H-theorem in quantum physics

PubMed Central

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.

2016-01-01

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571

H-theorem in quantum physics

DOE PAGES

Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; ...

2016-09-12

Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less

De Finetti representation theorem for infinite-dimensional quantum systems and applications to quantum cryptography.

PubMed

Renner, R; Cirac, J I

2009-03-20

We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.

Geometry of the Adiabatic Theorem

ERIC Educational Resources Information Center

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

Analysis of non locality proofs in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2012-02-01

Two kinds of non-locality theorems in Quantum Mechanics are taken into account: the theorems based on the criterion of reality and the quite different theorem proposed by Stapp. In the present work the analyses of the theorem due to Greenberger, Horne, Shimony and Zeilinger, based on the criterion of reality, and of Stapp's argument are shown. The results of these analyses show that the alleged violations of locality cannot be considered definitive.

More on Weinberg's no-go theorem in quantum gravity

NASA Astrophysics Data System (ADS)

Nagahama, Munehiro; Oda, Ichiro

2018-05-01

We complement Weinberg's no-go theorem on the cosmological constant problem in quantum gravity by generalizing it to the case of a scale-invariant theory. Our analysis makes use of the effective action and the BRST symmetry in a manifestly covariant quantum gravity instead of the classical Lagrangian density and the G L (4 ) symmetry in classical gravity. In this sense, our proof is very general since it does not depend on details of quantum gravity and holds true for general gravitational theories which are invariant under diffeomorphisms. As an application of our theorem, we comment on an idea that in the asymptotic safety scenario the functional renormalization flow drives a cosmological constant to zero, solving the cosmological constant problem without reference to fine tuning of parameters. Finally, we also comment on the possibility of extending the Weinberg theorem in quantum gravity to the case where the translational invariance is spontaneously broken.

Efficiency and formalism of quantum games

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

Lee, C.F.; Johnson, Neil F.

We show that quantum games are more efficient than classical games and provide a saturated upper bound for this efficiency. We also demonstrate that the set of finite classical games is a strict subset of the set of finite quantum games. Our analysis is based on a rigorous formulation of quantum games, from which quantum versions of the minimax theorem and the Nash equilibrium theorem can be deduced.

Quantum probability rule: a generalization of the theorems of Gleason and Busch

NASA Astrophysics Data System (ADS)

Barnett, Stephen M.; Cresser, James D.; Jeffers, John; Pegg, David T.

2014-04-01

Busch's theorem deriving the standard quantum probability rule can be regarded as a more general form of Gleason's theorem. Here we show that a further generalization is possible by reducing the number of quantum postulates used by Busch. We do not assume that the positive measurement outcome operators are effects or that they form a probability operator measure. We derive a more general probability rule from which the standard rule can be obtained from the normal laws of probability when there is no measurement outcome information available, without the need for further quantum postulates. Our general probability rule has prediction-retrodiction symmetry and we show how it may be applied in quantum communications and in retrodictive quantum theory.

On One Possible Generalization of the Regression Theorem

NASA Astrophysics Data System (ADS)

Bogolubov, N. N.; Soldatov, A. V.

2018-03-01

A general approach to derivation of formally exact closed time-local or time-nonlocal evolution equations for non-equilibrium multi-time correlations functions made of observables of an open quantum system interacting simultaneously with external time-dependent classical fields and dissipative environment is discussed. The approach allows for the subsequent treatment of these equations within a perturbative scheme assuming that the system-environment interaction is weak.

A General No-Cloning Theorem for an infinite Multiverse

NASA Astrophysics Data System (ADS)

Gauthier, Yvon

2013-10-01

In this paper, I formulate a general no-cloning theorem which covers the quantum-mechanical and the theoretical quantum information cases as well as the cosmological multiverse theory. However, the main argument is topological and does not involve the peculiar copier devices of the quantum-mechanical and information-theoretic approaches to the no-cloning thesis. It is shown that a combinatorial set-theoretic treatment of the mathematical and physical spacetime continuum in cosmological or quantum-mechanical terms forbids an infinite (countable or uncountable) number of exact copies of finite elements (states) in the uncountable multiverse cosmology. The historical background draws on ideas from Weyl to Conway and Kochen on the free will theorem in quantum mechanics.

Strong converse theorems using Rényi entropies

NASA Astrophysics Data System (ADS)

Leditzky, Felix; Wilde, Mark M.; Datta, Nilanjana

2016-08-01

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint arXiv:1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.

Strong converse theorems using Rényi entropies

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

Leditzky, Felix; Datta, Nilanjana; Wilde, Mark M.

We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for themore » boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.« less

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

A Perron-Frobenius Type of Theorem for Quantum Operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng

2017-10-01

We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.

Adiabatic Theorem for Quantum Spin Systems

NASA Astrophysics Data System (ADS)

Bachmann, S.; De Roeck, W.; Fraas, M.

2017-08-01

The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.

Entanglement, space-time and the Mayer-Vietoris theorem

NASA Astrophysics Data System (ADS)

Patrascu, Andrei T.

2017-06-01

Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

Quantