights into the foundations of quantum statistical physics. Moreover, one can now analyse the information flows responsible for decoherence. These information flows explain how the perception of objective classical reality arises from the quantum substrate: the effective amplification that they represent accounts for the objective existence of the einselected states of macroscopic quantum systems through the redundancy of pointer state records in their environment-through quantum Darwinism This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Teleportation of entanglement over 143 km

PubMed Central

Herbst, Thomas; Scheidl, Thomas; Fink, Matthias; Handsteiner, Johannes; Wittmann, Bernhard; Ursin, Rupert; Zeilinger, Anton

2015-01-01

As a direct consequence of the no-cloning theorem, the deterministic amplification as in classical communication is impossible for unknown quantum states. This calls for more advanced techniques in a future global quantum network, e.g., for cloud quantum computing. A unique solution is the teleportation of an entangled state, i.e., entanglement swapping, representing the central resource to relay entanglement between distant nodes. Together with entanglement purification and a quantum memory it constitutes a so-called quantum repeater. Since the aforementioned building blocks have been individually demonstrated in laboratory setups only, the applicability of the required technology in real-world scenarios remained to be proven. Here we present a free-space entanglement-swapping experiment between the Canary Islands of La Palma and Tenerife, verifying the presence of quantum entanglement between two previously independent photons separated by 143 km. We obtained an expectation value for the entanglement-witness operator, more than 6 SDs beyond the classical limit. By consecutive generation of the two required photon pairs and space-like separation of the relevant measurement events, we also showed the feasibility of the swapping protocol in a long-distance scenario, where the independence of the nodes is highly demanded. Because our results already allow for efficient implementation of entanglement purification, we anticipate our research to lay the ground for a fully fledged quantum repeater over a realistic high-loss and even turbulent quantum channel. PMID:26578764

Teleportation of entanglement over 143 km.

PubMed

Herbst, Thomas; Scheidl, Thomas; Fink, Matthias; Handsteiner, Johannes; Wittmann, Bernhard; Ursin, Rupert; Zeilinger, Anton

2015-11-17

As a direct consequence of the no-cloning theorem, the deterministic amplification as in classical communication is impossible for unknown quantum states. This calls for more advanced techniques in a future global quantum network, e.g., for cloud quantum computing. A unique solution is the teleportation of an entangled state, i.e., entanglement swapping, representing the central resource to relay entanglement between distant nodes. Together with entanglement purification and a quantum memory it constitutes a so-called quantum repeater. Since the aforementioned building blocks have been individually demonstrated in laboratory setups only, the applicability of the required technology in real-world scenarios remained to be proven. Here we present a free-space entanglement-swapping experiment between the Canary Islands of La Palma and Tenerife, verifying the presence of quantum entanglement between two previously independent photons separated by 143 km. We obtained an expectation value for the entanglement-witness operator, more than 6 SDs beyond the classical limit. By consecutive generation of the two required photon pairs and space-like separation of the relevant measurement events, we also showed the feasibility of the swapping protocol in a long-distance scenario, where the independence of the nodes is highly demanded. Because our results already allow for efficient implementation of entanglement purification, we anticipate our research to lay the ground for a fully fledged quantum repeater over a realistic high-loss and even turbulent quantum channel.

Dynamics of entanglement in expanding quantum fields

NASA Astrophysics Data System (ADS)

Berges, Jürgen; Floerchinger, Stefan; Venugopalan, Raju

2018-04-01

We develop a functional real-time approach to computing the entanglement between spatial regions for Gaussian states in quantum field theory. The entanglement entropy is characterized in terms of local correlation functions on space-like Cauchy hypersurfaces. The framework is applied to explore an expanding light cone geometry in the particular case of the Schwinger model for quantum electrodynamics in 1+1 space-time dimensions. We observe that the entanglement entropy becomes extensive in rapidity at early times and that the corresponding local reduced density matrix is a thermal density matrix for excitations around a coherent field with a time dependent temperature. Since the Schwinger model successfully describes many features of multiparticle production in e + e - collisions, our results provide an attractive explanation in this framework for the apparent thermal nature of multiparticle production even in the absence of significant final state scattering.

Bispectrum from open inflation

NASA Astrophysics Data System (ADS)

Sugimura, Kazuyuki; Komatsu, Eiichiro

2013-11-01

We calculate the bispectrum of primordial curvature perturbations, ζ, generated during ``open inflation.'' Inflation occurs inside a bubble nucleated via quantum tunneling from the background false vacuum state. Our universe lives inside the bubble, which can be described as a Friedmann-Lemaȋtre-Robertson-Walker (FLRW) universe with negative spatial curvature, undergoing slow-roll inflation. We pay special attention to the issue of an initial state for quantum fluctuations. A ``vacuum state'' defined by a positive-frequency mode in de Sitter space charted by open coordinates is different from the Euclidean vacuum (which is equivalent to the so-called ``Bunch-Davies vacuum'' defined by a positive-frequency mode in de Sitter space charted by flat coordinates). Quantum tunneling (bubble nucleation) then modifies the initial state away from the original Euclidean vacuum. While most of the previous study on modifications of the initial quantum state introduces, by hand, an initial time at which the quantum state is modified as well as the form of the modification, an effective initial time naturally emerges and the form is fixed by quantum tunneling in open inflation models. Therefore, open inflation enables a self-consistent computation of the effect of a modified initial state on the bispectrum. We find a term which goes as langleζk1ζk2ζk3ranglepropto1/k12k34 in the so-called squeezed configurations, k3 << k1 ≈ k2, in agreement with the previous study on modifications of the initial state. The bispectrum in the exact folded limit, e.g., k1 = k2+k3, is also enhanced and remains finite. However, these terms are exponentially suppressed when the wavelength of ζ is smaller than the curvature radius of the universe. The leading-order bispectrum is equal to the usual one from single-field slow-roll inflation; the terms specific for open inflation arise only in the sub-leading order when the wavelength of ζ is smaller than the curvature radius.

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Excited-state relaxation in PbSe quantum dots

NASA Astrophysics Data System (ADS)

An, Joonhee M.; Califano, Marco; Franceschetti, Alberto; Zunger, Alex

2008-04-01

In solids the phonon-assisted, nonradiative decay from high-energy electronic excited states to low-energy electronic excited states is picosecond fast. It was hoped that electron and hole relaxation could be slowed down in quantum dots, due to the unavailability of phonons energy matched to the large energy-level spacings ("phonon-bottleneck"). However, excited-state relaxation was observed to be rather fast (⩽1ps) in InP, CdSe, and ZnO dots, and explained by an efficient Auger mechanism, whereby the excess energy of electrons is nonradiatively transferred to holes, which can then rapidly decay by phonon emission, by virtue of the densely spaced valence-band levels. The recent emergence of PbSe as a novel quantum-dot material has rekindled the hope for a slow down of excited-state relaxation because hole relaxation was deemed to be ineffective on account of the widely spaced hole levels. The assumption of sparse hole energy levels in PbSe was based on an effective-mass argument based on the light effective mass of the hole. Surprisingly, fast intraband relaxation times of 1-7ps were observed in PbSe quantum dots and have been considered contradictory with the Auger cooling mechanism because of the assumed sparsity of the hole energy levels. Our pseudopotential calculations, however, do not support the scenario of sparse hole levels in PbSe: Because of the existence of three valence-band maxima in the bulk PbSe band structure, hole energy levels are densely spaced, in contradiction with simple effective-mass models. The remaining question is whether the Auger decay channel is sufficiently fast to account for the fast intraband relaxation. Using the atomistic pseudopotential wave functions of Pb2046Se2117 and Pb260Se249 quantum dots, we explicitly calculated the electron-hole Coulomb integrals and the P →S electron Auger relaxation rate. We find that the Auger mechanism can explain the experimentally observed P →S intraband decay time scale without the need to invoke any exotic relaxation mechanisms.

Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

PubMed Central

Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming

2016-01-01

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634

Loss resilience for two-qubit state transmission using distributed phase sensitive amplification

DOE PAGES

Dailey, James; Agarwal, Anjali; Toliver, Paul; ...

2015-11-12

We transmit phase-encoded non-orthogonal quantum states through a 5-km long fibre-based distributed optical phase-sensitive amplifier (OPSA) using telecom-wavelength photonic qubit pairs. The gain is set to equal the transmission loss to probabilistically preserve input states during transmission. While neither state is optimally aligned to the OPSA, each input state is equally amplified with no measurable degradation in state quality. These results promise a new approach to reduce the effects of loss by encoding quantum information in a two-qubit Hilbert space which is designed to benefit from transmission through an OPSA.

Loss resilience for two-qubit state transmission using distributed phase sensitive amplification

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dailey, James; Agarwal, Anjali; Toliver, Paul

We transmit phase-encoded non-orthogonal quantum states through a 5-km long fibre-based distributed optical phase-sensitive amplifier (OPSA) using telecom-wavelength photonic qubit pairs. The gain is set to equal the transmission loss to probabilistically preserve input states during transmission. While neither state is optimally aligned to the OPSA, each input state is equally amplified with no measurable degradation in state quality. These results promise a new approach to reduce the effects of loss by encoding quantum information in a two-qubit Hilbert space which is designed to benefit from transmission through an OPSA.

Grassmann phase space theory and the Jaynes-Cummings model

NASA Astrophysics Data System (ADS)

Dalton, B. J.; Garraway, B. M.; Jeffers, J.; Barnett, S. M.

2013-07-01

The Jaynes-Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes-Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker-Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker-Planck equations from which c-number Langevin equations are often developed. However, atomic spin operators satisfy the standard angular momentum commutation rules rather than the commutation rules for bosonic annihilation and creation operators, and are in fact second order combinations of fermionic annihilation and creation operators. Though phase space methods in which the fermionic operators are represented directly by c-number phase space variables have not been successful, the anti-commutation rules for these operators suggest the possibility of using Grassmann variables—which have similar anti-commutation properties. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of phase space methods in quantum optics to treat fermionic systems by representing fermionic annihilation and creation operators directly by Grassmann phase space variables is rather rare. This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the TLA) can be used to treat the Jaynes-Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker-Planck equation involving both left and right Grassmann differentiations can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, in which the correspondence rules for the bosonic operators are non-standard and hence the Fokker-Planck equation is also unusual. Initial conditions, such as those above for initially uncorrelated states, are discussed and used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enable the six coupled equations for the new c-number functions-that are also equivalent to the canonical Grassmann distribution function-to be solved analytically, based on an ansatz from an earlier paper by Stenholm. It is then shown that the distribution function is exactly the same as that determined from the well-known solution based on coupled amplitude equations. In quantum-atom optics theories for many atom bosonic and fermionic systems are needed. With large atom numbers, treatments must often take into account many quantum modes—especially for fermions. Generalisations of phase space distribution functions of phase space variables for a few modes to phase space distribution functionals of field functions (which represent the field operators, c-number fields for bosons, Grassmann fields for fermions) are now being developed for large systems. For the fermionic case, the treatment of the simple two mode problem represented by the Jaynes-Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for fermionic applications in quantum-atom optics.

Systematic dimensionality reduction for continuous-time quantum walks of interacting fermions

NASA Astrophysics Data System (ADS)

Izaac, J. A.; Wang, J. B.

2017-09-01

To extend the continuous-time quantum walk (CTQW) to simulate P distinguishable particles on a graph G composed of N vertices, the Hamiltonian of the system is expanded to act on an NP-dimensional Hilbert space, in effect, simulating the multiparticle CTQW on graph G via a single-particle CTQW propagating on the Cartesian graph product G□P. The properties of the Cartesian graph product have been well studied, and classical simulation of multiparticle CTQWs are common in the literature. However, the above approach is generally applied as is when simulating indistinguishable particles, with the particle statistics then applied to the propagated NP state vector to determine walker probabilities. We address the following question: How can we modify the underlying graph structure G□P in order to simulate multiple interacting fermionic CTQWs with a reduction in the size of the state space? In this paper, we present an algorithm for systematically removing "redundant" and forbidden quantum states from consideration, which provides a significant reduction in the effective dimension of the Hilbert space of the fermionic CTQW. As a result, as the number of interacting fermions in the system increases, the classical computational resources required no longer increases exponentially for fixed N .

The Birth and Death of Redundancy in Decoherence and Quantum Darwinism

NASA Astrophysics Data System (ADS)

Riedel, Charles; Zurek, Wojciech; Zwolak, Michael

2012-02-01

Understanding the quantum-classical transition and the identification of a preferred classical domain through quantum Darwinism is based on recognizing high-redundancy states as both ubiquitous and exceptional. They are produced ubiquitously during decoherence, as has been demonstrated by the recent identification of very general conditions under which high-redundancy states develop. They are exceptional in that high-redundancy states occupy a very narrow corner of the global Hilbert space; states selected at random are overwelming likely to exhibit zero redundancy. In this letter, we examine the conditions and time scales for the transition from high-redundancy states to zero-redundancy states in many-body dynamics. We identify sufficient condition for the development of redundancy from product states and show that the destruction of redundancy can be accomplished even with highly constrained interactions.

Trapped atomic ions for quantum-limited metrology

NASA Astrophysics Data System (ADS)

Wineland, David

2017-04-01

Laser-beam-manipulated trapped ions are a candidate for large-scale quantum information processing and quantum simulation but the basic techniques used can also be applied to quantum-limited metrology and sensing. Some examples being explored at NIST are: 1) As charged harmonic oscillators, trapped ions can be used to sense electric fields; this can be used to characterize the electrode-surface-based noisy electric fields that compromise logic-gate fidelities and may eventually be used as a tool in surface science. 2) Since typical qubit logic gates depend on state-dependent forces, we can adapt the gate dynamics to sensitively detect additional forces. 3) We can use extensions of Bell inequality measurements to further restrict the degree of local realism possessed by Bell states. 4) We also briefly describe experiments for creation of Bell states using Hilbert space engineering. This work is a joint effort including the Ion-Storage group, the Quantum processing group, and the Computing and Communications Theory group at NIST, Boulder. Supported by IARPA, ONR, and the NIST Quantum Information Program.

Quantum-Bayesian coherence

NASA Astrophysics Data System (ADS)

Fuchs, Christopher A.; Schack, Rüdiger

2013-10-01

In the quantum-Bayesian interpretation of quantum theory (or QBism), the Born rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, the argument is given that it should be seen as an empirical addition to Bayesian reasoning itself. Particularly, it is shown how to view the Born rule as a normative rule in addition to usual Dutch-book coherence. It is a rule that takes into account how one should assign probabilities to the consequences of various intended measurements on a physical system, but explicitly in terms of prior probabilities for and conditional probabilities consequent upon the imagined outcomes of a special counterfactual reference measurement. This interpretation is exemplified by representing quantum states in terms of probabilities for the outcomes of a fixed, fiducial symmetric informationally complete measurement. The extent to which the general form of the new normative rule implies the full state-space structure of quantum mechanics is explored.

Effects of Number Scaling on Entangled States in Quantum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, Paul

A summary of number structure scaling is followed by a description of the effects of number scaling in nonrelativistic quantum mechanics. The description extends earlier work to include the effects on the states of two or more interacting particles. Emphasis is placed on the effects on entangled states. The resulting scaling field is generalized to describe the effects on these states. It is also seen that one can use fiber bundles with fibers associated with single locations of the underlying space to describe the effects of scaling on arbitrary numbers of particles.

Quantum coherent optical phase modulation in an ultrafast transmission electron microscope.

PubMed

Feist, Armin; Echternkamp, Katharina E; Schauss, Jakob; Yalunin, Sergey V; Schäfer, Sascha; Ropers, Claus

2015-05-14

Coherent manipulation of quantum systems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantum wavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven 'quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.

Quantum coherent optical phase modulation in an ultrafast transmission electron microscope

NASA Astrophysics Data System (ADS)

Feist, Armin; Echternkamp, Katharina E.; Schauss, Jakob; Yalunin, Sergey V.; Schäfer, Sascha; Ropers, Claus

2015-05-01

Coherent manipulation of quantum systems with light is expected to be a cornerstone of future information and communication technology, including quantum computation and cryptography. The transfer of an optical phase onto a quantum wavefunction is a defining aspect of coherent interactions and forms the basis of quantum state preparation, synchronization and metrology. Light-phase-modulated electron states near atoms and molecules are essential for the techniques of attosecond science, including the generation of extreme-ultraviolet pulses and orbital tomography. In contrast, the quantum-coherent phase-modulation of energetic free-electron beams has not been demonstrated, although it promises direct access to ultrafast imaging and spectroscopy with tailored electron pulses on the attosecond scale. Here we demonstrate the coherent quantum state manipulation of free-electron populations in an electron microscope beam. We employ the interaction of ultrashort electron pulses with optical near-fields to induce Rabi oscillations in the populations of electron momentum states, observed as a function of the optical driving field. Excellent agreement with the scaling of an equal-Rabi multilevel quantum ladder is obtained, representing the observation of a light-driven `quantum walk' coherently reshaping electron density in momentum space. We note that, after the interaction, the optically generated superposition of momentum states evolves into a train of attosecond electron pulses. Our results reveal the potential of quantum control for the precision structuring of electron densities, with possible applications ranging from ultrafast electron spectroscopy and microscopy to accelerator science and free-electron lasers.

Are Quantum Models for Order Effects Quantum?

NASA Astrophysics Data System (ADS)

Moreira, Catarina; Wichert, Andreas

2017-12-01

The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent disciplined called Quantum Cognition. These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. In quantum probability, events are characterised by a superposition state, which is represented by a state vector in a N-dimensional vector space. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order effects, but do we really need quantum principles for models that only involve projections? This work has two main goals. First, it is still not clear in the literature if a quantum projection model has any advantage towards a classical projection. We compared both models and concluded that the Quantum Projection model achieves the same results as its classical counterpart, because the quantum interference effects play no role in the computation of the probabilities. Second, it intends to propose an alternative relativistic interpretation for rotation parameters that are involved in both classical and quantum models. In the end, instead of interpreting these parameters as a similarity measure between questions, we propose that they emerge due to the lack of knowledge concerned with a personal basis state and also due to uncertainties towards the state of world and towards the context of the questions.

Macroscopicity of quantum superpositions on a one-parameter unitary path in Hilbert space

NASA Astrophysics Data System (ADS)

Volkoff, T. J.; Whaley, K. B.

2014-12-01

We analyze quantum states formed as superpositions of an initial pure product state and its image under local unitary evolution, using two measurement-based measures of superposition size: one based on the optimal quantum binary distinguishability of the branches of the superposition and another based on the ratio of the maximal quantum Fisher information of the superposition to that of its branches, i.e., the relative metrological usefulness of the superposition. A general formula for the effective sizes of these states according to the branch-distinguishability measure is obtained and applied to superposition states of N quantum harmonic oscillators composed of Gaussian branches. Considering optimal distinguishability of pure states on a time-evolution path leads naturally to a notion of distinguishability time that generalizes the well-known orthogonalization times of Mandelstam and Tamm and Margolus and Levitin. We further show that the distinguishability time provides a compact operational expression for the superposition size measure based on the relative quantum Fisher information. By restricting the maximization procedure in the definition of this measure to an appropriate algebra of observables, we show that the superposition size of, e.g., NOON states and hierarchical cat states, can scale linearly with the number of elementary particles comprising the superposition state, implying precision scaling inversely with the total number of photons when these states are employed as probes in quantum parameter estimation of a 1-local Hamiltonian in this algebra.

Coin state properties in quantum walks

PubMed Central

Andrade, R. F. S.

2013-01-01

Recent experimental advances have measured individual coin components in discrete time quantum walks, which have not received the due attention in most theoretical studies on the theme. Here is presented a detailed investigation of the properties of M, the difference between square modulus of coin states of discrete quantum walks on a linear chain. Local expectation values are obtained in terms of real and imaginary parts of the Fourier transformed wave function. A simple expression is found for the average difference between coin states in terms of an angle θ gauging the coin operator and its initial state. These results are corroborated by numerical integration of dynamical equations in real space. The local dependence is characterized both by large and short period modulations. The richness of revealed patterns suggests that the amount of information stored and retrieved from quantum walks is significantly enhanced if M is taken into account. PMID:23756358

Joint estimation of phase and phase diffusion for quantum metrology.

PubMed

Vidrighin, Mihai D; Donati, Gaia; Genoni, Marco G; Jin, Xian-Min; Kolthammer, W Steven; Kim, M S; Datta, Animesh; Barbieri, Marco; Walmsley, Ian A

2014-04-14

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer phase probed with relevant quantum states--split single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.

Hilbert's 17th Problem and the Quantumness of States

NASA Astrophysics Data System (ADS)

Korbicz, J. K.; Cirac, J. I.; Wehr, Jan; Lewenstein, M.

2005-04-01

A state of a quantum system can be regarded as classical (quantum) with respect to measurements of a set of canonical observables if and only if there exists (does not exist) a well defined, positive phase-space distribution, the so called Glauber-Sudarshan P representation. We derive a family of classicality criteria that requires that the averages of positive functions calculated using P representation must be positive. For polynomial functions, these criteria are related to Hilbert’s 17th problem, and have physical meaning of generalized squeezing conditions; alternatively, they may be interpreted as nonclassicality witnesses. We show that every generic nonclassical state can be detected by a polynomial that is a sum-of-squares of other polynomials. We introduce a very natural hierarchy of states regarding their degree of quantumness, which we relate to the minimal degree of a sum-of-squares polynomial that detects them.

Two-qubit correlations via a periodic plasmonic nanostructure

NASA Astrophysics Data System (ADS)

Iliopoulos, Nikos; Terzis, Andreas F.; Yannopapas, Vassilios; Paspalakis, Emmanuel

2016-02-01

We theoretically investigate the generation of quantum correlations by using two distant qubits in free space or mediated by a plasmonic nanostructure. We report both entanglement of formation as well as quantum discord and classical correlations. We have found that for proper initial state of the two-qubit system and distance between the two qubits we can produce quantum correlations taking significant value for a relatively large time interval so that it can be useful in quantum information and computation processes.

Two-qubit correlations via a periodic plasmonic nanostructure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Iliopoulos, Nikos; Terzis, Andreas F.; Yannopapas, Vassilios

2016-02-15

We theoretically investigate the generation of quantum correlations by using two distant qubits in free space or mediated by a plasmonic nanostructure. We report both entanglement of formation as well as quantum discord and classical correlations. We have found that for proper initial state of the two-qubit system and distance between the two qubits we can produce quantum correlations taking significant value for a relatively large time interval so that it can be useful in quantum information and computation processes.

Side-channel-free quantum key distribution.

PubMed

Braunstein, Samuel L; Pirandola, Stefano

2012-03-30

Quantum key distribution (QKD) offers the promise of absolutely secure communications. However, proofs of absolute security often assume perfect implementation from theory to experiment. Thus, existing systems may be prone to insidious side-channel attacks that rely on flaws in experimental implementation. Here we replace all real channels with virtual channels in a QKD protocol, making the relevant detectors and settings inside private spaces inaccessible while simultaneously acting as a Hilbert space filter to eliminate side-channel attacks. By using a quantum memory we find that we are able to bound the secret-key rate below by the entanglement-distillation rate computed over the distributed states.

No firewalls in quantum gravity: the role of discreteness of quantum geometry in resolving the information loss paradox

NASA Astrophysics Data System (ADS)

Perez, Alejandro

2015-04-01

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation can be described by a unitary evolution without the problems encountered by the standard remnant scenario or the schemes where information is assumed to come out with the radiation during evaporation (firewalls and complementarity). The final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler), which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach

NASA Astrophysics Data System (ADS)

Borrelli, Raffaele; Gelin, Maxim F.

2016-12-01

Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.

De Sitter Space Without Dynamical Quantum Fluctuations

NASA Astrophysics Data System (ADS)

Boddy, Kimberly K.; Carroll, Sean M.; Pollack, Jason

2016-06-01

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect.

Non-Gaussian quantum states generation and robust quantum non-Gaussianity via squeezing field

NASA Astrophysics Data System (ADS)

Tang, Xu-Bing; Gao, Fang; Wang, Yao-Xiong; Kuang, Sen; Shuang, Feng

2015-03-01

Recent studies show that quantum non-Gaussian states or using non-Gaussian operations can improve entanglement distillation, quantum swapping, teleportation, and cloning. In this work, employing a strategy of non-Gaussian operations (namely subtracting and adding a single photon), we propose a scheme to generate non-Gaussian quantum states named single-photon-added and -subtracted coherent (SPASC) superposition states by implementing Bell measurements, and then investigate the corresponding nonclassical features. By squeezed the input field, we demonstrate that robustness of non-Gaussianity can be improved. Controllable phase space distribution offers the possibility to approximately generate a displaced coherent superposition states (DCSS). The fidelity can reach up to F ≥ 0.98 and F ≥ 0.90 for size of amplitude z = 1.53 and 2.36, respectively. Project supported by the National Natural Science Foundation of China (Grant Nos. 61203061 and 61074052), the Outstanding Young Talent Foundation of Anhui Province, China (Grant No. 2012SQRL040), and the Natural Science Foundation of Anhui Province, China (Grant No. KJ2012Z035).

Quantum correlation properties in Matrix Product States of finite-number spin rings

NASA Astrophysics Data System (ADS)

Zhu, Jing-Min; He, Qi-Kai

2018-02-01

The organization and structure of quantum correlation (QC) of quantum spin-chains are very rich and complex. Hence the depiction and measures about the QC of finite-number spin rings deserved to be investigated intensively by using Matrix Product States(MPSs) in addition to the case with infinite-number. Here the dependencies of the geometric quantum discord(GQD) of two spin blocks on the total spin number, the spacing spin number and the environment parameter are presented in detail. We also compare the GQD with the total correlation(TC) and the classical correlation(CC) and illustrate its characteristics. Predictably, our findings may provide the potential of designing the optimal QC experimental detection proposals and pave the way for the designation of optimal quantum information processing schemes.

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

NASA Technical Reports Server (NTRS)

Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.

2018-01-01

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

Augmenting Phase Space Quantization to Introduce Additional Physical Effects

NASA Astrophysics Data System (ADS)

Robbins, Matthew P. G.

Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.

Optical Parametric Amplification of Single Photon: Statistical Properties and Quantum Interference

NASA Astrophysics Data System (ADS)

Xu, Xue-Xiang; Yuan, Hong-Chun

2014-05-01

By using phase space method, we theoretically investigate the quantum statistical properties and quantum interference of optical parametric amplification of single photon. The statistical properties, such as the Wigner function (WF), average photon number, photon number distribution and parity, are derived analytically for the fields of the two output ports. The results indicate that the fields in the output ports are multiphoton states rather than single photon state due to the amplification of the optical parametric amplifiers (OPA). In addition, the phase sensitivity is also examined by using the detection scheme of parity measurement.

Entanglement dynamics in critical random quantum Ising chain with perturbations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Yichen, E-mail: ychuang@caltech.edu

We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique. - Highlights: • We study the dynamical quantum phase transition between many-body localized phases. • We simulate the dynamics of a very long random spin chain with matrix product states. • We observe numerically super-logarithmic growth of entanglement entropy with time.

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds.

PubMed

Ferrie, Christopher; Blume-Kohout, Robin

2016-03-04

A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/sqrt[N])-in contrast to that of classical probability estimation, which is O(1/N)-where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.

Anomaly-free cosmological perturbations in effective canonical quantum gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barrau, Aurelien; Bojowald, Martin; Kagan, Mikhail

2015-05-01

This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of space-time, the classical perturbative treatment must be rethought carefully. The present discussion provides a unified picture of several previous works, together with new treatments of higher-order perturbations and the specification of initial states.

Evidence of quantum phase transition in real-space vacuum entanglement of higher derivative scalar quantum field theories.

PubMed

Kumar, S Santhosh; Shankaranarayanan, S

2017-11-17

In a bipartite set-up, the vacuum state of a free Bosonic scalar field is entangled in real space and satisfies the area-law- entanglement entropy scales linearly with area of the boundary between the two partitions. In this work, we show that the area law is violated in two spatial dimensional model Hamiltonian having dynamical critical exponent z = 3. The model physically corresponds to next-to-next-to-next nearest neighbour coupling terms on a lattice. The result reported here is the first of its kind of violation of area law in Bosonic systems in higher dimensions and signals the evidence of a quantum phase transition. We provide evidence for quantum phase transition both numerically and analytically using quantum Information tools like entanglement spectra, quantum fidelity, and gap in the energy spectra. We identify the cause for this transition due to the accumulation of large number of angular zero modes around the critical point which catalyses the change in the ground state wave function due to the next-to-next-to-next nearest neighbor coupling. Lastly, using Hubbard-Stratanovich transformation, we show that the effective Bosonic Hamiltonian can be obtained from an interacting fermionic theory and provide possible implications for condensed matter systems.

Practical Quantum Cryptography for Secure Free-Space Communications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buttler, W.T.; Hughes, R.J.; Kwiat, P.G.

1999-02-01

Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. The security of these transmissions is based on the inviolability of the laws of quantum mechanics and information-theoretically secure post-processing methods. An adversary can neither successfully tap the quantum transmissions, nor evade detection, owing to Heisenberg's uncertainty principle. In this paper we describe the theory of quantum cryptography, and the most recent results from our experimental free-space system with which we have demonstrated for the first time the feasibility of quantum key generation overmore » a point-to-point outdoor atmospheric path in daylight. We achieved a transmission distance of 0.5 km, which was limited only by the length of the test range. Our results provide strong evidence that cryptographic key material could be generated on demand between a ground station and a satellite (or between two satellites), allowing a satellite to be securely re-keyed on orbit. We present a feasibility analysis of surface-to-satellite quantum key generation.« less

FREE-SPACE QUANTUM CRYPTOGRAPHY IN DAYLIGHT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hughes, R.J.; Buttler, W.T.

2000-01-01

Quantum cryptography is an emerging technology in which two parties may simultaneously generate shared, secret cryptographic key material using the transmission of quantum states of light. The security of these transmissions is based on the inviolability of the laws of quantum mechanics and information-theoretically secure post-processing methods. An adversary can neither successfully tap the quantum transmissions, nor evade detection, owing to Heisenberg's uncertainty principle. In this paper we describe the theory of quantum cryptography, and the most recent results from our experimental free-space system with which we have demonstrated for the first time the feasibility of quantum key generation overmore » a point-to-point outdoor atmospheric path in daylight. We achieved a transmission distance of 0.5 km, which was limited only by the length of the test range. Our results provide strong evidence that cryptographic key material could be generated on demand between a ground station and a satellite (or between two satellites), allowing a satellite to be securely re-keyed on orbit. We present a feasibility analysis of surface-to-satellite quantum key generation.« less

A multiplexed light-matter interface for fibre-based quantum networks

PubMed Central

Saglamyurek, Erhan; Grimau Puigibert, Marcelli; Zhou, Qiang; Giner, Lambert; Marsili, Francesco; Verma, Varun B.; Woo Nam, Sae; Oesterling, Lee; Nippa, David; Oblak, Daniel; Tittel, Wolfgang

2016-01-01

Processing and distributing quantum information using photons through fibre-optic or free-space links are essential for building future quantum networks. The scalability needed for such networks can be achieved by employing photonic quantum states that are multiplexed into time and/or frequency, and light-matter interfaces that are able to store and process such states with large time-bandwidth product and multimode capacities. Despite important progress in developing such devices, the demonstration of these capabilities using non-classical light remains challenging. Here, employing the atomic frequency comb quantum memory protocol in a cryogenically cooled erbium-doped optical fibre, we report the quantum storage of heralded single photons at a telecom-wavelength (1.53 μm) with a time-bandwidth product approaching 800. Furthermore, we demonstrate frequency-multimode storage and memory-based spectral-temporal photon manipulation. Notably, our demonstrations rely on fully integrated quantum technologies operating at telecommunication wavelengths. With improved storage efficiency, our light-matter interface may become a useful tool in future quantum networks. PMID:27046076

A multiplexed light-matter interface for fibre-based quantum networks.

PubMed

Saglamyurek, Erhan; Grimau Puigibert, Marcelli; Zhou, Qiang; Giner, Lambert; Marsili, Francesco; Verma, Varun B; Woo Nam, Sae; Oesterling, Lee; Nippa, David; Oblak, Daniel; Tittel, Wolfgang

2016-04-05

Processing and distributing quantum information using photons through fibre-optic or free-space links are essential for building future quantum networks. The scalability needed for such networks can be achieved by employing photonic quantum states that are multiplexed into time and/or frequency, and light-matter interfaces that are able to store and process such states with large time-bandwidth product and multimode capacities. Despite important progress in developing such devices, the demonstration of these capabilities using non-classical light remains challenging. Here, employing the atomic frequency comb quantum memory protocol in a cryogenically cooled erbium-doped optical fibre, we report the quantum storage of heralded single photons at a telecom-wavelength (1.53 μm) with a time-bandwidth product approaching 800. Furthermore, we demonstrate frequency-multimode storage and memory-based spectral-temporal photon manipulation. Notably, our demonstrations rely on fully integrated quantum technologies operating at telecommunication wavelengths. With improved storage efficiency, our light-matter interface may become a useful tool in future quantum networks.

Quantum Entanglement in Random Physical States

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Santra, Siddhartha; Zanardi, Paolo

2012-07-01

Most states in the Hilbert space are maximally entangled. This fact has proven useful to investigate—among other things—the foundations of statistical mechanics. Unfortunately, most states in the Hilbert space of a quantum many-body system are not physically accessible. We define physical ensembles of states acting on random factorized states by a circuit of length k of random and independent unitaries with local support. We study the typicality of entanglement by means of the purity of the reduced state. We find that for a time k=O(1), the typical purity obeys the area law. Thus, the upper bounds for area law are actually saturated, on average, with a variance that goes to zero for large systems. Similarly, we prove that by means of local evolution a subsystem of linear dimensions L is typically entangled with a volume law when the time scales with the size of the subsystem. Moreover, we show that for large values of k the reduced state becomes very close to the completely mixed state.

Quantum storage of orbital angular momentum entanglement in an atomic ensemble.

PubMed

Ding, Dong-Sheng; Zhang, Wei; Zhou, Zhi-Yuan; Shi, Shuai; Xiang, Guo-Yong; Wang, Xi-Shi; Jiang, Yun-Kun; Shi, Bao-Sen; Guo, Guang-Can

2015-02-06

Constructing a quantum memory for a photonic entanglement is vital for realizing quantum communication and network. Because of the inherent infinite dimension of orbital angular momentum (OAM), the photon's OAM has the potential for encoding a photon in a high-dimensional space, enabling the realization of high channel capacity communication. Photons entangled in orthogonal polarizations or optical paths had been stored in a different system, but there have been no reports on the storage of a photon pair entangled in OAM space. Here, we report the first experimental realization of storing an entangled OAM state through the Raman protocol in a cold atomic ensemble. We reconstruct the density matrix of an OAM entangled state with a fidelity of 90.3%±0.8% and obtain the Clauser-Horne-Shimony-Holt inequality parameter S of 2.41±0.06 after a programed storage time. All results clearly show the preservation of entanglement during the storage.

Generalized thermalization for integrable system under quantum quench.

PubMed

Muralidharan, Sushruth; Lochan, Kinjalk; Shankaranarayanan, S

2018-01-01

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the generalized Gibbs ensemble description for this infinite-dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve toward the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a generalized Gibbs ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states that would potentially not be described by the generalized Gibbs ensemble description.

Quantum Gibbs Samplers: The Commuting Case

NASA Astrophysics Data System (ADS)

Kastoryano, Michael J.; Brandão, Fernando G. S. L.

2016-06-01

We analyze the problem of preparing quantum Gibbs states of lattice spin Hamiltonians with local and commuting terms on a quantum computer and in nature. Our central result is an equivalence between the behavior of correlations in the Gibbs state and the mixing time of the semigroup which drives the system to thermal equilibrium (the Gibbs sampler). We introduce a framework for analyzing the correlation and mixing properties of quantum Gibbs states and quantum Gibbs samplers, which is rooted in the theory of non-commutative {mathbb{L}_p} spaces. We consider two distinct classes of Gibbs samplers, one of them being the well-studied Davies generator modelling the dynamics of a system due to weak-coupling with a large Markovian environment. We show that their spectral gap is independent of system size if, and only if, a certain strong form of clustering of correlations holds in the Gibbs state. Therefore every Gibbs state of a commuting Hamiltonian that satisfies clustering of correlations in this strong sense can be prepared efficiently on a quantum computer. As concrete applications of our formalism, we show that for every one-dimensional lattice system, or for systems in lattices of any dimension at temperatures above a certain threshold, the Gibbs samplers of commuting Hamiltonians are always gapped, giving an efficient way of preparing the associated Gibbs states on a quantum computer.

Three-body problem in d-dimensional space: Ground state, (quasi)-exact-solvability

NASA Astrophysics Data System (ADS)

Turbiner, Alexander V.; Miller, Willard; Escobar-Ruiz, M. A.

2018-02-01

As a straightforward generalization and extension of our previous paper [A. V. Turbiner et al., "Three-body problem in 3D space: Ground state, (quasi)-exact-solvability," J. Phys. A: Math. Theor. 50, 215201 (2017)], we study the aspects of the quantum and classical dynamics of a 3-body system with equal masses, each body with d degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this type. The quantum (and classical) Hamiltonian for which these states are eigenfunctions is derived. It corresponds to a three-dimensional quantum particle moving in a curved space with special d-dimension-independent metric in a certain d-dependent singular potential, while at d = 1, it elegantly degenerates to a two-dimensional particle moving in flat space. It admits a description in terms of pure geometrical characteristics of the interaction triangle which is defined by the three relative distances. The kinetic energy of the system is d-independent; it has a hidden sl(4, R) Lie (Poisson) algebra structure, alternatively, the hidden algebra h(3) typical for the H3 Calogero model as in the d = 3 case. We find an exactly solvable three-body S3-permutationally invariant, generalized harmonic oscillator-type potential as well as a quasi-exactly solvable three-body sextic polynomial type potential with singular terms. For both models, an extra first order integral exists. For d = 1, the whole family of 3-body (two-dimensional) Calogero-Moser-Sutherland systems as well as the Tremblay-Turbiner-Winternitz model is reproduced. It is shown that a straightforward generalization of the 3-body (rational) Calogero model to d > 1 leads to two primitive quasi-exactly solvable problems. The extension to the case of non-equal masses is straightforward and is briefly discussed.

Quantum annealing with parametrically driven nonlinear oscillators

NASA Astrophysics Data System (ADS)

Puri, Shruti

While progress has been made towards building Ising machines to solve hard combinatorial optimization problems, quantum speedups have so far been elusive. Furthermore, protecting annealers against decoherence and achieving long-range connectivity remain important outstanding challenges. With the hope of overcoming these challenges, I introduce a new paradigm for quantum annealing that relies on continuous variable states. Unlike the more conventional approach based on two-level systems, in this approach, quantum information is encoded in two coherent states that are stabilized by parametrically driving a nonlinear resonator. I will show that a fully connected Ising problem can be mapped onto a network of such resonators, and outline an annealing protocol based on adiabatic quantum computing. During the protocol, the resonators in the network evolve from vacuum to coherent states representing the ground state configuration of the encoded problem. In short, the system evolves between two classical states following non-classical dynamics. As will be supported by numerical results, this new annealing paradigm leads to superior noise resilience. Finally, I will discuss a realistic circuit QED realization of an all-to-all connected network of parametrically driven nonlinear resonators. The continuous variable nature of the states in the large Hilbert space of the resonator provides new opportunities for exploring quantum phase transitions and non-stoquastic dynamics during the annealing schedule.

Excluding joint probabilities from quantum theory

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Danageozian, Arshag

2018-03-01

Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g., via quasiprobabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are noncontextual and are consistent with all constraints expected from a quantum probability. We study two noncommuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts with theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two noncommuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not excluded anymore, but they are still constrained by imprecise probabilities.

The generalized Lyapunov theorem and its application to quantum channels

NASA Astrophysics Data System (ADS)

Burgarth, Daniel; Giovannetti, Vittorio

2007-05-01

We give a simple and physically intuitive necessary and sufficient condition for a map acting on a compact metric space to be mixing (i.e. infinitely many applications of the map transfer any input into a fixed convergency point). This is a generalization of the 'Lyapunov direct method'. First we prove this theorem in topological spaces and for arbitrary continuous maps. Finally we apply our theorem to maps which are relevant in open quantum systems and quantum information, namely quantum channels. In this context, we also discuss the relations between mixing and ergodicity (i.e. the property that there exists only a single input state which is left invariant by a single application of the map) showing that the two are equivalent when the invariant point of the ergodic map is pure.

Complex quantum network geometries: Evolution and phase transitions

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Complex quantum network geometries: Evolution and phase transitions.

PubMed

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, Paul

This paper describes the effects of a complex scalar scaling field on quantum mechanics. The field origin is an extension of the gauge freedom for basis choice in gauge theories to the underlying scalar field. The extension is based on the idea that the value of a number at one space time point does not determine the value at another point. This, combined with the description of mathematical systems as structures of different types, results in the presence of separate number fields and vector spaces as structures, at different space time locations. Complex number structures and vector spaces at eachmore » location are scaled by a complex space time dependent scaling factor. The effect of this scaling factor on several physical and geometric quantities has been described in other work. Here the emphasis is on quantum mechanics of one and two particles, their states and properties. Multiparticle states are also briefly described. The effect shows as a complex, nonunitary, scalar field connection on a fiber bundle description of nonrelativistic quantum mechanics. Here, the lack of physical evidence for the presence of this field so far means that the coupling constant of this field to fermions is very small. It also means that the gradient of the field must be very small in a local region of cosmological space and time. Outside this region, there are no restrictions on the field gradient.« less

Avoiding irreversible dynamics in quantum systems

NASA Astrophysics Data System (ADS)

Karasik, Raisa Iosifovna

2009-10-01

Devices that exploit laws of quantum physics offer revolutionary advances in computation and communication. However, building such devices presents an enormous challenge, since it would require technologies that go far beyond current capabilities. One of the main obstacles to building a quantum computer and devices needed for quantum communication is decoherence or noise that originates from the interaction between a quantum system and its environment, and which leads to the destruction of the fragile quantum information. Encoding into decoherence-free subspaces (DFS) provides an important strategy for combating decoherence effects in quantum systems and constitutes the focus of my dissertation. The theory of DFS relies on the existence of certain symmetries in the decoherence process, which allow some states of a quantum system to be completely decoupled from the environment and thus to experience no decoherence. In this thesis I describe various approaches to DFS that are developed in the current literature. Although the general idea behind various approaches to DFS is the same, I show that different mathematical definitions of DFS actually have different physical meaning. I provide a rigorous definition of DFS for every approach, explaining its physical meaning and relation to other definitions. I also examine the theory of DFS for Markovian systems. These are systems for which the environment has no memory, i.e., any change in the environment affects the quantum system instantaneously. Examples of such systems include many systems in quantum optics that have been proposed for implementation of a quantum computer, such as atomic and molecular gases, trapped ions, and quantum dots. Here I develop a rigorous theory that provides necessary and sufficient conditions for the existence of DFS. This theory allows us to identify a special new class of DFS that was not known before. Under particular circumstances, dynamics of a quantum system can connive together with the interactions between the system and its environment in a special way to reduce decoherence. This property is used to discover new DFS that rely on rather counterintuitive phenomenon, which I call an "incoherent generation of coherences." I also provide examples of physical systems that support such states. These DFS can be used to suppress & coherence, but may not be sufficient for performing full quantum computation. I also explore the possibility of physically generating the DFS that are useful for quantum computation. For quantum computation we need to preserve at least two quantum states to encode the quantum analogue of classical bits. Here I aim to generate DFS in a system composed from a large collection of atoms or molecules and I need to determine how one should position atoms or molecules in 3D space so that the overall system possesses a DFS with at least two states (i.e., non-trivial DFS). I show that for many Markovian systems, non-trivial DFS can exist only when particles are located in exactly the same position in space. This, of course, is not possible in the real world. For these systems, I also show that states in DFS are states with infinite lifetime. However, for all practical applications we just need long-lived states. Thus in reality, we do just need to bring quantum particles close together to generate an imperfect DFS, i.e. a collection of long-lived states. This can be achieved, for example, for atoms within a single molecule.

The Gtr-Model a Universal Framework for Quantum-Like Measurements

NASA Astrophysics Data System (ADS)

Aerts, Diederik; Bianchi, Massimiliano Sassoli De

We present a very general geometrico-dynamical description of physical or more abstract entities, called the general tension-reduction (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the model is the hypothesis that indeterminism manifests as a consequence of unavoidable uctuations in the experimental context, in accordance with the hidden-measurements interpretation of quantum mechanics. When the structure of the state space is Hilbertian, and measurements are of the universal kind, i.e., are the result of an average over all possible ways of selecting an outcome, the GTR-model provides the same predictions of the Born rule, and therefore provides a natural completed version of quantum mechanics. However, when the structure of the state space is non-Hilbertian and/or not all possible ways of selecting an outcome are available to be actualized, the predictions of the model generally differ from the quantum ones, especially when sequential measurements are considered. Some paradigmatic examples will be discussed, taken from physics and human cognition. Particular attention will be given to some known psychological effects, like question order effects and response replicability, which we show are able to generate non-Hilbertian statistics. We also suggest a realistic interpretation of the GTR-model, when applied to human cognition and decision, which we think could become the generally adopted interpretative framework in quantum cognition research.

Superdense teleportation using hyperentangled photons

PubMed Central

Graham, Trent M.; Bernstein, Herbert J.; Wei, Tzu-Chieh; Junge, Marius; Kwiat, Paul G

2015-01-01

Transmitting quantum information between two remote parties is a requirement for many quantum applications; however, direct transmission of states is often impossible because of noise and loss in the communication channel. Entanglement-enhanced state communication can be used to avoid this issue, but current techniques require extensive experimental resources to transmit large quantum states deterministically. To reduce these resource requirements, we use photon pairs hyperentangled in polarization and orbital angular momentum to implement superdense teleportation, which can communicate a specific class of single-photon ququarts. We achieve an average fidelity of 87.0(1)%, almost twice the classical limit of 44% with reduced experimental resources than traditional techniques. We conclude by discussing the information content of this constrained set of states and demonstrate that this set has an exponentially larger state space volume than the lower-dimensional general states with the same number of state parameters. PMID:26018201

Shell Filling and Magnetic Anisotropy In A Few Hole Silicon Metal-Oxide-Semiconductor Quantum Dot

NASA Astrophysics Data System (ADS)

Hamilton, Alex; Li., R.; Liles, S. D.; Yang, C. H.; Hudson, F. E.; Veldhorst, M. E.; Dzurak, A. S.

There is growing interest in hole spin states in group IV materials for quantum information applications. The near-absence of nuclear spins in group IV crystals promises long spin coherence times, while the strong spin-orbit interaction of the hole states provides fast electrical spin manipulation methods. However, the level-mixing and magnetic field dependence of the p-orbital hole states is non-trivial in nanostructures, and is not as well understood as for electron systems. In this work, we study the hole states in a gate-defined silicon metal-oxide-semiconductor quantum dot. Using an adjacent charge sensor, we monitor quantum dot orbital level spacing down to the very last hole, and find the standard two-dimensional (2D) circular dot shell filling structure. We can change the shell filling sequence by applying an out-of-plane magnetic field. However, when the field is applied in-plane, the shell filling is not changed. This magnetic field anisotropy suggests that the confined hole states are Ising-like.

Toward quantum plasmonic networks

DOE PAGES

Holtfrerich, M. W.; Dowran, M.; Davidson, R.; ...

2016-08-30

Here, we demonstrate the transduction of macroscopic quantum entanglement by independent, distant plasmonic structures embedded in separate thin silver films. In particular, we show that the plasmon-mediated transmission through each film conserves spatially dependent, entangled quantum images, opening the door for the implementation of parallel quantum protocols, super-resolution imaging, and quantum plasmonic sensing geometries at the nanoscale level. The conservation of quantum information by the transduction process shows that continuous variable multi-mode entanglement is momentarily transferred from entangled beams of light to the space-like separated, completely independent plasmonic structures, thus providing a first important step toward establishing a multichannel quantummore » network across separate solid-state substrates.« less

Yang-Mills matrix mechanics and quantum phases

NASA Astrophysics Data System (ADS)

Pandey, Mahul; Vaidya, Sachindeo

The SU(2) Yang-Mills matrix model coupled to fundamental fermions is studied in the adiabatic limit, and quantum critical behavior is seen at special corners of the gauge field configuration space. The quantum scalar potential for the gauge field induced by the fermions diverges at the corners, and is intimately related to points of enhanced degeneracy of the fermionic Hamiltonian. This in turn leads to superselection sectors in the Hilbert space of the gauge field, the ground states in different sectors being orthogonal to each other. The SU(2) Yang-Mills matrix model coupled to two Weyl fermions has three quantum phases. When coupled to a massless Dirac fermion, the number of quantum phases is four. One of these phases is the color-spin locked phase. This paper is an extended version of the lectures given by the second author (SV) at the International Workshop on Quantum Physics: Foundations and Applications, Bangalore, in February 2016, and is based on [1].

Free-Space Quantum Signatures Using Heterodyne Measurements

NASA Astrophysics Data System (ADS)

Croal, Callum; Peuntinger, Christian; Heim, Bettina; Khan, Imran; Marquardt, Christoph; Leuchs, Gerd; Wallden, Petros; Andersson, Erika; Korolkova, Natalia

2016-09-01

Digital signatures guarantee the authorship of electronic communications. Currently used "classical" signature schemes rely on unproven computational assumptions for security, while quantum signatures rely only on the laws of quantum mechanics to sign a classical message. Previous quantum signature schemes have used unambiguous quantum measurements. Such measurements, however, sometimes give no result, reducing the efficiency of the protocol. Here, we instead use heterodyne detection, which always gives a result, although there is always some uncertainty. We experimentally demonstrate feasibility in a real environment by distributing signature states through a noisy 1.6 km free-space channel. Our results show that continuous-variable heterodyne detection improves the signature rate for this type of scheme and therefore represents an interesting direction in the search for practical quantum signature schemes. For transmission values ranging from 100% to 10%, but otherwise assuming an ideal implementation with no other imperfections, the signature length is shorter by a factor of 2 to 10. As compared with previous relevant experimental realizations, the signature length in this implementation is several orders of magnitude shorter.

Quantum key distribution without the wavefunction

NASA Astrophysics Data System (ADS)

Niestegge, Gerd

A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and abstract access than commonly thought. The results include some generalizations of the Hilbert space version of quantum key distribution, but are based upon a general nonclassical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution; this is a purely algebraic property of the quantum logic and represents the transition probability between the outcomes of two consecutive quantum measurements.

Monte Carlo wave-function description of losses in a one-dimensional Bose gas and cooling to the ground state by quantum feedback

NASA Astrophysics Data System (ADS)

Schemmer, M.; Johnson, A.; Photopoulos, R.; Bouchoule, I.

2017-04-01

The effect of atom losses on a homogeneous one-dimensional Bose gas lying within the quasicondensate regime is investigated using a Monte Carlo wave-function approach. The evolution of the system is calculated, conditioned by the loss sequence, namely, the times of individual losses and the position of the removed atoms. We describe the gas within the linearized Bogoliubov approach. For each mode, we find that, for a given quantum trajectory, the state of the system converges towards a coherent state, i.e., the ground state, displaced in phase space. We show that, provided losses are recorded with a temporal and spatially resolved detector, quantum feedback can be implemented and cooling to the ground state of one or several modes can be realized.

Hyperspherical Slater determinant approach to few-body fractional quantum Hall states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Bin, E-mail: yanbin@purdue.edu; Wooten, Rachel E.; Daily, Kevin M.

2017-05-15

In a recent study (Daily et al., 2015), a hyperspherical approach has been developed to study few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion problems in the quantum Hall region, as well as the study of inter-Landau level collective excitations (Rittenhouse et al., 2016; Wooten et al., 2016). However, the hyperspherical method as it is normally implemented requires a subsidiary (anti-)symmetrization process, which limits its computational effectiveness. The present work overcomes these difficulties and extends the power of this method by implementing a representation of the hyperspherical many-body basismore » space in terms of Slater determinants of single particle eigenfunctions. A clear connection between the hyperspherical representation and the conventional single particle picture is presented, along with a compact operator representation of the theoretical framework. - Highlights: • A hyperspherical method has been implemented to study the quantum Hall effect. • The hyperspherical many-body basis space is represented with Slater determinants. • Example numerical studies of the 4- and 8-electron systems are presented.« less

Higher-Order Statistical Correlations and Mutual Information Among Particles in a Quantum Well

NASA Astrophysics Data System (ADS)

Yépez, V. S.; Sagar, R. P.; Laguna, H. G.

2017-12-01

The influence of wave function symmetry on statistical correlation is studied for the case of three non-interacting spin-free quantum particles in a unidimensional box, in position and in momentum space. Higher-order statistical correlations occurring among the three particles in this quantum system is quantified via higher-order mutual information and compared to the correlation between pairs of variables in this model, and to the correlation in the two-particle system. The results for the higher-order mutual information show that there are states where the symmetric wave functions are more correlated than the antisymmetric ones with same quantum numbers. This holds in position as well as in momentum space. This behavior is opposite to that observed for the correlation between pairs of variables in this model, and the two-particle system, where the antisymmetric wave functions are in general more correlated. These results are also consistent with those observed in a system of three uncoupled oscillators. The use of higher-order mutual information as a correlation measure, is monitored and examined by considering a superposition of states or systems with two Slater determinants.

Establishing and storing of deterministic quantum entanglement among three distant atomic ensembles.

PubMed

Yan, Zhihui; Wu, Liang; Jia, Xiaojun; Liu, Yanhong; Deng, Ruijie; Li, Shujing; Wang, Hai; Xie, Changde; Peng, Kunchi

2017-09-28

It is crucial for the physical realization of quantum information networks to first establish entanglement among multiple space-separated quantum memories and then, at a user-controlled moment, to transfer the stored entanglement to quantum channels for distribution and conveyance of information. Here we present an experimental demonstration on generation, storage, and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. The off-line prepared multipartite entanglement of optical modes is mapped into three distant atomic ensembles to establish entanglement of atomic spin waves via electromagnetically induced transparency light-matter interaction. Then the stored atomic entanglement is transferred into a tripartite quadrature entangled state of light, which is space-separated and can be dynamically allocated to three quantum channels for conveying quantum information. The existence of entanglement among three released optical modes verifies that the system has the capacity to preserve multipartite entanglement. The presented protocol can be directly extended to larger quantum networks with more nodes.Continuous-variable encoding is a promising approach for quantum information and communication networks. Here, the authors show how to map entanglement from three spatial optical modes to three separated atomic samples via electromagnetically induced transparency, releasing it later on demand.

Six-State Quantum Key Distribution Using Photons with Orbital Angular Momentum

NASA Astrophysics Data System (ADS)

Li, Jun-Lin; Wang, Chuan

2010-11-01

A new implementation of high-dimensional quantum key distribution (QKD) protocol is discussed. Using three mutual unbiased bases, we present a d-level six-state QKD protocol that exploits the orbital angular momentum with the spatial mode of the light beam. The protocol shows that the feature of a high capacity since keys are encoded using photon modes in d-level Hilbert space. The devices for state preparation and measurement are also discussed. This protocol has high security and the alignment of shared reference frames is not needed between sender and receiver.

Entanglement Entropy of the Six-Dimensional Horowitz-Strominger Black Hole

NASA Astrophysics Data System (ADS)

Li, Huai-Fan; Zhang, Sheng-Li; Wu, Yue-Qin; Ren, Zhao

By using the entanglement entropy method, the statistical entropy of the Bose and Fermi fields in a thin film is calculated and the Bekenstein-Hawking entropy of six-dimensional Horowitz-Strominger black hole is obtained. Here, the Bose and Fermi fields are entangled with the quantum states in six-dimensional Horowitz-Strominger black hole and the fields are outside of the horizon. The divergence of brick-wall model is avoided without any cutoff by the new equation of state density obtained with the generalized uncertainty principle. The calculation implies that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole. The black hole entropy is a quantum effect. It is an intrinsic characteristic of space-time. The ultraviolet cutoff in the brick-wall model is unreasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. Using the quantum statistical method, we directly calculate the partition function of the Bose and Fermi fields under the background of the six-dimensional black hole. The difficulty in solving the wave equations of various particles is overcome.

Accurate and Robust Unitary Transformations of a High-Dimensional Quantum System

NASA Astrophysics Data System (ADS)

Anderson, B. E.; Sosa-Martinez, H.; Riofrío, C. A.; Deutsch, Ivan H.; Jessen, Poul S.

2015-06-01

Unitary transformations are the most general input-output maps available in closed quantum systems. Good control protocols have been developed for qubits, but questions remain about the use of optimal control theory to design unitary maps in high-dimensional Hilbert spaces, and about the feasibility of their robust implementation in the laboratory. Here we design and implement unitary maps in a 16-dimensional Hilbert space associated with the 6 S1 /2 ground state of 133Cs, achieving fidelities >0.98 with built-in robustness to static and dynamic perturbations. Our work has relevance for quantum information processing and provides a template for similar advances on other physical platforms.

Phase operator problem and macroscopic extension of quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ozawa, M.

1997-06-01

To find the Hermitian phase operator of a single-mode electromagnetic field in quantum mechanics, the Schr{umlt o}dinger representation is extended to a larger Hilbert space augmented by states with infinite excitation by nonstandard analysis. The Hermitian phase operator is shown to exist on the extended Hilbert space. This operator is naturally considered as the controversial limit of the approximate phase operators on finite dimensional spaces proposed by Pegg and Barnett. The spectral measure of this operator is a Naimark extension of the optimal probability operator-valued measure for the phase parameter found by Helstrom. Eventually, the two promising approaches to themore » statistics of the phase in quantum mechanics are synthesized by means of the Hermitian phase operator in the macroscopic extension of the Schr{umlt o}dinger representation. {copyright} 1997 Academic Press, Inc.« less

Quantum epistemology from subquantum ontology: Quantum mechanics from theory of classical random fields

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2017-02-01

The scientific methodology based on two descriptive levels, ontic (reality as it is) and epistemic (observational), is briefly presented. Following Schrödinger, we point to the possible gap between these two descriptions. Our main aim is to show that, although ontic entities may be unaccessible for observations, they can be useful for clarification of the physical nature of operational epistemic entities. We illustrate this thesis by the concrete example: starting with the concrete ontic model preceding quantum mechanics (the latter is treated as an epistemic model), namely, prequantum classical statistical field theory (PCSFT), we propose the natural physical interpretation for the basic quantum mechanical entity-the quantum state ("wave function"). The correspondence PCSFT ↦ QM is not straightforward, it couples the covariance operators of classical (prequantum) random fields with the quantum density operators. We use this correspondence to clarify the physical meaning of the pure quantum state and the superposition principle-by using the formalism of classical field correlations. In classical mechanics the phase space description can be considered as the ontic description, here states are given by points λ =(x , p) of phase space. The dynamics of the ontic state is given by the system of Hamiltonian equations.We can also consider probability distributions on the phase space (or equivalently random variables valued in it). We call them probabilistic ontic states. Dynamics of probabilistic ontic states is given by the Liouville equation.In classical physics we can (at least in principle) measure both the coordinate and momentum and hence ontic states can be treated as epistemic states as well (or it is better to say that here epistemic states can be treated as ontic states). Probabilistic ontic states represent probabilities for outcomes of joint measurement of position and momentum.However, this was a very special, although very important, example of description of physical phenomena. In general there are no reasons to expect that properties of ontic states are approachable through our measurements. There is a gap between ontic and epistemic descriptions, cf. also with 't Hooft [49,50] and G G. Groessing et al. [51]. In general the presence of such a gap also implies unapproachability of the probabilistic ontic states, i.e., probability distributions on the space of ontic states. De Broglie [28] called such probability distributions hidden probabilities and distinguished them sharply from probability distributions of measurements outcomes, see also Lochak [29]. (The latter distributions are described by the quantum formalism.)This ontic-epistemic approach based on the combination of two descriptive levels for natural phenomena is closely related to the old Bild conception which was originated in the works of Hertz. Later it was heavily explored by Schrödinger in the quantum domain, see, e.g., [8,11] for detailed analysis. According to Hertz one cannot expect to construct a complete theoretical model based explicitly on observable quantities. The complete theoretical model can contain quantities which are unapproachable for external measurement inspection. For example, Hertz by trying to create a mechanical model for Maxwell's electromagnetism invented hidden masses. The main distinguishing property of a theoretical model (in contrast to an observational model) is the continuity of description, i.e., the absence of gaps in description. From this viewpoint, the quantum mechanical description is not continuous: there is a gap between premeasurement dynamics and the measurement outcome. QM cannot say anything what happens in the process of measurement, this is the well known measurement problem of QM [32], cf. [52,53]. Continuity of description is closely related to causality. However, here we cannot go in more detail, see [8,11].The important question is about interrelation between two levels of description, ontic-epistemic (or theoretical-observational). In the introduction we have already cited Schrödinger who emphasized the possible complexity of this interrelation. In particular, in general there is no reason to expect a straightforward coupling of the form, cf. [9,10]:

Molecular engineering with artificial atoms: designing a material platform for scalable quantum spintronics and photonics

NASA Astrophysics Data System (ADS)

Doty, Matthew F.; Ma, Xiangyu; Zide, Joshua M. O.; Bryant, Garnett W.

2017-09-01

Self-assembled InAs Quantum Dots (QDs) are often called "artificial atoms" and have long been of interest as components of quantum photonic and spintronic devices. Although there has been substantial progress in demonstrating optical control of both single spins confined to a single QD and entanglement between two separated QDs, the path toward scalable quantum photonic devices based on spins remains challenging. Quantum Dot Molecules, which consist of two closely-spaced InAs QDs, have unique properties that can be engineered with the solid state analog of molecular engineering in which the composition, size, and location of both the QDs and the intervening barrier are controlled during growth. Moreover, applied electric, magnetic, and optical fields can be used to modulate, in situ, both the spin and optical properties of the molecular states. We describe how the unique photonic properties of engineered Quantum Dot Molecules can be leveraged to overcome long-standing challenges to the creation of scalable quantum devices that manipulate single spins via photonics.

Radio frequency measurements of tunnel couplings and singlet–triplet spin states in Si:P quantum dots

PubMed Central

House, M. G.; Kobayashi, T.; Weber, B.; Hile, S. J.; Watson, T. F.; van der Heijden, J.; Rogge, S.; Simmons, M. Y.

2015-01-01

Spin states of the electrons and nuclei of phosphorus donors in silicon are strong candidates for quantum information processing applications given their excellent coherence times. Designing a scalable donor-based quantum computer will require both knowledge of the relationship between device geometry and electron tunnel couplings, and a spin readout strategy that uses minimal physical space in the device. Here we use radio frequency reflectometry to measure singlet–triplet states of a few-donor Si:P double quantum dot and demonstrate that the exchange energy can be tuned by at least two orders of magnitude, from 20 μeV to 8 meV. We measure dot–lead tunnel rates by analysis of the reflected signal and show that they change from 100 MHz to 22 GHz as the number of electrons on a quantum dot is increased from 1 to 4. These techniques present an approach for characterizing, operating and engineering scalable qubit devices based on donors in silicon. PMID:26548556

Probing free-space quantum channels with laboratory-based experiments

NASA Astrophysics Data System (ADS)

Bohmann, M.; Kruse, R.; Sperling, J.; Silberhorn, C.; Vogel, W.

2017-06-01

Atmospheric channels are a promising candidate to establish secure quantum communication on a global scale. However, due to their turbulent nature, it is crucial to understand the impact of the atmosphere on the quantum properties of light and examine it experimentally. In this paper, we introduce a method to probe atmospheric free-space links with quantum light on a laboratory scale. In contrast to previous works, our method models arbitrary intensity losses caused by turbulence to emulate general atmospheric conditions. This allows us to characterize turbulent quantum channels in a well-controlled manner. To implement this technique, we perform a series of measurements with different constant attenuations and simulate the fluctuating losses by combining the obtained data. We directly test the proposed method with an on-chip source of nonclassical light and a time-bin-multiplexed detection system. With the obtained data, we characterize the nonclassicality of the generated states for different atmospheric noise models and analyze a postselection protocol. This general technique in atmospheric quantum optics allows for studying turbulent quantum channels and predicting their properties for future applications.

Entanglement as minimal discord over state extensions

NASA Astrophysics Data System (ADS)

Luo, Shunlong

2016-09-01

The characterization and quantification of quantum correlations, which play an instrumental role in exploring and exploiting the quantum world, have been extensively and intensively studied in the past few decades. Of special prominence and significance are the concepts of entanglement and discord, which are usually regarded as very distinctive quantum correlations, with the latter going beyond the former. In this work we establish a direct and natural link between entanglement and discord via state extensions and reveal that entanglement is actually the intrinsic discord, by which we mean that entanglement is the irreducible residue of discord viewed from ambient spaces. Our approach, taking into account the contextuality of a quantum state and being of a global nature, stands in sharp contrast to the local operations and classical communication paradigm of entanglement, which focuses on the state itself via a local approach. Furthermore, we introduce a figure of merit which, on the one hand, captures the essence of entanglement, i.e., nonlocality and quantumness of correlations, and, on the other hand, leads to a quantitative decomposition of total correlations into classical correlations, dissonance, and entanglement. This demystifies the meaning of entanglement from the perspective of quantum measurements and provides a unified framework for the interplay of various correlations in terms of quantum measurements and mutual information.

Entanglement spectroscopy on a quantum computer

NASA Astrophysics Data System (ADS)

Johri, Sonika; Steiger, Damian S.; Troyer, Matthias

2017-11-01

We present a quantum algorithm to compute the entanglement spectrum of arbitrary quantum states. The interesting universal part of the entanglement spectrum is typically contained in the largest eigenvalues of the density matrix which can be obtained from the lower Renyi entropies through the Newton-Girard method. Obtaining the p largest eigenvalues (λ1>λ2⋯>λp ) requires a parallel circuit depth of O [p (λ1/λp) p] and O [p log(N )] qubits where up to p copies of the quantum state defined on a Hilbert space of size N are needed as the input. We validate this procedure for the entanglement spectrum of the topologically ordered Laughlin wave function corresponding to the quantum Hall state at filling factor ν =1 /3 . Our scaling analysis exposes the tradeoffs between time and number of qubits for obtaining the entanglement spectrum in the thermodynamic limit using finite-size digital quantum computers. We also illustrate the utility of the second Renyi entropy in predicting a topological phase transition and in extracting the localization length in a many-body localized system.

E-Invariant Quantized Motion of Valence Quarks

NASA Astrophysics Data System (ADS)

Kreymer, E. L.

2018-06-01

In sub-proton space wave processes are impossible. The analog of the Klein-Gordon equation in sub-proton space is elliptical and describes a stationary system with a constant number of particles. For dynamical processes, separation of variables is used and in each quantum of motion of the quark two states are distinguished: a localization state and a translation state with infinite velocity. Alternation of these states describes the motion of a quark. The mathematical expectations of the lifetimes of the localization states and the spatial extents of the translation states for a free quark and for a quark in a centrally symmetric potential are found. The action after one quantum of motion is equal to the Planck constant. The one-sided Laplace transform is used to determine the Green's function. Use of path integrals shows that the quantized trajectory of a quark is a broken line enveloping the classical trajectory of oscillation of the quark. Comparison of the calculated electric charge distribution in a proton with its experimental value gives satisfactory results. A hypothesis is formulated, according to which the three Grand Geometries of space correspond to the three main interactions of elementary particles.

Twenty Seven Years of Quantum Cryptography!

NASA Astrophysics Data System (ADS)

Hughes, Richard

2011-03-01

One of the fundamental goals of cryptographic research is to minimize the assumptions underlying the protocols that enable secure communications between pairs or groups of users. In 1984, building on earlier research by Stephen Wiesner, Charles Bennett and Gilles Brassard showed how quantum physics could be harnessed to provide information-theoretic security for protocols such as the distribution of cryptographic keys, which enables two parties to secure their conventional communications. Bennett and Brassard and colleagues performed a proof-of-principle quantum key distribution (QKD) experiment with single-photon quantum state transmission over a 32-cm air path in 1991. This seminal experiment led other researchers to explore QKD in optical fibers and over line-of-sight outdoor atmospheric paths (``free-space''), resulting in dramatic increases in range, bit rate and security. These advances have been enabled by improvements in sources and single-photon detectors. Also in 1991 Artur Ekert showed how the security of QKD could be related to quantum entanglement. This insight led to a deeper understanding and proof of QKD security with practical sources and detectors in the presence of transmission loss and channel noise. Today, QKD has been implemented over ranges much greater than 100km in both fiber and free-space, multi-node network testbeds have been demonstrated, and satellite-based QKD is under study in several countries. ``Quantum hacking'' researchers have shown the importance of extending security considerations to the classical devices that produce and detect the photon quantum states. New quantum cryptographic protocols such as secure identification have been proposed, and others such as quantum secret splitting have been demonstrated. It is now possible to envision quantum cryptography providing a more secure alternative to present-day cryptographic methods for many secure communications functions. My talk will survey these remarkable developments.

Time Scale for Adiabaticity Breakdown in Driven Many-Body Systems and Orthogonality Catastrophe

NASA Astrophysics Data System (ADS)

Lychkovskiy, Oleg; Gamayun, Oleksandr; Cheianov, Vadim

2017-11-01

The adiabatic theorem is a fundamental result in quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time slowly enough. The theorem has an impressive record of applications ranging from foundations of quantum field theory to computational molecular dynamics. In light of this success it is remarkable that a practicable quantitative understanding of what "slowly enough" means is limited to a modest set of systems mostly having a small Hilbert space. Here we show how this gap can be bridged for a broad natural class of physical systems, namely, many-body systems where a small move in the parameter space induces an orthogonality catastrophe. In this class, the conditions for adiabaticity are derived from the scaling properties of the parameter-dependent ground state without a reference to the excitation spectrum. This finding constitutes a major simplification of a complex problem, which otherwise requires solving nonautonomous time evolution in a large Hilbert space.

Quantum capacity of quantum black holes

NASA Astrophysics Data System (ADS)

Adami, Chris; Bradler, Kamil

2014-03-01

The fate of quantum entanglement interacting with a black hole has been an enduring mystery, not the least because standard curved space field theory does not address the interaction of black holes with matter. We discuss an effective Hamiltonian of matter interacting with a black hole that has a precise analogue in quantum optics and correctly reproduces both spontaneous and stimulated Hawking radiation with grey-body factors. We calculate the quantum capacity of this channel in the limit of perfect absorption, as well as in the limit of a perfectly reflecting black hole (a white hole). We find that the white hole is an optimal quantum cloner, and is isomorphic to the Unruh channel with positive quantum capacity. The complementary channel (across the horizon) is entanglement-breaking with zero capacity, avoiding a violation of the quantum no-cloning theorem. The black hole channel on the contrary has vanishing capacity, while its complement has positive capacity instead. Thus, quantum states can be reconstructed faithfully behind the black hole horizon, but not outside. This work sheds new light on black hole complementarity because it shows that black holes can both reflect and absorb quantum states without violating the no-cloning theorem, and makes quantum firewalls obsolete.

Geometric Defects in Quantum Hall States

NASA Astrophysics Data System (ADS)

Gromov, Andrey

I will describe a geometric analogue of Laughlin quasiholes in fractional quantum Hall (FQH) states. These ``quasiholes'' are generated by an insertion of quantized fluxes of curvature - which can be modeled by branch points of a certain Riemann surface - and, consequently, are related to genons. Unlike quasiholes, the genons are not excitations, but extrinsic defects. Fusion of genons describes the response of an FQH state to a process that changes (effective) topology of the physical space. These defects are abelian for IQH states and non-abelian for FQH states. I will explain how to calculate an electric charge, geometric spin and adiabatic mutual statistics of the these defects. Leo Kadanoff Fellowship.

Universal quantum computation with temporal-mode bilayer square lattices

NASA Astrophysics Data System (ADS)

Alexander, Rafael N.; Yokoyama, Shota; Furusawa, Akira; Menicucci, Nicolas C.

2018-03-01

We propose an experimental design for universal continuous-variable quantum computation that incorporates recent innovations in linear-optics-based continuous-variable cluster state generation and cubic-phase gate teleportation. The first ingredient is a protocol for generating the bilayer-square-lattice cluster state (a universal resource state) with temporal modes of light. With this state, measurement-based implementation of Gaussian unitary gates requires only homodyne detection. Second, we describe a measurement device that implements an adaptive cubic-phase gate, up to a random phase-space displacement. It requires a two-step sequence of homodyne measurements and consumes a (non-Gaussian) cubic-phase state.

Unambiguous discrimination between linearly dependent equidistant states with multiple copies

NASA Astrophysics Data System (ADS)

Zhang, Wen-Hai; Ren, Gang

2018-07-01

Linearly independent quantum states can be unambiguously discriminated, but linearly dependent ones cannot. For linearly dependent quantum states, however, if C copies of the single states are available, then they may form linearly independent states, and can be unambiguously discriminated. We consider unambiguous discrimination among N = D + 1 linearly dependent states given that C copies are available and that the single copies span a D-dimensional space with equal inner products. The maximum unambiguous discrimination probability is derived for all C with equal a priori probabilities. For this classification of the linearly dependent equidistant states, our result shows that if C is even then adding a further copy fails to increase the maximum discrimination probability.

Current correlations for the transport of interacting electrons through parallel quantum dots in a photon cavity

NASA Astrophysics Data System (ADS)

Gudmundsson, Vidar; Abdullah, Nzar Rauf; Sitek, Anna; Goan, Hsi-Sheng; Tang, Chi-Shung; Manolescu, Andrei

2018-06-01

We calculate the current correlations for the steady-state electron transport through multi-level parallel quantum dots embedded in a short quantum wire, that is placed in a non-perfect photon cavity. We account for the electron-electron Coulomb interaction, and the para- and diamagnetic electron-photon interactions with a stepwise scheme of configuration interactions and truncation of the many-body Fock spaces. In the spectral density of the temporal current-current correlations we identify all the transitions, radiative and non-radiative, active in the system in order to maintain the steady state. We observe strong signs of two types of Rabi oscillations.

Metrologically useful states of spin-1 Bose condensates with macroscopic magnetization

NASA Astrophysics Data System (ADS)

Kajtoch, Dariusz; Pawłowski, Krzysztof; Witkowska, Emilia

2018-02-01

We study theoretically the usefulness of spin-1 Bose condensates with macroscopic magnetization in a homogeneous magnetic field for quantum metrology. We demonstrate Heisenberg scaling of the quantum Fisher information for states in thermal equilibrium. The scaling applies to both antiferromagnetic and ferromagnetic interactions. The effect preserves as long as fluctuations of magnetization are sufficiently small. Scaling of the quantum Fisher information with the total particle number is derived within the mean-field approach in the zero-temperature limit and exactly in the high-magnetic-field limit for any temperature. The precision gain is intuitively explained owing to subtle features of the quasidistribution function in the phase space.

Quasiparticle-continuum level repulsion in a quantum magnet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Plumb, K. W.; Hwang, Kyusung; Qiu, Y.

2015-11-30

When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided. Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids. But, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum. Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. Here,more » we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states, in our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu 2PO 6.« less

On the nonlocal predictions of quantum optics

NASA Technical Reports Server (NTRS)

Marshall, Trevor W.; Santos, Emilio; Vidiella-Barranco, Antonio

1994-01-01

We give a definition of locality in quantum optics based upon Bell's work, and show that locality has been violated in no experiment performed up to now. We argue that the interpretation of the Wigner function as a probability density gives a very attractive local realistic picture of quantum optics provided that this function is nonnegative. We conjecture that this is the case for all states which can be realized in the laboratory. In particular, we believe that the usual representation of 'single photon states' by a Fock state of the Hilbert space is not correct and that a more physical, although less simple mathematically, representation involves density matrices. We study in some detail the experiment showing anticorrelation after a beam splitter and prove that it naturally involves a positive Wigner function. Our (quantum) predictions for this experiment disagree with the ones reported in the literature.

Incomplete Detection of Nonclassical Phase-Space Distributions

NASA Astrophysics Data System (ADS)

Bohmann, M.; Tiedau, J.; Bartley, T.; Sperling, J.; Silberhorn, C.; Vogel, W.

2018-02-01

We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.

Quantum correlations of lights in macroscopic environments

NASA Astrophysics Data System (ADS)

Sua, Yong Meng

This dissertation presents a detailed study in exploring quantum correlations of lights in macroscopic environments. We have explored quantum correlations of single photons, weak coherent states, and polarization-correlated/polarization-entangled photons in macroscopic environments. These included macroscopic mirrors, macroscopic photon number, spatially separated observers, noisy photons source and propagation medium with loss or disturbances. We proposed a measurement scheme for observing quantum correlations and entanglement in the spatial properties of two macroscopic mirrors using single photons spatial compass state. We explored the phase space distribution features of spatial compass states, such as chessboard pattern by using the Wigner function. The displacement and tilt correlations of the two mirrors were manifested through the propensities of the compass states. This technique can be used to extract Einstein-Podolsky-Rosen correlations (EPR) of the two mirrors. We then formulated the discrete-like property of the propensity P b(m,n), which can be used to explore environmental perturbed quantum jumps of the EPR correlations in phase space. With single photons spatial compass state, the variances in position and momentum are much smaller than standard quantum limit when using a Gaussian TEM 00 beam. We observed intrinsic quantum correlations of weak coherent states between two parties through balanced homodyne detection. Our scheme can be used as a supplement to decoy-state BB84 protocol and differential phase-shift QKD protocol. We prepared four types of bipartite correlations +/- cos2(theta1 +/- theta 2) that shared between two parties. We also demonstrated bits correlations between two parties separated by 10 km optical fiber. The bits information will be protected by the large quantum phase fluctuation of weak coherent states, adding another physical layer of security to these protocols for quantum key distribution. Using 10 m of highly nonlinear fiber (HNLF) at 77 K, we observed coincidence to accidental-coincidence ratio of 130+/-5 for correlated photon-pair and Two-Photon Interference visibility >98% entangled photon-pair. We also verified the non-local behavior of polarization-entangled photon pair by violating Clauser-Horne-Shimony-Holt Bell's inequality by more than 12 standard deviations. With the HNLF at 300 K (77 K), photon-pair production rate about factor 3(2) higher than a 300 m dispersion-shifted fiber is observed. Then, we studied quantum correlation and interference of photon-pairs; with one photon of the photon-pair experiencing multiple scattering in a random medium. We observed that depolarization noise photon in multiple scattering degrading the purity of photon-pair, and the existence of Raman noise photon in a photon-pair source will contribute to the depolarization affect. We found that quantum correlation of polarization-entangled photon-pair is better preserved than polarization-correlated photon-pair as one photon of the photon-pair scattered through a random medium. Our findings showed that high purity polarization-entangled photon-pair is better candidate for long distance quantum key distribution.

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

DOE PAGES

Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; ...

2015-06-11

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as dualsmore » of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.« less

Continuous-variable entanglement distillation of non-Gaussian mixed states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dong Ruifang; Lassen, Mikael; Department of Physics, Technical University of Denmark, Building 309, DK-2800 Lyngby

2010-07-15

Many different quantum-information communication protocols such as teleportation, dense coding, and entanglement-based quantum key distribution are based on the faithful transmission of entanglement between distant location in an optical network. The distribution of entanglement in such a network is, however, hampered by loss and noise that is inherent in all practical quantum channels. Thus, to enable faithful transmission one must resort to the protocol of entanglement distillation. In this paper we present a detailed theoretical analysis and an experimental realization of continuous variable entanglement distillation in a channel that is inflicted by different kinds of non-Gaussian noise. The continuous variablemore » entangled states are generated by exploiting the third order nonlinearity in optical fibers, and the states are sent through a free-space laboratory channel in which the losses are altered to simulate a free-space atmospheric channel with varying losses. We use linear optical components, homodyne measurements, and classical communication to distill the entanglement, and we find that by using this method the entanglement can be probabilistically increased for some specific non-Gaussian noise channels.« less

Generalized Geometric Quantum Speed Limits

NASA Astrophysics Data System (ADS)

Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.

2016-04-01

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

Coherent states on horospheric three-dimensional Lobachevsky space

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurochkin, Yu., E-mail: y.kurochkin@ifanbel.bas-net.by; Shoukavy, Dz., E-mail: shoukavy@ifanbel.bas-net.by; Rybak, I., E-mail: Ivan.Rybak@astro.up.pt

2016-08-15

In the paper it is shown that due to separation of variables in the Laplace-Beltrami operator (Hamiltonian of a free quantum particle) in horospheric and quasi-Cartesian coordinates of three dimensional Lobachevsky space, it is possible to introduce standard (“conventional” according to Perelomov [Generalized Coherent States and Their Applications (Springer-Verlag, 1986), p. 320]) coherent states. Some problems (oscillator on horosphere, charged particle in analogy of constant uniform magnetic field) where coherent states are suitable for treating were considered.

Beyond the Quantum

NASA Astrophysics Data System (ADS)

Nieuwenhuizen, Theo M.; Mehmani, Bahar; Špička, Václav; Aghdami, Maryam J.; Khrennikov, Andrei Yu

2007-09-01

pt. A. Introductions. The mathematical basis for deterministic quantum mechanics / G.'t Hooft. What did we learn from quantum gravity? / A. Ashtekar. Bose-Einstein condensates and EPR quantum non-locality / F. Laloe. The quantum measurement process: lessons from an exactly solvable model / A.E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen -- pt. B. Quantum mechanics and quantum information. POVMs: a small but important step beyond standard quantum mechanics / W. M. de Muynck. State reduction by measurements with a null result / G. Nienhuis. Solving open questions in the Bose-Einstein condensation of an ideal gas via a hybrid mixture of laser and statistical physics / M. Kim, A. Svidzinsky and M.O. Scully. Twin-Photon light scattering and causality / G. Puentes, A. Aiello and J. P. Woerdman. Simultaneous measurement of non-commuting observables / G. Aquino and B. Mehmani. Quantum decoherence and gravitational waves / M.T. Jaekel ... [et al.]. Role of various entropies in the black hole information loss problem / Th. M. Nieuwenhuizen and I.V. Volovich. Quantum and super-quantum correlations / G.S. Jaeger -- pt. C. Long distance correlations and bell inequalities. Understanding long-distance quantum correlations / L. Marchildon. Connection of probability models to EPR experiments: probability spaces and Bell's theorem / K. Hess and W. Philipp. Fair sampling vs no-signalling principle in EPR experiments / G. Adenier and A. Yu. Khrennikov -- pt. D. Mathematical foundations. Where the mathematical structure of quantum mechanics comes from / G.M. D'Ariano. Phase space description of quantum mechanics and non-commutative geometry: Wigner-Moyal and Bohm in a wider context / B.J. Hiley. Quantum mechanics as simple algorithm for approximation of classical integrals / A. Yu. Khrennikov. Noncommutative quantum mechanics viewed from Feynman Formalism / J. Lages ... [et al.]. Beyond the quantum in Snyder space / J.F.S. van Huele and M. K. Transtrum -- pt. E. Stochastic electrodynamics. Some quantum experiments from the point of view of Stochastic electrodynamics / V. Spicka ... [et al.]. On the ergodic behaviour of atomic systems under the action of the zero-point radiation field / L. De La Peña and A. M. Cetto. Inertia and the vacuum-view on the emergence of the inertia reaction force / A. Rueda and H. Sunahata -- pt. F. Models for the electron. Rotating Hopf-Kinks: oscillators in the sense of de Broglie / U. Enz. Kerr-Newman particles: symmetries and other properties / H.I. Arcos and J.G. Pereira. Kerr geometry beyond the quantum theory / Th. M. Nieuwenhuizen -- pt. G. Philosophical considerations. Probability in non-collapse interpretations of a quantum mechanics / D. Dieks. The Schrödinger-Park paradox about the concept of "State" in quantum statistical mechanics and quantum information theory is still open: one more reason to go beyond? / G.P. Beretta. The conjecture that local realism is possible / E. Santos -- pt. H. The round table. Round table discussion / A.M. Cetto ... [et al.].

Emergence of entanglement with temperature and time in factorization-surface states

NASA Astrophysics Data System (ADS)

Chanda, Titas; Das, Tamoghna; Sadhukhan, Debasis; Pal, Amit Kumar; SenDe, Aditi; Sen, Ujjwal

2018-01-01

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting with the system through that spin-pair via a repetitive quantum interaction.

Influence of Γ-X band mixing on the excited donor in a parabolic quantum well

NASA Astrophysics Data System (ADS)

Raghuvaran, T.; Shanthi, R. Vijaya; D'Reuben, A. Merwyn Jasper; Nithiananthi, P.

2013-06-01

Equally spaced energy levels of Parabolic Quantum Well are perturbed due to the application of hydrostatic pressure. It will modify the electronic and optical behavior of high Potential devices. The variation of excited state donor binding energy due to Γ-X band mixing at critical cross over pressures in a Parabolic GaAs/AlxGa1-x As quantum well has been investigated in the effective mass approximation using variational method.

Phase space theory of evaporation in neon clusters: the role of quantum effects.

PubMed

Calvo, F; Parneix, P

2009-12-31

Unimolecular evaporation of neon clusters containing between 14 and 148 atoms is theoretically investigated in the framework of phase space theory. Quantum effects are incorporated in the vibrational densities of states, which include both zero-point and anharmonic contributions, and in the possible tunneling through the centrifugal barrier. The evaporation rates, kinetic energy released, and product angular momentum are calculated as a function of excess energy or temperature in the parent cluster and compared to the classical results. Quantum fluctuations are found to generally increase both the kinetic energy released and the angular momentum of the product, but the effects on the rate constants depend nontrivially on the excess energy. These results are interpreted as due to the very few vibrational states available in the product cluster when described quantum mechanically. Because delocalization also leads to much narrower thermal energy distributions, the variations of evaporation observables as a function of canonical temperature appear much less marked than in the microcanonical ensemble. While quantum effects tend to smooth the caloric curve in the product cluster, the melting phase change clearly keeps a signature on these observables. The microcanonical temperature extracted from fitting the kinetic energy released distribution using an improved Arrhenius form further suggests a backbending in the quantum Ne(13) cluster that is absent in the classical system. Finally, in contrast to delocalization effects, quantum tunneling through the centrifugal barrier does not play any appreciable role on the evaporation kinetics of these rather heavy clusters.

Stochastic analysis of surface roughness models in quantum wires

NASA Astrophysics Data System (ADS)

Nedjalkov, Mihail; Ellinghaus, Paul; Weinbub, Josef; Sadi, Toufik; Asenov, Asen; Dimov, Ivan; Selberherr, Siegfried

2018-07-01

We present a signed particle computational approach for the Wigner transport model and use it to analyze the electron state dynamics in quantum wires focusing on the effect of surface roughness. Usually surface roughness is considered as a scattering model, accounted for by the Fermi Golden Rule, which relies on approximations like statistical averaging and in the case of quantum wires incorporates quantum corrections based on the mode space approach. We provide a novel computational approach to enable physical analysis of these assumptions in terms of phase space and particles. Utilized is the signed particles model of Wigner evolution, which, besides providing a full quantum description of the electron dynamics, enables intuitive insights into the processes of tunneling, which govern the physical evolution. It is shown that the basic assumptions of the quantum-corrected scattering model correspond to the quantum behavior of the electron system. Of particular importance is the distribution of the density: Due to the quantum confinement, electrons are kept away from the walls, which is in contrast to the classical scattering model. Further quantum effects are retardation of the electron dynamics and quantum reflection. Far from equilibrium the assumption of homogeneous conditions along the wire breaks even in the case of ideal wire walls.

The MFA ground states for the extended Bose-Hubbard model with a three-body constraint

NASA Astrophysics Data System (ADS)

Panov, Yu. D.; Moskvin, A. S.; Vasinovich, E. V.; Konev, V. V.

2018-05-01

We address the intensively studied extended bosonic Hubbard model (EBHM) with truncation of the on-site Hilbert space to the three lowest occupation states n = 0 , 1 , 2 in frames of the S = 1 pseudospin formalism. Similar model was recently proposed to describe the charge degree of freedom in a model high-T c cuprate with the on-site Hilbert space reduced to the three effective valence centers, nominally Cu1+;2+;3+. With small corrections the model becomes equivalent to a strongly anisotropic S = 1 quantum magnet in an external magnetic field. We have applied a generalized mean-field approach and quantum Monte-Carlo technique for the model 2D S = 1 system with a two-particle transport to find the ground state phase with its evolution under deviation from half-filling.

Nonlinear quantum Rabi model in trapped ions

NASA Astrophysics Data System (ADS)

Cheng, Xiao-Hang; Arrazola, Iñigo; Pedernales, Julen S.; Lamata, Lucas; Chen, Xi; Solano, Enrique

2018-02-01

We study the nonlinear dynamics of trapped-ion models far away from the Lamb-Dicke regime. This nonlinearity induces a blockade on the propagation of quantum information along the Hilbert space of the Jaynes-Cummings and quantum Rabi models. We propose to use this blockade as a resource for the dissipative generation of high-number Fock states. Also, we compare the linear and nonlinear cases of the quantum Rabi model in the ultrastrong and deep strong-coupling regimes. Moreover, we propose a scheme to simulate the nonlinear quantum Rabi model in all coupling regimes. This can be done via off-resonant nonlinear red- and blue-sideband interactions in a single trapped ion, yielding applications as a dynamical quantum filter.

Special Relativity at the Quantum Scale

PubMed Central

Lam, Pui K.

2014-01-01

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point. PMID:25531675

Special relativity at the quantum scale.

PubMed

Lam, Pui K

2014-01-01

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's "checker-board" trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum "coordinates". This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.

A Quantum-Based Similarity Method in Virtual Screening.

PubMed

Al-Dabbagh, Mohammed Mumtaz; Salim, Naomie; Himmat, Mubarak; Ahmed, Ali; Saeed, Faisal

2015-10-02

One of the most widely-used techniques for ligand-based virtual screening is similarity searching. This study adopted the concepts of quantum mechanics to present as state-of-the-art similarity method of molecules inspired from quantum theory. The representation of molecular compounds in mathematical quantum space plays a vital role in the development of quantum-based similarity approach. One of the key concepts of quantum theory is the use of complex numbers. Hence, this study proposed three various techniques to embed and to re-represent the molecular compounds to correspond with complex numbers format. The quantum-based similarity method that developed in this study depending on complex pure Hilbert space of molecules called Standard Quantum-Based (SQB). The recall of retrieved active molecules were at top 1% and top 5%, and significant test is used to evaluate our proposed methods. The MDL drug data report (MDDR), maximum unbiased validation (MUV) and Directory of Useful Decoys (DUD) data sets were used for experiments and were represented by 2D fingerprints. Simulated virtual screening experiment show that the effectiveness of SQB method was significantly increased due to the role of representational power of molecular compounds in complex numbers forms compared to Tanimoto benchmark similarity measure.

Construction of high-dimensional universal quantum logic gates using a Λ system coupled with a whispering-gallery-mode microresonator.

PubMed

He, Ling Yan; Wang, Tie-Jun; Wang, Chuan

2016-07-11

High-dimensional quantum system provides a higher capacity of quantum channel, which exhibits potential applications in quantum information processing. However, high-dimensional universal quantum logic gates is difficult to achieve directly with only high-dimensional interaction between two quantum systems and requires a large number of two-dimensional gates to build even a small high-dimensional quantum circuits. In this paper, we propose a scheme to implement a general controlled-flip (CF) gate where the high-dimensional single photon serve as the target qudit and stationary qubits work as the control logic qudit, by employing a three-level Λ-type system coupled with a whispering-gallery-mode microresonator. In our scheme, the required number of interaction times between the photon and solid state system reduce greatly compared with the traditional method which decomposes the high-dimensional Hilbert space into 2-dimensional quantum space, and it is on a shorter temporal scale for the experimental realization. Moreover, we discuss the performance and feasibility of our hybrid CF gate, concluding that it can be easily extended to a 2n-dimensional case and it is feasible with current technology.

Maximal violation of a bipartite three-setting, two-outcome Bell inequality using infinite-dimensional quantum systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pal, Karoly F.; Vertesi, Tamas

2010-08-15

The I{sub 3322} inequality is the simplest bipartite two-outcome Bell inequality beyond the Clauser-Horne-Shimony-Holt (CHSH) inequality, consisting of three two-outcome measurements per party. In the case of the CHSH inequality the maximal quantum violation can already be attained with local two-dimensional quantum systems; however, there is no such evidence for the I{sub 3322} inequality. In this paper a family of measurement operators and states is given which enables us to attain the maximum quantum value in an infinite-dimensional Hilbert space. Further, it is conjectured that our construction is optimal in the sense that measuring finite-dimensional quantum systems is not enoughmore » to achieve the true quantum maximum. We also describe an efficient iterative algorithm for computing quantum maximum of an arbitrary two-outcome Bell inequality in any given Hilbert space dimension. This algorithm played a key role in obtaining our results for the I{sub 3322} inequality, and we also applied it to improve on our previous results concerning the maximum quantum violation of several bipartite two-outcome Bell inequalities with up to five settings per party.« less

Topos quantum theory on quantization-induced sheaves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kunji, E-mail: nakayama@law.ryukoku.ac.jp

2014-10-15

In this paper, we construct a sheaf-based topos quantum theory. It is well known that a topos quantum theory can be constructed on the topos of presheaves on the category of commutative von Neumann algebras of bounded operators on a Hilbert space. Also, it is already known that quantization naturally induces a Lawvere-Tierney topology on the presheaf topos. We show that a topos quantum theory akin to the presheaf-based one can be constructed on sheaves defined by the quantization-induced Lawvere-Tierney topology. That is, starting from the spectral sheaf as a state space of a given quantum system, we construct sheaf-basedmore » expressions of physical propositions and truth objects, and thereby give a method of truth-value assignment to the propositions. Furthermore, we clarify the relationship to the presheaf-based quantum theory. We give translation rules between the sheaf-based ingredients and the corresponding presheaf-based ones. The translation rules have “coarse-graining” effects on the spaces of the presheaf-based ingredients; a lot of different proposition presheaves, truth presheaves, and presheaf-based truth-values are translated to a proposition sheaf, a truth sheaf, and a sheaf-based truth-value, respectively. We examine the extent of the coarse-graining made by translation.« less

Real-space decoupling transformation for quantum many-body systems.

PubMed

Evenbly, G; Vidal, G

2014-06-06

We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).

Twisted photon entanglement through turbulent air across Vienna

PubMed Central

Krenn, Mario; Handsteiner, Johannes; Fink, Matthias; Fickler, Robert; Zeilinger, Anton

2015-01-01

Photons with a twisted phase front can carry a discrete, in principle, unbounded amount of orbital angular momentum (OAM). The large state space allows for complex types of entanglement, interesting both for quantum communication and for fundamental tests of quantum theory. However, the distribution of such entangled states over large distances was thought to be infeasible due to influence of atmospheric turbulence, indicating a serious limitation on their usefulness. Here we show that it is possible to distribute quantum entanglement encoded in OAM over a turbulent intracity link of 3 km. We confirm quantum entanglement of the first two higher-order levels (with OAM=± 1ℏ and ± 2ℏ). They correspond to four additional quantum channels orthogonal to all that have been used in long-distance quantum experiments so far. Therefore, a promising application would be quantum communication with a large alphabet. We also demonstrate that our link allows access to up to 11 quantum channels of OAM. The restrictive factors toward higher numbers are technical limitations that can be circumvented with readily available technologies. PMID:26578763

Twisted photon entanglement through turbulent air across Vienna.

PubMed

Krenn, Mario; Handsteiner, Johannes; Fink, Matthias; Fickler, Robert; Zeilinger, Anton

2015-11-17

Photons with a twisted phase front can carry a discrete, in principle, unbounded amount of orbital angular momentum (OAM). The large state space allows for complex types of entanglement, interesting both for quantum communication and for fundamental tests of quantum theory. However, the distribution of such entangled states over large distances was thought to be infeasible due to influence of atmospheric turbulence, indicating a serious limitation on their usefulness. Here we show that it is possible to distribute quantum entanglement encoded in OAM over a turbulent intracity link of 3 km. We confirm quantum entanglement of the first two higher-order levels (with OAM=± 1ħ and ± 2ħ). They correspond to four additional quantum channels orthogonal to all that have been used in long-distance quantum experiments so far. Therefore, a promising application would be quantum communication with a large alphabet. We also demonstrate that our link allows access to up to 11 quantum channels of OAM. The restrictive factors toward higher numbers are technical limitations that can be circumvented with readily available technologies.

Workshop on Squeezed States and Uncertainty Relations

NASA Technical Reports Server (NTRS)

Han, Daesoo (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)

1992-01-01

The proceedings from the workshop are presented, and the focus was on the application of squeezed states. There are many who say that the potential for industrial applications is enormous, as the history of the conventional laser suggests. All those who worked so hard to produce squeezed states of light are continuing their efforts to construct more efficient squeezed-state lasers. Quite naturally, they are looking for new experiments using these lasers. The physical basis of squeezed states is the uncertainty relation in Fock space, which is also the basis for the creation and annihilation of particles in quantum field theory. Indeed, squeezed states provide a unique opportunity for field theoreticians to develop a measurement theory for quantum field theory.

Holonomic Quantum Control with Continuous Variable Systems.

PubMed

Albert, Victor V; Shu, Chi; Krastanov, Stefan; Shen, Chao; Liu, Ren-Bao; Yang, Zhen-Biao; Schoelkopf, Robert J; Mirrahimi, Mazyar; Devoret, Michel H; Jiang, Liang

2016-04-08

Universal computation of a quantum system consisting of superpositions of well-separated coherent states of multiple harmonic oscillators can be achieved by three families of adiabatic holonomic gates. The first gate consists of moving a coherent state around a closed path in phase space, resulting in a relative Berry phase between that state and the other states. The second gate consists of "colliding" two coherent states of the same oscillator, resulting in coherent population transfer between them. The third gate is an effective controlled-phase gate on coherent states of two different oscillators. Such gates should be realizable via reservoir engineering of systems that support tunable nonlinearities, such as trapped ions and circuit QED.

Collective fluorescence and decoherence of a few nearly identical quantum dots

NASA Astrophysics Data System (ADS)

Sitek, Anna; Machnikowski, Paweł

2007-01-01

We study the collective interaction of excitons in closely spaced artificial molecules and arrays of nearly identical quantum dots with the electromagnetic modes. We discuss how collective fluorescence builds up in the presence of a small mismatch of the transition energy. We show that a superradiant state of a single exciton in a molecule of two dots with realistic energy mismatch undergoes a two-rate decay. We also analyze the stability of subdecoherent states for nonidentical systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Znojil, Miloslav

For many quantum models an apparent non-Hermiticity of observables just corresponds to their hidden Hermiticity in another, physical Hilbert space. For these models we show that the existence of observables which are manifestly time-dependent may require the use of a manifestly time-dependent representation of the physical Hilbert space of states.

Universal Quantum Computing with Measurement-Induced Continuous-Variable Gate Sequence in a Loop-Based Architecture.

PubMed

Takeda, Shuntaro; Furusawa, Akira

2017-09-22

We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault tolerantly by a known scheme for encoding a qubit in an infinite-dimensional Hilbert space of a single light mode.

Universal Quantum Computing with Measurement-Induced Continuous-Variable Gate Sequence in a Loop-Based Architecture

NASA Astrophysics Data System (ADS)

Takeda, Shuntaro; Furusawa, Akira

2017-09-01

We propose a scalable scheme for optical quantum computing using measurement-induced continuous-variable quantum gates in a loop-based architecture. Here, time-bin-encoded quantum information in a single spatial mode is deterministically processed in a nested loop by an electrically programmable gate sequence. This architecture can process any input state and an arbitrary number of modes with almost minimum resources, and offers a universal gate set for both qubits and continuous variables. Furthermore, quantum computing can be performed fault tolerantly by a known scheme for encoding a qubit in an infinite-dimensional Hilbert space of a single light mode.

Applications of rigged Hilbert spaces in quantum mechanics and signal processing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, Paseo Belén 7, 47011 Valladolid; Gadella, M., E-mail: manuelgadella1@gmail.com

Simultaneous use of discrete and continuous bases in quantum systems is not possible in the context of Hilbert spaces, but only in the more general structure of rigged Hilbert spaces (RHS). In addition, the relevant operators in RHS (but not in Hilbert space) are a realization of elements of a Lie enveloping algebra and support representations of semigroups. We explicitly construct here basis dependent RHS of the line and half-line and relate them to the universal enveloping algebras of the Weyl-Heisenberg algebra and su(1, 1), respectively. The complete sub-structure of both RHS and of the operators acting on them ismore » obtained from their algebraic structures or from the related fractional Fourier transforms. This allows us to describe both quantum and signal processing states and their dynamics. Two relevant improvements are introduced: (i) new kinds of filters related to restrictions to subspaces and/or the elimination of high frequency fluctuations and (ii) an operatorial structure that, starting from fix objects, describes their time evolution.« less

Quantum multicriticality in disordered Weyl semimetals

NASA Astrophysics Data System (ADS)

Luo, Xunlong; Xu, Baolong; Ohtsuki, Tomi; Shindou, Ryuichi

2018-01-01

In electronic band structure of solid-state material, two band-touching points with linear dispersion appear in pairs in the momentum space. When they annihilate each other, the system undergoes a quantum phase transition from a three-dimensional (3D) Weyl semimetal (WSM) phase to a band insulator phase such as a Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a "magnetic dipole"-like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases: a renormalized WSM phase, a CI phase, and a diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band-touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states, and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized WSM phase turns out to be a direct phase transition whose critical exponent ν =0.80 ±0.01 . We interpret these numerical results by a renormalization group analysis on the critical theory.

LETTER TO THE EDITOR: Landau levels on the hyperbolic plane

NASA Astrophysics Data System (ADS)

Fakhri, H.; Shariati, M.

2004-11-01

The quantum states of a spinless charged particle on a hyperbolic plane in the presence of a uniform magnetic field with a generalized quantization condition are proved to be the bases of the irreducible Hilbert representation spaces of the Lie algebra u(1, 1). The dynamical symmetry group U(1, 1) with the explicit form of the Lie algebra generators is extracted. It is also shown that the energy has an infinite-fold degeneracy in each of the representation spaces which are allocated to the different values of the magnetic field strength. Based on the simultaneous shift of two parameters, it is also noted that the quantum states realize the representations of Lie algebra u(2) by shifting the magnetic field strength.

Test of mutually unbiased bases for six-dimensional photonic quantum systems

PubMed Central

D'Ambrosio, Vincenzo; Cardano, Filippo; Karimi, Ebrahim; Nagali, Eleonora; Santamato, Enrico; Marrucci, Lorenzo; Sciarrino, Fabio

2013-01-01

In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a “qusix”), encoded exploiting polarization and orbital angular momentum of photons. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution. PMID:24067548

Test of mutually unbiased bases for six-dimensional photonic quantum systems.

PubMed

D'Ambrosio, Vincenzo; Cardano, Filippo; Karimi, Ebrahim; Nagali, Eleonora; Santamato, Enrico; Marrucci, Lorenzo; Sciarrino, Fabio

2013-09-25

In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low as six, the identification of a maximal set of MUBs remains an open problem, although there is strong numerical evidence that no more than three simultaneous MUBs do exist. Here, by exploiting a newly developed holographic technique, we implement and test different sets of three MUBs for a single photon six-dimensional quantum state (a "qusix"), encoded exploiting polarization and orbital angular momentum of photons. A close agreement is observed between theory and experiments. Our results can find applications in state tomography, quantitative wave-particle duality, quantum key distribution.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Diez-Tejedor, Alberto; Sudarsky, Daniel, E-mail: alberto.diez@nucleares.unam.mx, E-mail: sudarsky@nucleares.unam.mx

Inflation plays a central role in our current understanding of the universe. According to the standard viewpoint, the homogeneous and isotropic mode of the inflaton field drove an early phase of nearly exponential expansion of the universe, while the quantum fluctuations (uncertainties) of the other modes gave rise to the seeds of cosmic structure. However, if we accept that the accelerated expansion led the universe into an essentially homogeneous and isotropic space-time, with the state of all the matter fields in their vacuum (except for the zero mode of the inflaton field), we can not escape the conclusion that themore » state of the universe as a whole would remain always homogeneous and isotropic. It was recently proposed in [A. Perez, H. Sahlmann and D. Sudarsky, {sup O}n the quantum origin of the seeds of cosmic structure{sup ,} Class. Quant. Grav. 23 (2006) 2317–2354] that a collapse (representing physics beyond the established paradigm, and presumably associated with a quantum-gravity effect à la Penrose) of the state function of the inflaton field might be the missing element, and thus would be responsible for the emergence of the primordial inhomogeneities. Here we will discuss a formalism that relies strongly on quantum field theory on curved space-times, and within which we can implement a detailed description of such a process. The picture that emerges clarifies many aspects of the problem, and is conceptually quite transparent. Nonetheless, we will find that the results lead us to argue that the resulting picture is not fully compatible with a purely geometric description of space-time.« less

Quantum Search in Hilbert Space

NASA Technical Reports Server (NTRS)

Zak, Michail

2003-01-01

A proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.

Hybrid Quantum-Classical Approach to Quantum Optimal Control.

PubMed

Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

2017-04-14

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

Photovoltaic driven multiple quantum well optical modulator

NASA Technical Reports Server (NTRS)

Maserjian, Joseph (Inventor)

1990-01-01

Multiple quantum well (MQW) structures (12) are utilized to provide real-time, reliable, high-performance, optically-addressed spatial-light modulators (SLM) (10). The optically-addressed SLM comprises a vertical stack of quantum well layers (12a) within the penetration depth of an optical write signal 18, a plurality of space charge barriers (12b) having predetermined tunneling times by control of doping and thickness. The material comprising the quantum well layers has a lower bandgap than that of the space charge barrier layers. The write signal modulates a read signal (20). The modulation sensitivity of the device is high and no external voltage source is required. In a preferred embodiment, the SLM having interleaved doped semiconductor layers for driving the MQW photovoltaically is characterized by the use of a shift analogous to the Moss-Burnstein shift caused by the filling of two-dimensional states in the multiple quantum wells, thus allowing high modulation sensitivity in very narrow wells. Arrays (30) may be formed with a plurality of the modulators.

Room temperature single photon source using fiber-integrated hexagonal boron nitride

NASA Astrophysics Data System (ADS)

Vogl, Tobias; Lu, Yuerui; Lam, Ping Koy

2017-07-01

Single photons are a key resource for quantum optics and optical quantum information processing. The integration of scalable room temperature quantum emitters into photonic circuits remains to be a technical challenge. Here we utilize a defect center in hexagonal boron nitride (hBN) attached by Van der Waals force onto a multimode fiber as a single photon source. We perform an optical characterization of the source in terms of spectrum, state lifetime, power saturation and photostability. A special feature of our source is that it allows for easy switching between fiber-coupled and free space single photon generation modes. In order to prove the quantum nature of the emission we measure the second-order correlation function {{g}(2)}≤ft(τ \\right) . For both fiber-coupled and free space emission, the {{g}(2)}≤ft(τ \\right) dips below 0.5 indicating operation in the single photon regime. The results so far demonstrate the feasibility of 2D material single photon sources for scalable photonic quantum information processing.

Three examples of quantum dynamics on the half-line with smooth bouncing

NASA Astrophysics Data System (ADS)

Almeida, C. R.; Bergeron, H.; Gazeau, J.-P.; Scardua, A. C.

2018-05-01

This article is an introductory presentation of the quantization of the half-plane based on affine coherent states (ACS). The half-plane carries a natural affine symmetry, i.e. it is a homogeneous space for the 1d-affine group, and it is viewed as the phase space for the dynamics of a positive physical quantity evolving with time. Its affine symmetry is preserved due to the covariance of this type of quantization. We promote the interest of such a procedure for transforming a classical model into a quantum one, since the singularity at the origin is systematically removed, and the arbitrariness of boundary conditions for the Schrödinger operator can be easily overcome. We explain some important mathematical aspects of the method. Three elementary examples of applications are presented, the quantum breathing of a massive sphere, the quantum smooth bouncing of a charged sphere, and a smooth bouncing of "dust" sphere as a simple model of quantum Newtonian cosmology.

Asymmetric band gaps in a Rashba film system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carbone, C.; Moras, P.; Sheverdyaeva, P. M.

The joint effect of exchange and Rashba spin-orbit interactions is examined on the surface and quantum well states of Ag 2 Bi -terminated Ag films grown on ferromagnetic Fe(110). The system displays a particular combination of time-reversal and translational symmetry breaking that strongly influences its electronic structure. Angle-resolved photoemission reveals asymmetric band-gap openings, due to spin-selective hybridization between Rashba-split surface states and exchange-split quantum well states. This results in an unequal number of states along positive and negative reciprocal space directions. We suggest that the peculiar asymmetry of the discovered electronic structure can have significant influence on spin-polarized transport properties.

Semi-stochastic full configuration interaction quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Holmes, Adam; Petruzielo, Frank; Khadilkar, Mihir; Changlani, Hitesh; Nightingale, M. P.; Umrigar, C. J.

2012-02-01

In the recently proposed full configuration interaction quantum Monte Carlo (FCIQMC) [1,2], the ground state is projected out stochastically, using a population of walkers each of which represents a basis state in the Hilbert space spanned by Slater determinants. The infamous fermion sign problem manifests itself in the fact that walkers of either sign can be spawned on a given determinant. We propose an improvement on this method in the form of a hybrid stochastic/deterministic technique, which we expect will improve the efficiency of the algorithm by ameliorating the sign problem. We test the method on atoms and molecules, e.g., carbon, carbon dimer, N2 molecule, and stretched N2. [4pt] [1] Fermion Monte Carlo without fixed nodes: a Game of Life, death and annihilation in Slater Determinant space. George Booth, Alex Thom, Ali Alavi. J Chem Phys 131, 050106, (2009).[0pt] [2] Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo. Deidre Cleland, George Booth, and Ali Alavi. J Chem Phys 132, 041103 (2010).

Ultrafast universal quantum control of a quantum-dot charge qubit using Landau–Zener–Stückelberg interference

PubMed Central

Cao, Gang; Li, Hai-Ou; Tu, Tao; Wang, Li; Zhou, Cheng; Xiao, Ming; Guo, Guang-Can; Jiang, Hong-Wen; Guo, Guo-Ping

2013-01-01

A basic requirement for quantum information processing is the ability to universally control the state of a single qubit on timescales much shorter than the coherence time. Although ultrafast optical control of a single spin has been achieved in quantum dots, scaling up such methods remains a challenge. Here we demonstrate complete control of the quantum-dot charge qubit on the picosecond scale, orders of magnitude faster than the previously measured electrically controlled charge- or spin-based qubits. We observe tunable qubit dynamics in a charge-stability diagram, in a time domain, and in a pulse amplitude space of the driven pulse. The observations are well described by Landau–Zener–Stückelberg interference. These results establish the feasibility of a full set of all-electrical single-qubit operations. Although our experiment is carried out in a solid-state architecture, the technique is independent of the physical encoding of the quantum information and has the potential for wider applications. PMID:23360992

A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

NASA Astrophysics Data System (ADS)

Po, Hoi Chun; Zhou, Qi

2015-08-01

Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

Quantum geometric phase in Majorana's stellar representation: mapping onto a many-body Aharonov-Bohm phase.

PubMed

Bruno, Patrick

2012-06-15

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

Quantum Geometric Phase in Majorana's Stellar Representation: Mapping onto a Many-Body Aharonov-Bohm Phase

NASA Astrophysics Data System (ADS)

Bruno, Patrick

2012-06-01

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

Free-Space Quantum Signatures Using Heterodyne Measurements.

PubMed

Croal, Callum; Peuntinger, Christian; Heim, Bettina; Khan, Imran; Marquardt, Christoph; Leuchs, Gerd; Wallden, Petros; Andersson, Erika; Korolkova, Natalia

2016-09-02

Digital signatures guarantee the authorship of electronic communications. Currently used "classical" signature schemes rely on unproven computational assumptions for security, while quantum signatures rely only on the laws of quantum mechanics to sign a classical message. Previous quantum signature schemes have used unambiguous quantum measurements. Such measurements, however, sometimes give no result, reducing the efficiency of the protocol. Here, we instead use heterodyne detection, which always gives a result, although there is always some uncertainty. We experimentally demonstrate feasibility in a real environment by distributing signature states through a noisy 1.6 km free-space channel. Our results show that continuous-variable heterodyne detection improves the signature rate for this type of scheme and therefore represents an interesting direction in the search for practical quantum signature schemes. For transmission values ranging from 100% to 10%, but otherwise assuming an ideal implementation with no other imperfections, the signature length is shorter by a factor of 2 to 10. As compared with previous relevant experimental realizations, the signature length in this implementation is several orders of magnitude shorter.

Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

DOE PAGES

Ferrie, Christopher; Blume-Kohout, Robin

2016-03-04

A minimax estimator has the minimum possible error (“risk”) in the worst case. Here we construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1/more » $$\\sqrt{N}$$ ) —in contrast to that of classical probability estimation, which is O (1/N) —where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. Lastly, this makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.« less

Quantum entanglement of local operators in conformal field theories.

PubMed

Nozaki, Masahiro; Numasawa, Tokiro; Takayanagi, Tadashi

2014-03-21

We introduce a series of quantities which characterize a given local operator in any conformal field theory from the viewpoint of quantum entanglement. It is defined by the increased amount of (Rényi) entanglement entropy at late time for an excited state defined by acting the local operator on the vacuum. We consider a conformal field theory on an infinite space and take the subsystem in the definition of the entanglement entropy to be its half. We calculate these quantities for a free massless scalar field theory in two, four and six dimensions. We find that these results are interpreted in terms of quantum entanglement of a finite number of states, including Einstein-Podolsky-Rosen states. They agree with a heuristic picture of propagations of entangled particles.

Grassmann phase space theory and the Jaynes–Cummings model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dalton, B.J., E-mail: bdalton@swin.edu.au; Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne, Victoria 3122; Garraway, B.M.

2013-07-15

The Jaynes–Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherentmore » state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker–Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker–Planck equations from which c-number Langevin equations are often developed. However, atomic spin operators satisfy the standard angular momentum commutation rules rather than the commutation rules for bosonic annihilation and creation operators, and are in fact second order combinations of fermionic annihilation and creation operators. Though phase space methods in which the fermionic operators are represented directly by c-number phase space variables have not been successful, the anti-commutation rules for these operators suggest the possibility of using Grassmann variables—which have similar anti-commutation properties. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of phase space methods in quantum optics to treat fermionic systems by representing fermionic annihilation and creation operators directly by Grassmann phase space variables is rather rare. This paper shows that phase space methods using a positive P type distribution function involving both c-number variables (for the cavity mode) and Grassmann variables (for the TLA) can be used to treat the Jaynes–Cummings model. Although it is a Grassmann function, the distribution function is equivalent to six c-number functions of the two bosonic variables. Experimental quantities are given as bosonic phase space integrals involving the six functions. A Fokker–Planck equation involving both left and right Grassmann differentiations can be obtained for the distribution function, and is equivalent to six coupled equations for the six c-number functions. The approach used involves choosing the canonical form of the (non-unique) positive P distribution function, in which the correspondence rules for the bosonic operators are non-standard and hence the Fokker–Planck equation is also unusual. Initial conditions, such as those above for initially uncorrelated states, are discussed and used to determine the initial distribution function. Transformations to new bosonic variables rotating at the cavity frequency enable the six coupled equations for the new c-number functions–that are also equivalent to the canonical Grassmann distribution function–to be solved analytically, based on an ansatz from an earlier paper by Stenholm. It is then shown that the distribution function is exactly the same as that determined from the well-known solution based on coupled amplitude equations. In quantum–atom optics theories for many atom bosonic and fermionic systems are needed. With large atom numbers, treatments must often take into account many quantum modes—especially for fermions. Generalisations of phase space distribution functions of phase space variables for a few modes to phase space distribution functionals of field functions (which represent the field operators, c-number fields for bosons, Grassmann fields for fermions) are now being developed for large systems. For the fermionic case, the treatment of the simple two mode problem represented by the Jaynes–Cummings model is a useful test case for the future development of phase space Grassmann distribution functional methods for fermionic applications in quantum–atom optics. -- Highlights: •Novel phase space theory of the Jaynes–Cummings model using Grassmann variables. •Fokker–Planck equations solved analytically. •Results agree with the standard quantum optics treatment. •Grassmann phase space theory applicable to fermion many-body problems.« less

A squeezed light source operated under high vacuum

PubMed Central

Wade, Andrew R.; Mansell, Georgia L.; Chua, Sheon S. Y.; Ward, Robert L.; Slagmolen, Bram J. J.; Shaddock, Daniel A.; McClelland, David E.

2015-01-01

Non-classical squeezed states of light are becoming increasingly important to a range of metrology and other quantum optics applications in cryptography, quantum computation and biophysics. Applications such as improving the sensitivity of advanced gravitational wave detectors and the development of space-based metrology and quantum networks will require robust deployable vacuum-compatible sources. To date non-linear photonics devices operated under high vacuum have been simple single pass systems, testing harmonic generation and the production of classically correlated photon pairs for space-based applications. Here we demonstrate the production under high-vacuum conditions of non-classical squeezed light with an observed 8.6 dB of quantum noise reduction down to 10 Hz. Demonstration of a resonant non-linear optical device, for the generation of squeezed light under vacuum, paves the way to fully exploit the advantages of in-vacuum operations, adapting this technology for deployment into new extreme environments. PMID:26657616

Dynamics for a 2-vertex quantum gravity model

NASA Astrophysics Data System (ADS)

Borja, Enrique F.; Díaz-Polo, Jacobo; Garay, Iñaki; Livine, Etera R.

2010-12-01

We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N)-invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.

A squeezed light source operated under high vacuum

NASA Astrophysics Data System (ADS)

Wade, Andrew R.; Mansell, Georgia L.; Chua, Sheon S. Y.; Ward, Robert L.; Slagmolen, Bram J. J.; Shaddock, Daniel A.; McClelland, David E.

2015-12-01

Non-classical squeezed states of light are becoming increasingly important to a range of metrology and other quantum optics applications in cryptography, quantum computation and biophysics. Applications such as improving the sensitivity of advanced gravitational wave detectors and the development of space-based metrology and quantum networks will require robust deployable vacuum-compatible sources. To date non-linear photonics devices operated under high vacuum have been simple single pass systems, testing harmonic generation and the production of classically correlated photon pairs for space-based applications. Here we demonstrate the production under high-vacuum conditions of non-classical squeezed light with an observed 8.6 dB of quantum noise reduction down to 10 Hz. Demonstration of a resonant non-linear optical device, for the generation of squeezed light under vacuum, paves the way to fully exploit the advantages of in-vacuum operations, adapting this technology for deployment into new extreme environments.

Quantum versus classical dynamics in the optical centrifuge

NASA Astrophysics Data System (ADS)

Armon, Tsafrir; Friedland, Lazar

2017-09-01

The interplay between classical and quantum-mechanical evolution in the optical centrifuge (OC) is discussed. The analysis is based on the quantum-mechanical formalism starting from either the ground state or a thermal ensemble. Two resonant mechanisms are identified, i.e., the classical autoresonance and the quantum-mechanical ladder climbing, yielding different dynamics and rotational excitation efficiencies. The rotating-wave approximation is used to analyze the two resonant regimes in the associated dimensionless two-parameter space and calculate the OC excitation efficiency. The results show good agreement between numerical simulations and theory and are relevant to existing experimental setups.

Classical simulation of quantum many-body systems

NASA Astrophysics Data System (ADS)

Huang, Yichen

Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D gapped systems. Note that the ground-state energy of 1D gapless Hamiltonians is computationally intractable even in the presence of translational invariance. It is tempting to extend methods and tools in 1D to two and higher dimensions (2+D), e.g., matrix product states are generalized to tensor network states. Since an area law for entanglement (if formulated properly) implies efficient matrix product state representations in 1D, an interesting question is whether a similar implication holds in 2+D. Roughly speaking, we show that an area law for entanglement (in any reasonable formulation) does not always imply efficient tensor network representations of the ground states of 2+D local Hamiltonians even in the presence of translational invariance. It should be emphasized that this result does not contradict with the common sense that in practice quantum states with more entanglement usually require more space to be stored classically; rather, it demonstrates that the relationship between entanglement and efficient classical representations is still far from being well understood. Excited eigenstates participate in the dynamics of quantum systems and are particularly relevant to the phenomenon of many-body localization (absence of transport at finite temperature in strongly correlated systems). We study the entanglement of excited eigenstates in random spin chains and expect that its singularities coincide with dynamical quantum phase transitions. This expectation is confirmed in the disordered quantum Ising chain using both analytical and numerical methods. Finally, we study the problem of generating ground states (possibly with topological order) in 1D gapped systems using quantum circuits. This is an interesting problem both in theory and in practice. It not only characterizes the essential difference between the entanglement patterns that give rise to trivial and nontrivial topological order, but also quantifies the difficulty of preparing quantum states with a quantum computer (in experiments).

Two-Photon Quantum Entanglement from Type-II Spontaneous Parametric Down-Conversion

NASA Astrophysics Data System (ADS)

Pittman, Todd Butler

The concept of two (or more) particle entanglement lies at the heart of many fascinating questions concerning the foundations of quantum mechanics. The counterintuitive nonlocal behavior of entangled states led Einstein, Podolsky, and Rosen (EPR) to ask their famous 1935 question, "Can quantum mechanical description of reality be considered complete?". Although the debate has been raging on for more than 60 years, there is still no absolutely conclusive answer to this question. For if entangled states exist and can be observed, then accepting quantum mechanics as a complete theory requires a drastic overhaul of one's physical intuition with regards to the common sense notions of locality and reality put forth by EPR. Contained herein are the results of research investigating various non-classical features of the two-photon entangled states produced in Type-II Spontaneous Parametric Down -Conversion (SPDC). Through a series of experiments we have manifest the nonlocal nature of the quantum mechanical "two-photon effective wavefunction" (or Biphoton) realized by certain photon-counting coincidence measurements performed on these states. In particular, we examine a special double entanglement, in which the states are seen to be simultaneously entangled in both spin and space-time variables. The observed phenomena based on this double entanglement lead to many interesting results which defy classical explanation, but are well described within the framework of quantum mechanics. The implications provide a unique perspective concerning the nature of the photon, and the concept of quantum entanglement.

Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albert, Julian; Kaiser, Dustin; Engel, Volker

2016-05-07

Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion ismore » treated on the same footing.« less

Practical system for the generation of pulsed quantum frequency combs.

PubMed

Roztocki, Piotr; Kues, Michael; Reimer, Christian; Wetzel, Benjamin; Sciara, Stefania; Zhang, Yanbing; Cino, Alfonso; Little, Brent E; Chu, Sai T; Moss, David J; Morandotti, Roberto

2017-08-07

The on-chip generation of large and complex optical quantum states will enable low-cost and accessible advances for quantum technologies, such as secure communications and quantum computation. Integrated frequency combs are on-chip light sources with a broad spectrum of evenly-spaced frequency modes, commonly generated by four-wave mixing in optically-excited nonlinear micro-cavities, whose recent use for quantum state generation has provided a solution for scalable and multi-mode quantum light sources. Pulsed quantum frequency combs are of particular interest, since they allow the generation of single-frequency-mode photons, required for scaling state complexity towards, e.g., multi-photon states, and for quantum information applications. However, generation schemes for such pulsed combs have, to date, relied on micro-cavity excitation via lasers external to the sources, being neither versatile nor power-efficient, and impractical for scalable realizations of quantum technologies. Here, we introduce an actively-modulated, nested-cavity configuration that exploits the resonance pass-band characteristic of the micro-cavity to enable a mode-locked and energy-efficient excitation. We demonstrate that the scheme allows the generation of high-purity photons at large coincidence-to-accidental ratios (CAR). Furthermore, by increasing the repetition rate of the excitation field via harmonic mode-locking (i.e. driving the cavity modulation at harmonics of the fundamental repetition rate), we managed to increase the pair production rates (i.e. source efficiency), while maintaining a high CAR and photon purity. Our approach represents a significant step towards the realization of fully on-chip, stable, and versatile sources of pulsed quantum frequency combs, crucial for the development of accessible quantum technologies.

Uncertainty relations as Hilbert space geometry

NASA Technical Reports Server (NTRS)

Braunstein, Samuel L.

1994-01-01

Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.

Phase space information in a non-linear quantum system containing a Kerr-like medium through Su(1, 1)-algebraic treatment

NASA Astrophysics Data System (ADS)

Mohamed, Abdel-Baset A.

2018-05-01

Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.

Grassmann phase space methods for fermions. I. Mode theory

NASA Astrophysics Data System (ADS)

Dalton, B. J.; Jeffers, J.; Barnett, S. M.

2016-07-01

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggest the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. The theory of Grassmann phase space methods for fermions based on separate modes is developed, showing how the distribution function is defined and used to determine quantum correlation functions, Fock state populations and coherences via Grassmann phase space integrals, how the Fokker-Planck equations are obtained and then converted into equivalent Ito equations for stochastic Grassmann variables. The fermion distribution function is an even Grassmann function, and is unique. The number of c-number Wiener increments involved is 2n2, if there are n modes. The situation is somewhat different to the bosonic c-number case where only 2 n Wiener increments are involved, the sign of the drift term in the Ito equation is reversed and the diffusion matrix in the Fokker-Planck equation is anti-symmetric rather than symmetric. The un-normalised B distribution is of particular importance for determining Fock state populations and coherences, and as pointed out by Plimak, Collett and Olsen, the drift vector in its Fokker-Planck equation only depends linearly on the Grassmann variables. Using this key feature we show how the Ito stochastic equations can be solved numerically for finite times in terms of c-number stochastic quantities. Averages of products of Grassmann stochastic variables at the initial time are also involved, but these are determined from the initial conditions for the quantum state. The detailed approach to the numerics is outlined, showing that (apart from standard issues in such numerics) numerical calculations for Grassmann phase space theories of fermion systems could be carried out without needing to represent Grassmann phase space variables on the computer, and only involving processes using c-numbers. We compare our approach to that of Plimak, Collett and Olsen and show that the two approaches differ. As a simple test case we apply the B distribution theory and solve the Ito stochastic equations to demonstrate coupling between degenerate Cooper pairs in a four mode fermionic system involving spin conserving interactions between the spin 1 / 2 fermions, where modes with momenta - k , + k-each associated with spin up, spin down states, are involved.

Quantum Structure of Space and Time

NASA Astrophysics Data System (ADS)

Duff, M. J.; Isham, C. J.

2012-07-01

Foreword Abdus Salam; Preface; List of participants; Part I. Quantum Gravity, Fields and Topology: 1. Some remarks on gravity and quantum mechanics Roger Penrose; 2. An experimental test of quantum gravity Don N. Page and C. D. Geilker; 3. Quantum mechanical origin of the sandwich theorem in classical gravitation theory Claudio Teitelboim; 4. θ-States induced by the diffeomorphism group in canonically quantized gravity C. J. Isham; 5. Strong coupling quantum gravity: an introduction Martin Pilati; 6. Quantizing fourth order gravity theories S. M. Christensen; 7. Green's functions, states and renormalisation M. R. Brown and A. C. Ottewill; 8. Introduction to quantum regge calculus Martin Roček and Ruth Williams; 9. Spontaneous symmetry breaking in curved space-time D. J. Toms; 10. Spontaneous symmetry breaking near a black hole M. S. Fawcett and B. F. Whiting; 11. Yang-Mills vacua in a general three-space G. Kunstatter; 12. Fermion fractionization in physics R. Jackiw; Part II. Supergravity: 13. The new minimal formulation of N=1 supergravity and its tensor calculus M. F. Sohnius and P. C. West; 14. A new deteriorated energy-momentum tensor M. J. Duff and P. K. Townsend; 15. Off-shell N=2 and N=4 supergravity in five dimensions P. Howe; 16. Supergravity in high dimensions P. van Niewenhuizen; 17. Building linearised extended supergravities J. G. Taylor; 18. (Super)gravity in the complex angular momentum plane M. T. Grisaru; 19. The multiplet structure of solitons in the O(2) supergravity theory G. W. Gibbons; 20. Ultra-violet properties of supersymmetric gauge theory S. Ferrara; 21. Extended supercurrents and the ultra-violet finiteness of N=4 supersymmetric Yang-Mills theories K. S. Stelle; 22. Duality rotations B. Zumino; Part III. Cosmology and the Early Universe: 23. Energy, stability and cosmological constant S. Deser; 24. Phase transitions in the early universe T. W. B. Kibble; 25. Complete cosmological theories L. P. Grishchuk and Ya. B. Zeldovich; 26. The cosmological constant and the weak anthropic principle S. W. Hawking.

Varieties of Orthocomplemented Lattices Induced by Łukasiewicz-Groupoid-Valued Mappings

NASA Astrophysics Data System (ADS)

Matoušek, Milan; Pták, Pavel

2017-12-01

In the logico-algebraic approach to the foundation of quantum mechanics we sometimes identify the set of events of the quantum experiment with an orthomodular lattice ("quantum logic"). The states are then usually associated with (normalized) finitely additive measures ("states"). The conditions imposed on states then define classes of orthomodular lattices that are sometimes found to be universal-algebraic varieties. In this paper we adopt a conceptually different approach, we relax orthomodular to orthocomplemented and we replace the states with certain subadditive mappings that range in the Łukasiewicz groupoid. We then show that when we require a type of "fulness" of these mappings, we obtain varieties of orthocomplemented lattices. Some of these varieties contain the projection lattice in a Hilbert space so there is a link to quantum logic theories. Besides, on the purely algebraic side, we present a characterization of orthomodular lattices among the orthocomplemented ones. - The intention of our approach is twofold. First, we recover some of the Mayet varieties in a principally different way (indeed, we also obtain many other new varieties). Second, by introducing an interplay of the lattice, measure-theoretic and fuzzy-set notions we intend to add to the concepts of quantum axiomatics.

Self-testing through EPR-steering

NASA Astrophysics Data System (ADS)

Šupić, Ivan; Hoban, Matty J.

2016-07-01

The verification of quantum devices is an important aspect of quantum information, especially with the emergence of more advanced experimental implementations of quantum computation and secure communication. Within this, the theory of device-independent robust self-testing via Bell tests has reached a level of maturity now that many quantum states and measurements can be verified without direct access to the quantum systems: interaction with the devices is solely classical. However, the requirements for this robust level of verification are daunting and require high levels of experimental accuracy. In this paper we discuss the possibility of self-testing where we only have direct access to one part of the quantum device. This motivates the study of self-testing via EPR-steering, an intermediate form of entanglement verification between full state tomography and Bell tests. Quantum non-locality implies EPR-steering so results in the former can apply in the latter, but we ask what advantages may be gleaned from the latter over the former given that one can do partial state tomography? We show that in the case of self-testing a maximally entangled two-qubit state, or ebit, EPR-steering allows for simpler analysis and better error tolerance than in the case of full device-independence. On the other hand, this improvement is only a constant improvement and (up to constants) is the best one can hope for. Finally, we indicate that the main advantage in self-testing based on EPR-steering could be in the case of self-testing multi-partite quantum states and measurements. For example, it may be easier to establish a tensor product structure for a particular party’s Hilbert space even if we do not have access to their part of the global quantum system.

Local temperature in quantum thermal states

NASA Astrophysics Data System (ADS)

García-Saez, Artur; Ferraro, Alessandro; Acín, Antonio

2009-05-01

We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. In a classical system the temperature behaves as an intensive magnitude, above a certain block size, regardless of the actual value of the temperature itself. However, a deviation from this behavior is expected in quantum systems. In particular, we see that under some conditions the description of the blocks as thermal states with the same global temperature as the whole chain fails. We analyze this issue by employing the quantum fidelity as a figure of merit, singling out in detail the departure from the classical behavior. As it may be expected, we see that quantum features are more prominent at low temperatures and are affected by the presence of zero-temperature quantum phase transitions. Interestingly, we show that the blocks can be considered indeed as thermal states with a high fidelity, provided an effective local temperature is properly identified. Such a result may originate from typical properties of reduced subsystems of energy-constrained Hilbert spaces. Finally, the relation between local and global temperatures is analyzed as a function of the size of the blocks and the system parameters.

Electrical control of a long-lived spin qubit in a Si/SiGe quantum dot.

PubMed

Kawakami, E; Scarlino, P; Ward, D R; Braakman, F R; Savage, D E; Lagally, M G; Friesen, Mark; Coppersmith, S N; Eriksson, M A; Vandersypen, L M K

2014-09-01

Nanofabricated quantum bits permit large-scale integration but usually suffer from short coherence times due to interactions with their solid-state environment. The outstanding challenge is to engineer the environment so that it minimally affects the qubit, but still allows qubit control and scalability. Here, we demonstrate a long-lived single-electron spin qubit in a Si/SiGe quantum dot with all-electrical two-axis control. The spin is driven by resonant microwave electric fields in a transverse magnetic field gradient from a local micromagnet, and the spin state is read out in the single-shot mode. Electron spin resonance occurs at two closely spaced frequencies, which we attribute to two valley states. Thanks to the weak hyperfine coupling in silicon, a Ramsey decay timescale of 1 μs is observed, almost two orders of magnitude longer than the intrinsic timescales in GaAs quantum dots, whereas gate operation times are comparable to those reported in GaAs. The spin echo decay time is ~40 μs, both with one and four echo pulses, possibly limited by intervalley scattering. These advances strongly improve the prospects for quantum information processing based on quantum dots.

Quasi-one-dimensional density of states in a single quantum ring.

PubMed

Kim, Heedae; Lee, Woojin; Park, Seongho; Kyhm, Kwangseuk; Je, Koochul; Taylor, Robert A; Nogues, Gilles; Dang, Le Si; Song, Jin Dong

2017-01-05

Generally confinement size is considered to determine the dimensionality of nanostructures. While the exciton Bohr radius is used as a criterion to define either weak or strong confinement in optical experiments, the binding energy of confined excitons is difficult to measure experimentally. One alternative is to use the temperature dependence of the radiative recombination time, which has been employed previously in quantum wells and quantum wires. A one-dimensional loop structure is often assumed to model quantum rings, but this approximation ceases to be valid when the rim width becomes comparable to the ring radius. We have evaluated the density of states in a single quantum ring by measuring the temperature dependence of the radiative recombination of excitons, where the photoluminescence decay time as a function of temperature was calibrated by using the low temperature integrated intensity and linewidth. We conclude that the quasi-continuous finely-spaced levels arising from the rotation energy give rise to a quasi-one-dimensional density of states, as long as the confined exciton is allowed to rotate around the opening of the anisotropic ring structure, which has a finite rim width.

The Unruh quantum Otto engine

NASA Astrophysics Data System (ADS)

Arias, Enrique; de Oliveira, Thiago R.; Sarandy, M. S.

2018-02-01

We introduce a quantum heat engine performing an Otto cycle by using the thermal properties of the quantum vacuum. Since Hawking and Unruh, it has been established that the vacuum space, either near a black hole or for an accelerated observer, behaves as a bath of thermal radiation. In this work, we present a fully quantum Otto cycle, which relies on the Unruh effect for a single quantum bit (qubit) in contact with quantum vacuum fluctuations. By using the notions of quantum thermodynamics and perturbation theory we obtain that the quantum vacuum can exchange heat and produce work on the qubit. Moreover, we obtain the efficiency and derive the conditions to have both a thermodynamic and a kinematic cycle in terms of the initial populations of the excited state, which define a range of allowed accelerations for the Unruh engine.

Nanosatellites for quantum science and technology

NASA Astrophysics Data System (ADS)

Oi, Daniel K. L.; Ling, Alex; Grieve, James A.; Jennewein, Thomas; Dinkelaker, Aline N.; Krutzik, Markus

2017-01-01

Bringing quantum science and technology to the space frontier offers exciting prospects for both fundamental physics and applications such as long-range secure communication and space-borne quantum probes for inertial sensing with enhanced accuracy and sensitivity. But despite important terrestrial pathfinding precursors on common microgravity platforms and promising proposals to exploit the significant advantages of space quantum missions, large-scale quantum test beds in space are yet to be realised due to the high costs and lead times of traditional 'Big Space' satellite development. But the 'small space' revolution, spearheaded by the rise of nanosatellites such as CubeSats, is an opportunity to greatly accelerate the progress of quantum space missions by providing easy and affordable access to space and encouraging agile development. We review space quantum science and technology, CubeSats and their rapidly developing capabilities and how they can be used to advance quantum satellite systems.

The harmonic state of quantum cascade lasers: origin, control, and prospective applications [Invited].

PubMed

Piccardo, Marco; Chevalier, Paul; Mansuripur, Tobias S; Kazakov, Dmitry; Wang, Yongrui; Rubin, Noah A; Meadowcroft, Lauren; Belyanin, Alexey; Capasso, Federico

2018-04-16

The recently discovered ability of the quantum cascade laser to produce a harmonic frequency comb has attracted new interest in these devices for both applications and fundamental laser physics. In this review we present an extensive experimental phenomenology of the harmonic state, including its appearance in mid-infrared and terahertz quantum cascade lasers, studies of its destabilization induced by delayed optical feedback, and the assessment of its frequency comb nature. A theoretical model explaining its origin as due to the mutual interaction of population gratings and population pulsations inside the laser cavity will be described. We explore different approaches to control the spacing of the harmonic state, such as optical injection seeding and variation of the device temperature. Prospective applications of the harmonic state include microwave and terahertz generation, picosecond pulse generation in the mid-infrared, and broadband spectroscopy.

Hand-waving and interpretive dance: an introductory course on tensor networks

NASA Astrophysics Data System (ADS)

Bridgeman, Jacob C.; Chubb, Christopher T.

2017-06-01

The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases using tensor networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states. The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/quantum information. For each lecture, several problems are given, with worked solutions in an ancillary file.

Quantum exhaustive key search with simplified-DES as a case study.

PubMed

Almazrooie, Mishal; Samsudin, Azman; Abdullah, Rosni; Mutter, Kussay N

2016-01-01

To evaluate the security of a symmetric cryptosystem against any quantum attack, the symmetric algorithm must be first implemented on a quantum platform. In this study, a quantum implementation of a classical block cipher is presented. A quantum circuit for a classical block cipher of a polynomial size of quantum gates is proposed. The entire work has been tested on a quantum mechanics simulator called libquantum. First, the functionality of the proposed quantum cipher is verified and the experimental results are compared with those of the original classical version. Then, quantum attacks are conducted by using Grover's algorithm to recover the secret key. The proposed quantum cipher is used as a black box for the quantum search. The quantum oracle is then queried over the produced ciphertext to mark the quantum state, which consists of plaintext and key qubits. The experimental results show that for a key of n-bit size and key space of N such that [Formula: see text], the key can be recovered in [Formula: see text] computational steps.

On-chip continuous-variable quantum entanglement

NASA Astrophysics Data System (ADS)

Masada, Genta; Furusawa, Akira

2016-09-01

Entanglement is an essential feature of quantum theory and the core of the majority of quantum information science and technologies. Quantum computing is one of the most important fruits of quantum entanglement and requires not only a bipartite entangled state but also more complicated multipartite entanglement. In previous experimental works to demonstrate various entanglement-based quantum information processing, light has been extensively used. Experiments utilizing such a complicated state need highly complex optical circuits to propagate optical beams and a high level of spatial interference between different light beams to generate quantum entanglement or to efficiently perform balanced homodyne measurement. Current experiments have been performed in conventional free-space optics with large numbers of optical components and a relatively large-sized optical setup. Therefore, they are limited in stability and scalability. Integrated photonics offer new tools and additional capabilities for manipulating light in quantum information technology. Owing to integrated waveguide circuits, it is possible to stabilize and miniaturize complex optical circuits and achieve high interference of light beams. The integrated circuits have been firstly developed for discrete-variable systems and then applied to continuous-variable systems. In this article, we review the currently developed scheme for generation and verification of continuous-variable quantum entanglement such as Einstein-Podolsky-Rosen beams using a photonic chip where waveguide circuits are integrated. This includes balanced homodyne measurement of a squeezed state of light. As a simple example, we also review an experiment for generating discrete-variable quantum entanglement using integrated waveguide circuits.

Quantum Measurement, Correlation, and Contextuality

NASA Astrophysics Data System (ADS)

Ozawa, Masanao

2011-03-01

The problem has long been discussed as to whether non-commuting observables are simultaneously measurable, since Heisenberg introduced the uncertainty principle in 1927. The problem was settled state-independently: Two observables are simultaneously measurable in every state if and only if the corresponding operators commute. However, the problem has been open for state-dependent formulation. Saying that two observables are nowhere commuting if there exist no common eigenstates, the problem at stake is whether nowhere commuting observable can be simultaneously measurable in a certain state. There have been two historical arguments claiming the case: (i) In an eigenstate of an observable A one can determine both the values of A and any other observable B . (ii) In an EPR state one can determine both the values of Q ⊗ 1 and P ⊗ 1 . In this talk, we give a necessary and sufficient condition for two observables to be simultaneously measurable in a given state, show that the above two cases actually satisfy the required mathematical conditions, and give a classification of all the possible simultaneous measurements of nowhere commuting observables for the Hilbert space with dimension 2. Related problems on quantum contextuality will also be discussed using a linguistic method based on quantum logic and quantum set theory.

Entanglement Entropy of Eigenstates of Quantum Chaotic Hamiltonians.

PubMed

Vidmar, Lev; Rigol, Marcos

2017-12-01

In quantum statistical mechanics, it is of fundamental interest to understand how close the bipartite entanglement entropy of eigenstates of quantum chaotic Hamiltonians is to maximal. For random pure states in the Hilbert space, the average entanglement entropy is known to be nearly maximal, with a deviation that is, at most, a constant. Here we prove that, in a system that is away from half filling and divided in two equal halves, an upper bound for the average entanglement entropy of random pure states with a fixed particle number and normally distributed real coefficients exhibits a deviation from the maximal value that grows with the square root of the volume of the system. Exact numerical results for highly excited eigenstates of a particle number conserving quantum chaotic model indicate that the bound is saturated with increasing system size.

Optical control of spin-dependent thermal transport in a quantum ring

NASA Astrophysics Data System (ADS)

Abdullah, Nzar Rauf

2018-05-01

We report on calculation of spin-dependent thermal transport through a quantum ring with the Rashba spin-orbit interaction. The quantum ring is connected to two electron reservoirs with different temperatures. Tuning the Rashba coupling constant, degenerate energy states are formed leading to a suppression of the heat and thermoelectric currents. In addition, the quantum ring is coupled to a photon cavity with a single photon mode and linearly polarized photon field. In a resonance regime, when the photon energy is approximately equal to the energy spacing between two lowest degenerate states of the ring, the polarized photon field can significantly control the heat and thermoelectric currents in the system. The roles of the number of photon initially in the cavity, and electron-photon coupling strength on spin-dependent heat and thermoelectric currents are presented.

Quantum localisation on the circle

NASA Astrophysics Data System (ADS)

Fresneda, Rodrigo; Gazeau, Jean Pierre; Noguera, Diego

2018-05-01

Covariant integral quantisation using coherent states for semi-direct product groups is implemented for the motion of a particle on the circle. In this case, the phase space is the cylinder, which is viewed as a left coset of the Euclidean group E(2). Coherent states issued from fiducial vectors are labeled by points in the cylinder and depend also on extra parameters. We carry out the corresponding quantisations of the basic classical observables, particularly the angular momentum and the 2π-periodic discontinuous angle function. We compute their corresponding lower symbols. The quantum localisation on the circle is examined through the properties of the angle operator yielded by our procedure, its spectrum and lower symbol, its commutator with the quantum angular momentum, and the resulting Heisenberg inequality. Comparison with other approaches to the long-standing question of the quantum angle is discussed.

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia

2018-02-01

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

Gravitationally self-bound quantum states in unstable potentials

NASA Astrophysics Data System (ADS)

Jääskeläinen, Markku

2018-04-01

Quantum mechanics at present cannot be unified with the theory of gravity at the deepest level, and to guide research towards the solution of this fundamental problem, we need to look for ways to observe or refute predictions originating from attempts to combine quantum theory with gravity. The influence of the gravitational field created by the material density given by the wave function itself gives rise to nontrivial phenomena. In this study I consider the wave function for the center-of-mass coordinate of a spherical mass distribution under the influence of the self-interaction of Newtonian gravity. I solve numerically for the ground state in the presence of an unstable potential and find that the energy of the free-space bound state can be lowered despite the nontrapping character of the potential. The center-of-mass ground state becomes increasingly localized for the used unstable potentials, although only in a limited parameter regime. The feebleness of the energy shift makes the observation of these effects demanding and requires further developments in the cooling of material particles. In addition, the influence of gravitational perturbations that are present in typical laboratory settings necessitates the use of extremely quiet and controlled environments such as those provided by recently proposed space-borne experiments.

Asymptotic states and the definition of the S-matrix in quantum gravity

NASA Astrophysics Data System (ADS)

Wiesendanger, C.

2013-04-01

Viewing gravitational energy-momentum p_G^\\mu as equal by observation, but different in essence from inertial energy-momentum p_I^\\mu naturally leads to the gauge theory of volume-preserving diffeomorphisms of an inner Minkowski space M4. The generalized asymptotic free scalar, Dirac and gauge fields in that theory are canonically quantized, the Fock spaces of stationary states are constructed and the gravitational limit—mapping the gravitational energy-momentum onto the inertial energy-momentum to account for their observed equality—is introduced. Next the S-matrix in quantum gravity is defined as the gravitational limit of the transition amplitudes of asymptotic in- to out-states in the gauge theory of volume-preserving diffeomorphisms. The so-defined S-matrix relates in- and out-states of observable particles carrying gravitational equal to inertial energy-momentum. Finally, generalized Lehmann-Symanzik-Zimmermann reduction formulae for scalar, Dirac and gauge fields are established which allow us to express S-matrix elements as the gravitational limit of truncated Fourier-transformed vacuum expectation values of time-ordered products of field operators of the interacting theory. Together with the generating functional of the latter established in Wiesendanger (2011 arXiv:1103.1012) any transition amplitude can in principle be computed consistently to any order in perturbative quantum gravity.

Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of Rényi-Wehrl entropy

NASA Astrophysics Data System (ADS)

Calixto, M.; Romera, E.

2015-02-01

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the Rényi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isostructural with silicene.

Free-space quantum key distribution by rotation-invariant twisted photons.

PubMed

Vallone, Giuseppe; D'Ambrosio, Vincenzo; Sponselli, Anna; Slussarenko, Sergei; Marrucci, Lorenzo; Sciarrino, Fabio; Villoresi, Paolo

2014-08-08

"Twisted photons" are photons carrying a well-defined nonzero value of orbital angular momentum (OAM). The associated optical wave exhibits a helical shape of the wavefront (hence the name) and an optical vortex at the beam axis. The OAM of light is attracting a growing interest for its potential in photonic applications ranging from particle manipulation, microscopy, and nanotechnologies to fundamental tests of quantum mechanics, classical data multiplexing, and quantum communication. Hitherto, however, all results obtained with optical OAM were limited to laboratory scale. Here, we report the experimental demonstration of a link for free-space quantum communication with OAM operating over a distance of 210 m. Our method exploits OAM in combination with optical polarization to encode the information in rotation-invariant photonic states, so as to guarantee full independence of the communication from the local reference frames of the transmitting and receiving units. In particular, we implement quantum key distribution, a protocol exploiting the features of quantum mechanics to guarantee unconditional security in cryptographic communication, demonstrating error-rate performances that are fully compatible with real-world application requirements. Our results extend previous achievements of OAM-based quantum communication by over 2 orders of magnitude in the link scale, providing an important step forward in achieving the vision of a worldwide quantum network.

Free-Space Quantum Key Distribution by Rotation-Invariant Twisted Photons

NASA Astrophysics Data System (ADS)

Vallone, Giuseppe; D'Ambrosio, Vincenzo; Sponselli, Anna; Slussarenko, Sergei; Marrucci, Lorenzo; Sciarrino, Fabio; Villoresi, Paolo

2014-08-01

"Twisted photons" are photons carrying a well-defined nonzero value of orbital angular momentum (OAM). The associated optical wave exhibits a helical shape of the wavefront (hence the name) and an optical vortex at the beam axis. The OAM of light is attracting a growing interest for its potential in photonic applications ranging from particle manipulation, microscopy, and nanotechnologies to fundamental tests of quantum mechanics, classical data multiplexing, and quantum communication. Hitherto, however, all results obtained with optical OAM were limited to laboratory scale. Here, we report the experimental demonstration of a link for free-space quantum communication with OAM operating over a distance of 210 m. Our method exploits OAM in combination with optical polarization to encode the information in rotation-invariant photonic states, so as to guarantee full independence of the communication from the local reference frames of the transmitting and receiving units. In particular, we implement quantum key distribution, a protocol exploiting the features of quantum mechanics to guarantee unconditional security in cryptographic communication, demonstrating error-rate performances that are fully compatible with real-world application requirements. Our results extend previous achievements of OAM-based quantum communication by over 2 orders of magnitude in the link scale, providing an important step forward in achieving the vision of a worldwide quantum network.

Non-Separability and Synchronicity: Pauli, Jung and a New Historical, Philosophical Perspective on Quantum Physics

NASA Astrophysics Data System (ADS)

Giannetto, E. A.; Pozzi, F.

We would like to discuss the historical emergence of quantum physics and quantum non-separability, by analysing Pauli's point of view in relation to Jung's ideas. Recent inquiries on EPR shows that quantum non-separability indicates an a-causal connection of the "quantum reality" for space-like intervals ("simultaneity region ") of world (measurement) events: this non-causal connection is the physical counterpart of what Jung called "synchronicity " with an assessment given also by Pauli. This does not imply any violation of mechanical causality by any introduction of action-at-a-distance. From a physical point of view a-causal connections can be interpreted as implying a particular quantum topology of space-time, which leads to a non-mechanistic conception of nature and which could be related to a holistic quantum dynamical reality of the world like Bohm's "holomovement" or "light". This kind of non-mechanistic conception of nature as well as the idea of non-separability of the world and of synchronicity, as stated by Jung itself, was developed by Leibnitz: from this point of view, we can look at quantum physics (as well as for relativity it was shown) as related to a new emergence of concepts belonging to the Leibnitzian (anti-Newtonian) tradition.

Quantum entanglement in inhomogeneous 1D systems

NASA Astrophysics Data System (ADS)

Ramírez, Giovanni

2018-04-01

The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our inhomogeneous system, the inhomogeneity parameter, h, allows us to tune different regimes where a volumetric violation of the area law appears. We apply the strong disorder renormalization group to describe the maximally entangled state of the system in a strong inhomogeneity regime. Moreover, in a weak inhomogeneity regime, we use a continuum approximation to describe the state as a thermo-field double in a conformal field theory with an effective temperature which is proportional to the inhomogeneity parameter of the system. The latter description also shows that the universal scaling features of this model are captured by a massless Dirac fermion in a curved space-time with constant negative curvature R = h2, providing another example of the relation between quantum entanglement and space-time geometry. The results we discuss here were already published before, but here we present a more didactic exposure of basic concepts of the rainbow system for the students attending the Latin American School of Physics "Marcos Moshinsky" 2017.

Rotations of a logical qubit using the quantum Zeno effect extended to a manifold

NASA Astrophysics Data System (ADS)

Touzard, S.; Grimm, A.; Leghtas, Z.; Mundhada, S. O.; Reinhold, P.; Heeres, R.; Axline, C.; Reagor, M.; Chou, K.; Blumoff, J.; Sliwa, K. M.; Shankar, S.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.

Encoding Quantum Information in the large Hilbert space of a harmonic oscillator has proven to have advantages over encoding in a register of physical qubits, but has also provided new challenges. While recent experiments have demonstrated quantum error correction using such an encoding based on superpositions of coherent states, these codes are still susceptible to non-corrected errors and lack controllability: compared to physical qubits it is hard to make arbitrary states and to perform operations on them. Our approach is to engineer the dynamics and the dissipation of a microwave cavity to implement a continuous dissipative measurement yielding two degenerate outcomes. This extends the quantum Zeno effect to a manifold, which in our case is spanned by two coherent states of opposite phases. In this second talk we present the result and analysis of an experiment that performs rotations on a logical qubit encoded in this protected manifold. Work supported by: ARO, ONR, AFOSR and YINQE.

Rotations of a logical qubit using the quantum Zeno effect extended to a manifold - Part 1

NASA Astrophysics Data System (ADS)

Grimm, A.; Touzard, S.; Leghtas, Z.; Mundhada, S. O.; Reinhold, P.; Heeres, R.; Axline, C.; Reagor, M.; Chou, K.; Blumoff, J.; Sliwa, K. M.; Shankar, S.; Frunzio, L.; Schoelkopf, R. J.; Mirrahimi, M.; Devoret, M. H.

Encoding Quantum Information in the large Hilbert space of a harmonic oscillator has proven to have advantages over encoding in a register of physical qubits, but has also provided new challenges. While recent experiments have demonstrated quantum error correction using such an encoding based on superpositions of coherent states, these codes are still susceptible to non-corrected errors and lack controllability: compared to physical qubits it is hard to make arbitrary states and to perform operations on them. Our approach is to engineer the dynamics and the dissipation of a microwave cavity to implement a continuous dissipative measurement yielding two degenerate outcomes. This extends the quantum Zeno effect to a manifold, which in our case is spanned by two coherent states of opposite phases. In this first talk we present the concept and architecture of an experiment that performs rotations on a logical qubit encoded in this protected manifold. Work supported by: ARO, ONR, AFOSR and YINQE.

Fermion-to-qubit mappings with varying resource requirements for quantum simulation

NASA Astrophysics Data System (ADS)

Steudtner, Mark; Wehner, Stephanie

2018-06-01

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. Interestingly, the minimal requirement of qubits for simulating Fermions seems to be agnostic of the actual number of particles as well as other symmetries. This leads to qubit requirements that are well above the minimal requirements as suggested by combinatorial considerations. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a nonlinear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with a more modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.

Long-distance quantum communication over noisy networks without long-time quantum memory

NASA Astrophysics Data System (ADS)

Mazurek, Paweł; Grudka, Andrzej; Horodecki, Michał; Horodecki, Paweł; Łodyga, Justyna; Pankowski, Łukasz; PrzysieŻna, Anna

2014-12-01

The problem of sharing entanglement over large distances is crucial for implementations of quantum cryptography. A possible scheme for long-distance entanglement sharing and quantum communication exploits networks whose nodes share Einstein-Podolsky-Rosen (EPR) pairs. In Perseguers et al. [Phys. Rev. A 78, 062324 (2008), 10.1103/PhysRevA.78.062324] the authors put forward an important isomorphism between storing quantum information in a dimension D and transmission of quantum information in a D +1 -dimensional network. We show that it is possible to obtain long-distance entanglement in a noisy two-dimensional (2D) network, even when taking into account that encoding and decoding of a state is exposed to an error. For 3D networks we propose a simple encoding and decoding scheme based solely on syndrome measurements on 2D Kitaev topological quantum memory. Our procedure constitutes an alternative scheme of state injection that can be used for universal quantum computation on 2D Kitaev code. It is shown that the encoding scheme is equivalent to teleporting the state, from a specific node into a whole two-dimensional network, through some virtual EPR pair existing within the rest of network qubits. We present an analytic lower bound on fidelity of the encoding and decoding procedure, using as our main tool a modified metric on space-time lattice, deviating from a taxicab metric at the first and the last time slices.

Mixed quantum/classical theory of rotationally and vibrationally inelastic scattering in space-fixed and body-fixed reference frames

NASA Astrophysics Data System (ADS)

Semenov, Alexander; Babikov, Dmitri

2013-11-01

We formulated the mixed quantum/classical theory for rotationally and vibrationally inelastic scattering process in the diatomic molecule + atom system. Two versions of theory are presented, first in the space-fixed and second in the body-fixed reference frame. First version is easy to derive and the resultant equations of motion are transparent, but the state-to-state transition matrix is complex-valued and dense. Such calculations may be computationally demanding for heavier molecules and/or higher temperatures, when the number of accessible channels becomes large. In contrast, the second version of theory requires some tedious derivations and the final equations of motion are rather complicated (not particularly intuitive). However, the state-to-state transitions are driven by real-valued sparse matrixes of much smaller size. Thus, this formulation is the method of choice from the computational point of view, while the space-fixed formulation can serve as a test of the body-fixed equations of motion, and the code. Rigorous numerical tests were carried out for a model system to ensure that all equations, matrixes, and computer codes in both formulations are correct.

Elementary derivation of the quantum propagator for the harmonic oscillator

NASA Astrophysics Data System (ADS)

Shao, Jiushu

2016-10-01

Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.

A hybrid quantum eraser scheme for characterization of free-space and fiber communication channels

NASA Astrophysics Data System (ADS)

Nape, Isaac; Kyeremah, Charlotte; Vallés, Adam; Rosales-Guzmán, Carmelo; Buah-Bassuah, Paul K.; Forbes, Andrew

2018-02-01

We demonstrate a simple projective measurement based on the quantum eraser concept that can be used to characterize the disturbances of any communication channel. Quantum erasers are commonly implemented as spatially separated path interferometric schemes. Here we exploit the advantages of redefining the which-path information in terms of spatial modes, replacing physical paths with abstract paths of orbital angular momentum (OAM). Remarkably, vector modes (natural modes of free-space and fiber) have a non-separable feature of spin-orbit coupled states, equivalent to the description of two independently marked paths. We explore the effects of fiber perturbations by probing a step-index optical fiber channel with a vector mode, relevant to high-order spatial mode encoding of information for ultra-fast fiber communications.

Excited-state quantum phase transitions in systems with two degrees of freedom: Level density, level dynamics, thermal properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stránský, Pavel; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510, México, D.F.; Macek, Michal

2014-06-15

Quantum systems with a finite number of freedom degrees f develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f, particularly f=2, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition. --more » Highlights: •ESQPTs found in infinite-size limit of systems with low numbers of freedom degrees f. •ESQPTs related to non-analytical evolutions of classical phase–space properties. •ESQPT signatures analyzed for general f, particularly f=2, extending known case f=1. •ESQPT signatures identified in smoothened density and flow of energy spectrum. •ESQPTs shown to induce a new type of thermodynamic anomalies.« less

Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO 4

DOE PAGES

Paddison, Joseph A. M.; Daum, Marcus; Dun, Zhiling; ...

2016-12-05

A quantum spin liquid (QSL) is an exotic state of matter in which electrons’ spins are quantum entangled over long distances, but do not show magnetic order in the zero-temperature limit. The observation of QSL states is a central aim of experimental physics, because they host collective excitations that transcend our knowledge of quantum matter; however, examples in real materials are scarce. We report neutron-scattering experiments on YbMgGaO 4, a QSL candidate in which Yb 3+ ions with effective spin-1/2 occupy a triangular lattice. Furthermore, our measurements reveal a continuum of magnetic excitations—the essential experimental hallmark of a QSL7—at verymore » low temperature (0.06 K). The origin of this peculiar excitation spectrum is a crucial question, because isotropic nearest-neighbour interactions do not yield a QSL ground state on the triangular lattice. In using measurements the field-polarized state, we identify antiferromagnetic next-nearest-neighbour interactions spin-space anisotropies and chemical disorder between the magnetic layers as key ingredients in YbMgGaO 4.« less

Quantum gravity as an information network self-organization of a 4D universe

NASA Astrophysics Data System (ADS)

Trugenberger, Carlo A.

2015-10-01

I propose a quantum gravity model in which the fundamental degrees of freedom are information bits for both discrete space-time points and links connecting them. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links. As a result of the frustration between these two terms, the ground state self-organizes as a new type of low-clustering graph with finite Hausdorff dimension 4. The spectral dimension is lower than the Hausdorff dimension: it coincides with the Hausdorff dimension 4 at a first quantum phase transition corresponding to an IR fixed point, while at a second quantum phase transition describing small scales space-time dissolves into disordered information bits. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. At finite temperatures the universe graph emerges without a big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe graph unfolds and expands by lowering its connectivity, a mechanism I have called topological expansion. The model admits topological black hole excitations corresponding to graphs containing holes with no space-time inside and with "Schwarzschild-like" horizons with a lower spectral dimension.

High-Dimensional Quantum Information Processing with Linear Optics

NASA Astrophysics Data System (ADS)

Fitzpatrick, Casey A.

Quantum information processing (QIP) is an interdisciplinary field concerned with the development of computers and information processing systems that utilize quantum mechanical properties of nature to carry out their function. QIP systems have become vastly more practical since the turn of the century. Today, QIP applications span imaging, cryptographic security, computation, and simulation (quantum systems that mimic other quantum systems). Many important strategies improve quantum versions of classical information system hardware, such as single photon detectors and quantum repeaters. Another more abstract strategy engineers high-dimensional quantum state spaces, so that each successful event carries more information than traditional two-level systems allow. Photonic states in particular bring the added advantages of weak environmental coupling and data transmission near the speed of light, allowing for simpler control and lower system design complexity. In this dissertation, numerous novel, scalable designs for practical high-dimensional linear-optical QIP systems are presented. First, a correlated photon imaging scheme using orbital angular momentum (OAM) states to detect rotational symmetries in objects using measurements, as well as building images out of those interactions is reported. Then, a statistical detection method using chains of OAM superpositions distributed according to the Fibonacci sequence is established and expanded upon. It is shown that the approach gives rise to schemes for sorting, detecting, and generating the recursively defined high-dimensional states on which some quantum cryptographic protocols depend. Finally, an ongoing study based on a generalization of the standard optical multiport for applications in quantum computation and simulation is reported upon. The architecture allows photons to reverse momentum inside the device. This in turn enables realistic implementation of controllable linear-optical scattering vertices for carrying out quantum walks on arbitrary graph structures, a powerful tool for any quantum computer. It is shown that the novel architecture provides new, efficient capabilities for the optical quantum simulation of Hamiltonians and topologically protected states. Further, these simulations use exponentially fewer resources than feedforward techniques, scale linearly to higher-dimensional systems, and use only linear optics, thus offering a concrete experimentally achievable implementation of graphical models of discrete-time quantum systems.

A lattice approach to spinorial quantum gravity

NASA Technical Reports Server (NTRS)

Renteln, Paul; Smolin, Lee

1989-01-01

A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.

The Principle of the Fermionic Projector: An Approach for Quantum Gravity?

NASA Astrophysics Data System (ADS)

Finster, Felix

In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection to the continuum theory and state recent results. In the last two sections, we speculate on how it might be possible to describe quantum gravity within this framework.

Decoherence of high-energy electrons in weakly disordered quantum Hall edge states

NASA Astrophysics Data System (ADS)

Nigg, Simon E.; Lunde, Anders Mathias

2016-07-01

We investigate theoretically the phase coherence of electron transport in edge states of the integer quantum Hall effect at filling factor ν =2 , in the presence of disorder and inter edge state Coulomb interaction. Within a Fokker-Planck approach, we calculate analytically the visibility of the Aharonov-Bohm oscillations of the current through an electronic Mach-Zehnder interferometer. In agreement with recent experiments, we find that the visibility is independent of the energy of the current-carrying electrons injected high above the Fermi sea. Instead, it is the amount of disorder at the edge that sets the phase space available for inter edge state energy exchange and thereby controls the visibility suppression.

Quantum cryptography for secure free-space communications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hughes, R.J.; Buttler, W.T.; Kwiat, P.G.

1999-03-01

The secure distribution of the secret random bit sequences known as key material, is an essential precursor to their use for the encryption and decryption of confidential communications. Quantum cryptography is a new technique for secure key distribution with single-photon transmissions: Heisenberg`s uncertainty principle ensures that an adversary can neither successfully tap the key transmissions, nor evade detection (eavesdropping raises the key error rate above a threshold value). The authors have developed experimental quantum cryptography systems based on the transmission of non-orthogonal photon polarization states to generate shared key material over line-of-sight optical links. Key material is built up usingmore » the transmission of a single-photon per bit of an initial secret random sequence. A quantum-mechanically random subset of this sequence is identified, becoming the key material after a data reconciliation stage with the sender. The authors have developed and tested a free-space quantum key distribution (QKD) system over an outdoor optical path of {approximately}1 km at Los Alamos National Laboratory under nighttime conditions. Results show that free-space QKD can provide secure real-time key distribution between parties who have a need to communicate secretly. Finally, they examine the feasibility of surface to satellite QKD.« less

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Wigner Function Reconstruction in Levitated Optomechanics

NASA Astrophysics Data System (ADS)

Rashid, Muddassar; Toroš, Marko; Ulbricht, Hendrik

2017-10-01

We demonstrate the reconstruction of theWigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the efect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

2017-12-01

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

Coherent state quantization of quaternions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Muraleetharan, B., E-mail: bbmuraleetharan@jfn.ac.lk, E-mail: santhar@gmail.com; Thirulogasanthar, K., E-mail: bbmuraleetharan@jfn.ac.lk, E-mail: santhar@gmail.com

Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols, and related quantities are analyzed. Quaternionic version of the harmonic oscillator and Weyl-Heisenberg algebra are also obtained.

Atomic Bose-Hubbard Systems with Single-Particle Control

NASA Astrophysics Data System (ADS)

Preiss, Philipp Moritz

Experiments with ultracold atoms in optical lattices provide outstanding opportunities to realize exotic quantum states due to a high degree of tunability and control. In this thesis, I present experiments that extend this control from global parameters to the level of individual particles. Using a quantum gas microscope for 87Rb, we have developed a single-site addressing scheme based on digital amplitude holograms. The system self-corrects for aberrations in the imaging setup and creates arbitrary beam profiles. We are thus able to shape optical potentials on the scale of single lattice sites and control the dynamics of individual atoms. We study the role of quantum statistics and interactions in the Bose-Hubbard model on the fundamental level of two particles. Bosonic quantum statistics are apparent in the Hong-Ou-Mandel interference of massive particles, which we observe in tailored double-well potentials. These underlying statistics, in combination with tunable repulsive interactions, dominate the dynamics in single- and two-particle quantum walks. We observe highly coherent position-space Bloch oscillations, bosonic bunching in Hanbury Brown-Twiss interference and the fermionization of strongly interacting bosons. Many-body states of indistinguishable quantum particles are characterized by large-scale spatial entanglement, which is difficult to detect in itinerant systems. Here, we extend the concept of Hong-Ou-Mandel interference from individual particles to many-body states to directly quantify entanglement entropy. We perform collective measurements on two copies of a quantum state and detect entanglement entropy through many-body interference. We measure the second order Renyi entropy in small Bose-Hubbard systems and detect the buildup of spatial entanglement across the superfluid-insulator transition. Our experiments open new opportunities for the single-particle-resolved preparation and characterization of many-body quantum states.

Tunneling time in space fractional quantum mechanics

NASA Astrophysics Data System (ADS)

Hasan, Mohammad; Mandal, Bhabani Prasad

2018-02-01

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary phase method. We show that tunneling time depends upon the width b of the barrier for b → ∞ and therefore Hartman effect doesn't exist in space fractional quantum mechanics. Interestingly we found that the tunneling time monotonically reduces with increasing b. The tunneling time is smaller in space fractional quantum mechanics as compared to the case of standard quantum mechanics. We recover the Hartman effect of standard quantum mechanics as a special case of space fractional quantum mechanics.

Exact Solution of a Two-Species Quantum Dimer Model for Pseudogap Metals

NASA Astrophysics Data System (ADS)

Feldmeier, Johannes; Huber, Sebastian; Punk, Matthias

2018-05-01

We present an exact ground state solution of a quantum dimer model introduced by Punk, Allais, and Sachdev [Quantum dimer model for the pseudogap metal, Proc. Natl. Acad. Sci. U.S.A. 112, 9552 (2015)., 10.1073/pnas.1512206112], which features ordinary bosonic spin-singlet dimers as well as fermionic dimers that can be viewed as bound states of spinons and holons in a hole-doped resonating valence bond liquid. Interestingly, this model captures several essential properties of the metallic pseudogap phase in high-Tc cuprate superconductors. We identify a line in parameter space where the exact ground state wave functions can be constructed at an arbitrary density of fermionic dimers. At this exactly solvable line the ground state has a huge degeneracy, which can be interpreted as a flat band of fermionic excitations. Perturbing around the exactly solvable line, this degeneracy is lifted and the ground state is a fractionalized Fermi liquid with a small pocket Fermi surface in the low doping limit.

Phase diagram and quench dynamics of the cluster-XY spin chain

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Adiabatic gate teleportation.

PubMed

Bacon, Dave; Flammia, Steven T

2009-09-18

The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. This construction allows for geometric robustness based upon the control of two independent qubit interactions. Further, our piecewise adiabatic evolution easily relates to the quantum circuit model, enabling the use of standard methods from fault-tolerance theory for establishing thresholds.

Phase diagram and quench dynamics of the cluster-XY spin chain.

PubMed

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Fate of the Hoop Conjecture in Quantum Gravity.

PubMed

Anzà, Fabio; Chirco, Goffredo

2017-12-08

We consider a closed region R of 3D quantum space described via SU(2) spin networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary ∂R and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interpret such phenomenon as a pregeometric analogue of Thorne's "hoop conjecture," at the core of the formation of a horizon in general relativity.

de Sitter space as a tensor network: Cosmic no-hair, complementarity, and complexity

NASA Astrophysics Data System (ADS)

Bao, Ning; Cao, ChunJun; Carroll, Sean M.; Chatwin-Davies, Aidan

2017-12-01

We investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). We also suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti-de Sitter space.

Complex Quantum Network Manifolds in Dimension d > 2 are Scale-Free

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph

2015-09-01

In quantum gravity, several approaches have been proposed until now for the quantum description of discrete geometries. These theoretical frameworks include loop quantum gravity, causal dynamical triangulations, causal sets, quantum graphity, and energetic spin networks. Most of these approaches describe discrete spaces as homogeneous network manifolds. Here we define Complex Quantum Network Manifolds (CQNM) describing the evolution of quantum network states, and constructed from growing simplicial complexes of dimension . We show that in d = 2 CQNM are homogeneous networks while for d > 2 they are scale-free i.e. they are characterized by large inhomogeneities of degrees like most complex networks. From the self-organized evolution of CQNM quantum statistics emerge spontaneously. Here we define the generalized degrees associated with the -faces of the -dimensional CQNMs, and we show that the statistics of these generalized degrees can either follow Fermi-Dirac, Boltzmann or Bose-Einstein distributions depending on the dimension of the -faces.

Coherent inflationary dynamics for Bose-Einstein condensates crossing a quantum critical point

NASA Astrophysics Data System (ADS)

Feng, Lei; Clark, Logan W.; Gaj, Anita; Chin, Cheng

2018-03-01

Quantum phase transitions, transitions between many-body ground states, are of extensive interest in research ranging from condensed-matter physics to cosmology1-4. Key features of the phase transitions include a stage with rapidly growing new order, called inflation in cosmology5, followed by the formation of topological defects6-8. How inflation is initiated and evolves into topological defects remains a hot topic of debate. Ultracold atomic gas offers a pristine and tunable platform to investigate quantum critical dynamics9-21. We report the observation of coherent inflationary dynamics across a quantum critical point in driven Bose-Einstein condensates. The inflation manifests in the exponential growth of density waves and populations in well-resolved momentum states. After the inflation stage, extended coherent dynamics is evident in both real and momentum space. We present an intuitive description of the quantum critical dynamics in our system and demonstrate the essential role of phase fluctuations in the formation of topological defects.

Silicon quantum processor with robust long-distance qubit couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tosi, Guilherme; Mohiyaddin, Fahd A.; Schmitt, Vivien

Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowingmore » selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.« less

Coherence in quantum estimation

NASA Astrophysics Data System (ADS)

Giorda, Paolo; Allegra, Michele

2018-01-01

The geometry of quantum states provides a unifying framework for estimation processes based on quantum probes, and it establishes the ultimate bounds of the achievable precision. We show a relation between the statistical distance between infinitesimally close quantum states and the second order variation of the coherence of the optimal measurement basis with respect to the state of the probe. In quantum phase estimation protocols, this leads to propose coherence as the relevant resource that one has to engineer and control to optimize the estimation precision. Furthermore, the main object of the theory i.e. the symmetric logarithmic derivative, in many cases allows one to identify a proper factorization of the whole Hilbert space in two subsystems. The factorization allows one to discuss the role of coherence versus correlations in estimation protocols; to show how certain estimation processes can be completely or effectively described within a single-qubit subsystem; and to derive lower bounds for the scaling of the estimation precision with the number of probes used. We illustrate how the framework works for both noiseless and noisy estimation procedures, in particular those based on multi-qubit GHZ-states. Finally we succinctly analyze estimation protocols based on zero-temperature critical behavior. We identify the coherence that is at the heart of their efficiency, and we show how it exhibits the non-analyticities and scaling behavior proper of a large class of quantum phase transitions.

Transport properties of silicon complementary-metal-oxide semiconductor quantum well field-effect transistors

NASA Astrophysics Data System (ADS)

Naquin, Clint Alan

Introducing explicit quantum transport into silicon (Si) transistors in a manner compatible with industrial fabrication has proven challenging, yet has the potential to transform the performance horizons of large scale integrated Si devices and circuits. Explicit quantum transport as evidenced by negative differential transconductances (NDTCs) has been observed in a set of quantum well (QW) n-channel metal-oxide-semiconductor (NMOS) transistors fabricated using industrial silicon complementary MOS processing. The QW potential was formed via lateral ion implantation doping on a commercial 45 nm technology node process line, and measurements of the transfer characteristics show NDTCs up to room temperature. Detailed gate length and temperature dependence characteristics of the NDTCs in these devices have been measured. Gate length dependence of NDTCs shows a correlation of the interface channel length with the number of NDTCs formed as well as with the gate voltage (VG) spacing between NDTCs. The VG spacing between multiple NDTCs suggests a quasi-parabolic QW potential profile. The temperature dependence is consistent with partial freeze-out of carrier concentration against a degenerately doped background. A folding amplifier frequency multiplier circuit using a single QW NMOS transistor to generate a folded current-voltage transfer function via a NDTC was demonstrated. Time domain data shows frequency doubling in the kHz range at room temperature, and Fourier analysis confirms that the output is dominated by the second harmonic of the input. De-embedding the circuit response characteristics from parasitic cable and contact impedances suggests that in the absence of parasitics the doubling bandwidth could be as high as 10 GHz in a monolithic integrated circuit, limited by the transresistance magnitude of the QW NMOS. This is the first example of a QW device fabricated by mainstream Si CMOS technology being used in a circuit application and establishes the feasibility of scalable CMOS circuits that exploit explicit quantum transport. Ongoing quantum transport simulations based off of the spatial dopant distribution suggests a quasi-parabolic potential profile. Energy spacings between resonant transmission states are not consistent with experimental data, suggesting that either the assumed transport model is incomplete, or scattering mechanisms significantly mix the quasi-bound states and broaden the energy spacings.

Real-time imaging of spin-to-orbital angular momentum hybrid remote state preparation

NASA Astrophysics Data System (ADS)

Erhard, Manuel; Qassim, Hammam; Mand, Harjaspreet; Karimi, Ebrahim; Boyd, Robert W.

2015-08-01

There exists two prominent methods to transfer information between two spatially separated parties, namely Alice (A) and Bob (B): quantum teleportation and remote state preparation. However, the difference between these methods is, in the teleportation scheme, the state to be transferred is completely unknown, whereas in state preparation it should be known to the sender. In addition, photonic state teleportation is probabilistic due to the impossibility of performing a two-particle complete Bell-state analysis with linear optics, while remote state preparation can be performed deterministically. Here we report the first realization of photonic hybrid remote state preparation from spin to orbital angular momentum degrees of freedom. In our scheme, the polarization state of photon A is transferred to orbital angular momentum of photon B. The prepared states are visualized in real time by means of an intensified CCD camera. The quality of the prepared states is verified by performing quantum state tomography, which confirms an average fidelity higher than 99.4%. We believe that this experiment paves the way towards a novel means of quantum communication in which encryption and decryption are carried out in naturally different Hilbert spaces, and therefore may provide a means for enhancing security.

Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance

NASA Astrophysics Data System (ADS)

Rovelli, Carlo; Gaul, Marcus

This series of lectures gives an introduction to the non-perturbative and background-independent formulation for a quantum theory of gravitation which is called loop quantum gravity . The Hilbert space of kinematical quantum states is constructed and a complete basis of spin network states is introduced. Afterwards an application of the formalism is provided by the spectral analysis of the area operator, which is the quantum analogue of the classical area function. This leads to one of the key results of loop quantum gravity obtained in the last few years: the derivation of the discreteness of the geometry and the computation of the quanta of area. Special importance is attached to the role played by the diffeomorphism group in order to clarify the notion of observability in general relativity - a concept far from being trivial. Finally an outlock onto a possible dynamical extension of the theory is given, leading to a "sum over histories" approach, namely a so-called spin foam model . Throughout the whole lecture great significance is attached to conceptual and interpretational issues.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ivanov, Sergei D., E-mail: sergei.ivanov@unirostock.de; Grant, Ian M.; Marx, Dominik

With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently andmore » thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.« less

Nanofabrication of Gate-defined GaAs/AlGaAs Lateral Quantum Dots

PubMed Central

Bureau-Oxton, Chloé; Camirand Lemyre, Julien; Pioro-Ladrière, Michel

2013-01-01

A quantum computer is a computer composed of quantum bits (qubits) that takes advantage of quantum effects, such as superposition of states and entanglement, to solve certain problems exponentially faster than with the best known algorithms on a classical computer. Gate-defined lateral quantum dots on GaAs/AlGaAs are one of many avenues explored for the implementation of a qubit. When properly fabricated, such a device is able to trap a small number of electrons in a certain region of space. The spin states of these electrons can then be used to implement the logical 0 and 1 of the quantum bit. Given the nanometer scale of these quantum dots, cleanroom facilities offering specialized equipment- such as scanning electron microscopes and e-beam evaporators- are required for their fabrication. Great care must be taken throughout the fabrication process to maintain cleanliness of the sample surface and to avoid damaging the fragile gates of the structure. This paper presents the detailed fabrication protocol of gate-defined lateral quantum dots from the wafer to a working device. Characterization methods and representative results are also briefly discussed. Although this paper concentrates on double quantum dots, the fabrication process remains the same for single or triple dots or even arrays of quantum dots. Moreover, the protocol can be adapted to fabricate lateral quantum dots on other substrates, such as Si/SiGe. PMID:24300661

Generalized quantum no-go theorems of pure states

NASA Astrophysics Data System (ADS)

Li, Hui-Ran; Luo, Ming-Xing; Lai, Hong

2018-07-01

Various results of the no-cloning theorem, no-deleting theorem and no-superposing theorem in quantum mechanics have been proved using the superposition principle and the linearity of quantum operations. In this paper, we investigate general transformations forbidden by quantum mechanics in order to unify these theorems. First, we prove that any useful information cannot be created from an unknown pure state which is randomly chosen from a Hilbert space according to the Harr measure. And then, we propose a unified no-go theorem based on a generalized no-superposing result. The new theorem includes the no-cloning theorem, no-anticloning theorem, no-partial-erasure theorem, no-splitting theorem, no-superposing theorem or no-encoding theorem as a special case. Moreover, it implies various new results. Third, we extend the new theorem into another form that includes the no-deleting theorem as a special case.

Remote creation of hybrid entanglement between particle-like and wave-like optical qubits

NASA Astrophysics Data System (ADS)

Morin, Olivier; Huang, Kun; Liu, Jianli; Le Jeannic, Hanna; Fabre, Claude; Laurat, Julien

2014-07-01

The wave-particle duality of light has led to two different encodings for optical quantum information processing. Several approaches have emerged based either on particle-like discrete-variable states (that is, finite-dimensional quantum systems) or on wave-like continuous-variable states (that is, infinite-dimensional systems). Here, we demonstrate the generation of entanglement between optical qubits of these different types, located at distant places and connected by a lossy channel. Such hybrid entanglement, which is a key resource for a variety of recently proposed schemes, including quantum cryptography and computing, enables information to be converted from one Hilbert space to the other via teleportation and therefore the connection of remote quantum processors based upon different encodings. Beyond its fundamental significance for the exploration of entanglement and its possible instantiations, our optical circuit holds promise for implementations of heterogeneous network, where discrete- and continuous-variable operations and techniques can be efficiently combined.

The Future of Theoretical Physics and Cosmology

NASA Astrophysics Data System (ADS)

Gibbons, G. W.; Shellard, E. P. S.; Rankin, S. J.

2009-08-01

Preface; List of contributors; 1. Introduction; Part I. Popular Symposium: 2. Our complex cosmos and its future Martin J. Rees; 3. Theories of everything and Hawking's wave function of the Universe James B. Hartle; 4. The problem of space-time singularities: implications for quantum gravity? Roger Penrose; 5. Warping spacetime Kip Thorne; 6. 60 years in a nutshell Stephen W. Hawking; Part II. Spacetime Singularities: 7. Cosmological perturbations and singularities George F. R. Ellis; 8. The quantum physics of chronology protection Matt Visser; 9. Energy dominance and the Hawking-Ellis vacuum conservation theorem Brandon Carter; 10. On the instability of extra space dimensions Roger Penrose; Part III. Black Holes: 11. Black hole uniqueness and the inner horizon stability problem Werner Israel; 12. Black holes in the real universe and their prospects as probes of relativistic gravity Martin J. Rees; 13. Primordial black holes Bernard Carr; 14. Black hole pair creation Simon F. Ross; 15. Black holes as accelerators Steven Giddings; Part IV. Hawking Radiation: 16. Black holes and string theory Malcolm Perry; 17. M theory and black hole quantum mechanics Joe Polchinski; 18. Playing with black strings Gary Horowitz; 19. Twenty years of debate with Stephen Leonard Susskind; Part V. Quantum Gravity: 20. Euclidean quantum gravity: the view from 2002 Gary Gibbons; 21. Zeta functions, anomalies and stable branes Ian Moss; 22. Some reflections on the status of conventional quantum theory when applied to quantum gravity Chris Isham; 23. Quantum geometry and its ramifications Abhay Ashtekar; 24. Topology change in quantum gravity Fay Dowker; Part VI. M Theory and Beyond: 25. The past and future of string theory Edward Witten; 26. String theory David Gross; 27. A brief description of string theory Michael Green; 28. The story of M Paul Townsend; 29. Gauged supergravity and holographic field theory Nick Warner; 30. 57 varieties in a NUTshell Chris Pope; Part VII. de Sitter Space: 31. Adventures in de Sitter space Raphael Bousso; 32. de Sitter space in non-critical string theory Andrew Strominger; 33. Supergravity, M theory and cosmology Renata Kallosh; Part VIII. Quantum Cosmology: 34. The state of the universe James B. Hartle; 35. Quantum cosmology Don Page; 36. Quantum cosmology and eternal inflation A. Vilenkin; 37. Probability in the deterministic theory known as quantum mechanics Bryce de Witt; 38. The interpretation of quantum cosmology and the problem of time J. Halliwell; 39. What local supersymmetry can do for quantum cosmology Peter D'Eath; Part IX. Cosmology: 40. Inflation and cosmological perturbations Alan Guth; 41. The future of cosmology: observational and computational prospects Paul Shellard; 42. The ekpyrotic universe and its cyclic extension Neil Turok; 43. Inflationary theory versus the ekpyrotic/cyclic scenario Andrei Linde; 44. Brane (new) worlds Pierre Binetruy; 45. Publications of Stephen Hawking; Index.

Self-starting harmonic frequency comb generation in a quantum cascade laser

NASA Astrophysics Data System (ADS)

Kazakov, Dmitry; Piccardo, Marco; Wang, Yongrui; Chevalier, Paul; Mansuripur, Tobias S.; Xie, Feng; Zah, Chung-en; Lascola, Kevin; Belyanin, Alexey; Capasso, Federico

2017-12-01

Optical frequency combs1,2 establish a rigid phase-coherent link between microwave and optical domains and are emerging as high-precision tools in an increasing number of applications3. Frequency combs with large intermodal spacing are employed in the field of microwave photonics for radiofrequency arbitrary waveform synthesis4,5 and for the generation of terahertz tones of high spectral purity in future wireless communication networks6,7. Here, we demonstrate self-starting harmonic frequency comb generation with a terahertz repetition rate in a quantum cascade laser. The large intermodal spacing caused by the suppression of tens of adjacent cavity modes originates from a parametric contribution to the gain due to temporal modulations of population inversion in the laser8,9. Using multiheterodyne self-detection, the mode spacing of the harmonic comb is shown to be uniform to within 5 × 10-12 parts of the central frequency. This new harmonic comb state extends the range of applications of quantum cascade laser frequency combs10-13.

Redundant Information and the Quantum-Classical Transition

ERIC Educational Resources Information Center

Riedel, Charles Jess

2012-01-01

A state selected at random from the Hilbert space of a many-body system is overwhelmingly likely to exhibit highly non-classical correlations. For these typical states, half of the environment must be measured by an observer to determine the state of a given subsystem. The objectivity of classical reality--the fact that multiple observers can each…

Anharmonic quantum mechanical systems do not feature phase space trajectories

NASA Astrophysics Data System (ADS)

Oliva, Maxime; Kakofengitis, Dimitris; Steuernagel, Ole

2018-07-01

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absence of trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.

Cooperative single-photon subradiant states in a three-dimensional atomic array

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jen, H.H., E-mail: sappyjen@gmail.com

2016-11-15

We propose a complete superradiant and subradiant states that can be manipulated and prepared in a three-dimensional atomic array. These subradiant states can be realized by absorbing a single photon and imprinting the spatially-dependent phases on the atomic system. We find that the collective decay rates and associated cooperative Lamb shifts are highly dependent on the phases we manage to imprint, and the subradiant state of long lifetime can be found for various lattice spacings and atom numbers. We also investigate both optically thin and thick atomic arrays, which can serve for systematic studies of super- and sub-radiance. Our proposal offers an alternative schememore » for quantum memory of light in a three-dimensional array of two-level atoms, which is applicable and potentially advantageous in quantum information processing. - Highlights: • Cooperative single-photon subradiant states in a three-dimensional atomic array. • Subradiant state manipulation via spatially-increasing phase imprinting. • Quantum storage of light in the subradiant state in two-level atoms.« less

Quantum robots and environments

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, P.

1998-08-01

Quantum robots and their interactions with environments of quantum systems are described, and their study justified. A quantum robot is a mobile quantum system that includes an on-board quantum computer and needed ancillary systems. Quantum robots carry out tasks whose goals include specified changes in the state of the environment, or carrying out measurements on the environment. Each task is a sequence of alternating computation and action phases. Computation phase activites include determination of the action to be carried out in the next phase, and recording of information on neighborhood environmental system states. Action phase activities include motion of themore » quantum robot and changes in the neighborhood environment system states. Models of quantum robots and their interactions with environments are described using discrete space and time. A unitary step operator T that gives the single time step dynamics is associated with each task. T=T{sub a}+T{sub c} is a sum of action phase and computation phase step operators. Conditions that T{sub a} and T{sub c} should satisfy are given along with a description of the evolution as a sum over paths of completed phase input and output states. A simple example of a task{emdash}carrying out a measurement on a very simple environment{emdash}is analyzed in detail. A decision tree for the task is presented and discussed in terms of the sums over phase paths. It is seen that no definite times or durations are associated with the phase steps in the tree, and that the tree describes the successive phase steps in each path in the sum over phase paths. {copyright} {ital 1998} {ital The American Physical Society}« less

Structure solution of network materials by solid-state NMR without knowledge of the crystallographic space group.

PubMed

Brouwer, Darren H

2013-01-01

An algorithm is presented for solving the structures of silicate network materials such as zeolites or layered silicates from solid-state (29)Si double-quantum NMR data for situations in which the crystallographic space group is not known. The algorithm is explained and illustrated in detail using a hypothetical two-dimensional network structure as a working example. The algorithm involves an atom-by-atom structure building process in which candidate partial structures are evaluated according to their agreement with Si-O-Si connectivity information, symmetry restraints, and fits to (29)Si double quantum NMR curves followed by minimization of a cost function that incorporates connectivity, symmetry, and quality of fit to the double quantum curves. The two-dimensional network material is successfully reconstructed from hypothetical NMR data that can be reasonably expected to be obtained for real samples. This advance in "NMR crystallography" is expected to be important for structure determination of partially ordered silicate materials for which diffraction provides very limited structural information. Copyright © 2013 Elsevier Inc. All rights reserved.

Quantum correlations are weaved by the spinors of the Euclidean primitives

PubMed Central

2018-01-01

The exceptional Lie group E8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which—thanks to their non-associativity—form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S3, with S7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S7, computed using manifestly local spinors within S3, thereby extending the stringent bounds of ±2 set by Bell inequalities to the bounds of ±22 on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell’s theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S3 and S7. PMID:29893385

Entangled spins and ghost-spins

NASA Astrophysics Data System (ADS)

Jatkar, Dileep P.; Narayan, K.

2017-09-01

We study patterns of quantum entanglement in systems of spins and ghost-spins regarding them as simple quantum mechanical toy models for theories containing negative norm states. We define a single ghost-spin as in [20] as a 2-state spin variable with an indefinite inner product in the state space. We find that whenever the spin sector is disentangled from the ghost-spin sector (both of which could be entangled within themselves), the reduced density matrix obtained by tracing over all the ghost-spins gives rise to positive entanglement entropy for positive norm states, while negative norm states have an entanglement entropy with a negative real part and a constant imaginary part. However when the spins are entangled with the ghost-spins, there are new entanglement patterns in general. For systems where the number of ghost-spins is even, it is possible to find subsectors of the Hilbert space where positive norm states always lead to positive entanglement entropy after tracing over the ghost-spins. With an odd number of ghost-spins however, we find that there always exist positive norm states with negative real part for entanglement entropy after tracing over the ghost-spins.

Quantum Dots Based Rad-Hard Computing and Sensors

NASA Technical Reports Server (NTRS)

Fijany, A.; Klimeck, G.; Leon, R.; Qiu, Y.; Toomarian, N.

2001-01-01

Quantum Dots (QDs) are solid-state structures made of semiconductors or metals that confine a small number of electrons into a small space. The confinement of electrons is achieved by the placement of some insulating material(s) around a central, well-conducting region. Thus, they can be viewed as artificial atoms. They therefore represent the ultimate limit of the semiconductor device scaling. Additional information is contained in the original extended abstract.

The Large, the Small and the Human Mind

NASA Astrophysics Data System (ADS)

Penrose, Roger; Longair, Malcolm; Abner Shimony, With; Cartwright, Nancy; Hawking, Stephen

2000-05-01

Foreword Malcolm Longair; 1. Space-time and cosmology Roger Penrose; 2. The mysteries of quantum physics Roger Penrose; 3. Physics and the mind Roger Penrose; 4. On mentality, quantum mechanics and the actualization of potentialities Abner Shimony; 5. Why physics? Nancy Cartwright; 6. The objections of an unashamed reductionist Stephen Hawking; 7. Response Roger Penrose; Appendix I: Goodstein's theorm and mathematical thinking; Appendix II: Experiments to test gravitationally induced state reduction.

A nonlinear ordinary differential equation associated with the quantum sojourn time

NASA Astrophysics Data System (ADS)

Benguria, Rafael D.; Duclos, Pierre; Fernández, Claudio; Sing-Long, Carlos

2010-11-01

We study a nonlinear ordinary differential equation on the half-line, with the Dirichlet boundary condition at the origin. This equation arises when studying the local maxima of the sojourn time for a free quantum particle whose states belong to an adequate subspace of the unit sphere of the corresponding Hilbert space. We establish several results concerning the existence and asymptotic behavior of the solutions.

[Carl Friedrich von Weizsäcker and the interpretations of quantum theory].

PubMed

Stöckler, Manfred

2014-01-01

What are 'interpretations' of quantum theory? What are the differences between Carl Friedrich von Weizsäkcker's approach and contemporary views? The various interpretations of quantum mechanics give diverse answers to questions concerning the relation between measuring process and standard time development, the embedding of quantum objects in space ('wave-particle-dualism'), and the reference of state vectors. Does the wave function describe states in the real world or does it refer to our knowledge about nature? First, some relevant conceptions in Weizsäcker's book The Structure of Physics (Der Aufbau der Physik, 1985) are introduced. In a second step I point out why his approach is not any longer present in contemporary debates. One reason is that Weizsäcker is mainly affected by classical philosophy (Platon, Aristoteles, Kant). He could not esteem the philosophy of science that was developed in the spirit of logical empiricism. So he lost interest in disputes with Anglo-Saxon philosophy of quantum mechanics. Especially his interpretation of probability and his analysis of the collapse of the state function as change in knowledge differ from contemporary standard views. In recent years, however, epistemic interpretations of quantum mechanics are proposed that share some of Weizsäcker's intuitions.

Secure communications using quantum cryptography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hughes, R.J.; Buttler, W.T.; Kwiat, P.G.

1997-08-01

The secure distribution of the secret random bit sequences known as {open_quotes}key{close_quotes} material, is an essential precursor to their use for the encryption and decryption of confidential communications. Quantum cryptography is an emerging technology for secure key distribution with single-photon transmissions, nor evade detection (eavesdropping raises the key error rate above a threshold value). We have developed experimental quantum cryptography systems based on the transmission of non-orthogonal single-photon states to generate shared key material over multi-kilometer optical fiber paths and over line-of-sight links. In both cases, key material is built up using the transmission of a single-photon per bit ofmore » an initial secret random sequence. A quantum-mechanically random subset of this sequence is identified, becoming the key material after a data reconciliation stage with the sender. In our optical fiber experiment we have performed quantum key distribution over 24-km of underground optical fiber using single-photon interference states, demonstrating that secure, real-time key generation over {open_quotes}open{close_quotes} multi-km node-to-node optical fiber communications links is possible. We have also constructed a quantum key distribution system for free-space, line-of-sight transmission using single-photon polarization states, which is currently undergoing laboratory testing. 7 figs.« less

Silicon quantum processor with robust long-distance qubit couplings.

PubMed

Tosi, Guilherme; Mohiyaddin, Fahd A; Schmitt, Vivien; Tenberg, Stefanie; Rahman, Rajib; Klimeck, Gerhard; Morello, Andrea

2017-09-06

Practical quantum computers require a large network of highly coherent qubits, interconnected in a design robust against errors. Donor spins in silicon provide state-of-the-art coherence and quantum gate fidelities, in a platform adapted from industrial semiconductor processing. Here we present a scalable design for a silicon quantum processor that does not require precise donor placement and leaves ample space for the routing of interconnects and readout devices. We introduce the flip-flop qubit, a combination of the electron-nuclear spin states of a phosphorus donor that can be controlled by microwave electric fields. Two-qubit gates exploit a second-order electric dipole-dipole interaction, allowing selective coupling beyond the nearest-neighbor, at separations of hundreds of nanometers, while microwave resonators can extend the entanglement to macroscopic distances. We predict gate fidelities within fault-tolerance thresholds using realistic noise models. This design provides a realizable blueprint for scalable spin-based quantum computers in silicon.Quantum computers will require a large network of coherent qubits, connected in a noise-resilient way. Tosi et al. present a design for a quantum processor based on electron-nuclear spins in silicon, with electrical control and coupling schemes that simplify qubit fabrication and operation.

Quantum free energy landscapes from ab initio path integral metadynamics: Double proton transfer in the formic acid dimer is concerted but not correlated.

PubMed

Ivanov, Sergei D; Grant, Ian M; Marx, Dominik

2015-09-28

With the goal of computing quantum free energy landscapes of reactive (bio)chemical systems in multi-dimensional space, we combine the metadynamics technique for sampling potential energy surfaces with the ab initio path integral approach to treating nuclear quantum motion. This unified method is applied to the double proton transfer process in the formic acid dimer (FAD), in order to study the nuclear quantum effects at finite temperatures without imposing a one-dimensional reaction coordinate or reducing the dimensionality. Importantly, the ab initio path integral metadynamics technique allows one to treat the hydrogen bonds and concomitant proton transfers in FAD strictly independently and thus provides direct access to the much discussed issue of whether the double proton transfer proceeds via a stepwise or concerted mechanism. The quantum free energy landscape we compute for this H-bonded molecular complex reveals that the two protons move in a concerted fashion from initial to product state, yet world-line analysis of the quantum correlations demonstrates that the protons are as quantum-uncorrelated at the transition state as they are when close to the equilibrium structure.

Entanglement and Weak Values: A Quantum Miracle Cookbook

NASA Astrophysics Data System (ADS)

Botero, Alonso

The concept of the weak value has proved to be a powerful and operationally grounded framework for the assignment of physical properties to a quantum system at any given time. More importantly, this framework has allowed us to identify a whole range of surprising quantum effects, or "miracles", which are readily testable but which lie buried "under the noise" when the results of measurements are not post-selected. In all cases, these miracles have to do with the fact that weak values can take values lying outside the conventional ranges of quantum expectation values. We explore the extent to which such miracles are possible within the weak value framework. As we show, given appropriate initial and final states, it is generally possible to produce any set of weak values that is consistent with the linearity of weak values, provided that the states are entangled states of the system with some external ancillary system. Through a simple constructive proof, we obtain a recipe for arbitrary quantum miracles, and give examples of some interesting applications. In particular, we show how the classical description of an infinitely-localized point in phase-space is contained in the weak-value framework augmented by quantum entanglement. [Editor's note: for a video of the talk given by Prof. Botero at the Aharonov-80 conference in 2012 at Chapman University, see http://quantum.chapman.edu/talk-27.

Quantum control and quantum tomography on neutral atom qudits

NASA Astrophysics Data System (ADS)

Sosa Martinez, Hector

Neutral atom systems are an appealing platform for the development and testing of quantum control and measurement techniques. This dissertation presents experimental investigations of control and measurement tools using as a testbed the 16-dimensional hyperfine manifold associated with the electronic ground state of cesium atoms. On the control side, we present an experimental realization of a protocol to implement robust unitary transformations in the presence of static and dynamic perturbations. We also present an experimental realization of inhomogeneous quantum control. Specifically, we demonstrate our ability to perform two different unitary transformations on atoms that see different light shifts from an optical addressing field. On the measurement side, we present experimental realizations of quantum state and process tomography. The state tomography project encompasses a comprehensive evaluation of several measurement strategies and state estimation algorithms. Our experimental results show that in the presence of experimental imperfections, there is a clear tradeoff between accuracy, efficiency and robustness in the reconstruction. The process tomography project involves an experimental demonstration of efficient reconstruction by using a set of intelligent probe states. Experimental results show that we are able to reconstruct unitary maps in Hilbert spaces with dimension ranging from d=4 to d=16. To the best of our knowledge, this is the first time that a unitary process in d=16 is successfully reconstructed in the laboratory.

Quantum error-correcting code for ternary logic

NASA Astrophysics Data System (ADS)

Majumdar, Ritajit; Basu, Saikat; Ghosh, Shibashis; Sur-Kolay, Susmita

2018-05-01

Ternary quantum systems are being studied because they provide more computational state space per unit of information, known as qutrit. A qutrit has three basis states, thus a qubit may be considered as a special case of a qutrit where the coefficient of one of the basis states is zero. Hence both (2 ×2 ) -dimensional and (3 ×3 ) -dimensional Pauli errors can occur on qutrits. In this paper, we (i) explore the possible (2 ×2 ) -dimensional as well as (3 ×3 ) -dimensional Pauli errors in qutrits and show that any pairwise bit swap error can be expressed as a linear combination of shift errors and phase errors, (ii) propose a special type of error called a quantum superposition error and show its equivalence to arbitrary rotation, (iii) formulate a nine-qutrit code which can correct a single error in a qutrit, and (iv) provide its stabilizer and circuit realization.

Entanglement via Faraday effect - an old tool at a new job for Quantum Networks

NASA Astrophysics Data System (ADS)

Polzik, Eugene

2002-05-01

A new approach to the problem of the quantum interface between light and atoms has been developed [1,2]. The method utilizes free space dispersive interaction of pulses of light with spin polarized atomic ensembles. Entanglement between the polarization state of light and the collective spin state of atoms is established by measurement, more precisely by detection of light in certain polarization basis. In the first demonstration of this approach [3] we have generated a long-lived entangled state of two separate macroscopic atomic samples by a polarization measurement on light transmitted through the samples. We then have shown that this approach also works for mapping of a quantum state of light onto long-lived atomic spin state [4] paving the road towards realization of the quantum memory for light. Progress with other communication protocols such as atomic state teleportation and multiparty networks will be presented. 1. A. Kuzmich and E. S. Polzik, Phys. Rev. Lett. (2000) 85, 5639. 2. Lu-Ming Duan, J.I. Cirac, P. Zoller and E. S. Polzik, Phys. Rev. Lett. (2000) 85, (25), 5643. 3. B. Julsgaard, A. Kozhekin, and E. S. Polzik, Nature, 413, 400 (2001). 4. J. L. Sorensen, B. Julsgaard, C. Schori and E. S. Polzik, submitted for publication.

Fundamentals of Free-Space Optical Communications

NASA Technical Reports Server (NTRS)

Dolinar, Sam; Moision, Bruce; Erkmen, Baris

2012-01-01

Free-space optical communication systems potentially gain many dBs over RF systems. There is no upper limit on the theoretically achievable photon efficiency when the system is quantum-noise-limited: a) Intensity modulations plus photon counting can achieve arbitrarily high photon efficiency, but with sub-optimal spectral efficiency. b) Quantum-ideal number states can achieve the ultimate capacity in the limit of perfect transmissivity. Appropriate error correction codes are needed to communicate reliably near the capacity limits. Poisson-modeled noises, detector losses, and atmospheric effects must all be accounted for: a) Theoretical models are used to analyze performance degradations. b) Mitigation strategies derived from this analysis are applied to minimize these degradations.

Positive contraction mappings for classical and quantum Schrödinger systems

NASA Astrophysics Data System (ADS)

Georgiou, Tryphon T.; Pavon, Michele

2015-03-01

The classical Schrödinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior. Jamison proved that the new law is obtained through a multiplicative functional transformation of the prior. This transformation is characterised by an automorphism on the space of endpoints probability measures, which has been studied by Fortet, Beurling, and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins by establishing solutions to Schrödinger systems for Markov chains. Our approach is based on the Hilbert metric and shows that the solution to the Schrödinger bridge is provided by the fixed point of a contractive map. We approach, in a similar manner, the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map for the cases where the marginals are either uniform or pure states. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.

High Storage Efficiency and Large Fractional Delay of EIT-Based Memory

NASA Astrophysics Data System (ADS)

Chen, Yi-Hsin; Lee, Meng-Jung; Wang, I.-Chung; Du, Shengwang; Chen, Yong-Fan; Chen, Ying-Cheng; Yu, Ite

2013-05-01

In long-distance quantum communication and optical quantum computation, an efficient and long-lived quantum memory is an important component. We first experimentally demonstrated that a time-space-reversing method plus the optimum pulse shape can improve the storage efficiency (SE) of light pulses to 78% in cold media based on the effect of electromagnetically induced transparency (EIT). We obtain a large fractional delay of 74 at 50% SE, which is the best record so far. The measured classical fidelity of the recalled pulse is higher than 90% and nearly independent of the storage time, implying that the optical memory maintains excellent phase coherence. Our results suggest the current result may be readily applied to single-photon quantum states due to quantum nature of the EIT light-matter inference. This study advances the EIT-based quantum memory in practical quantum information applications.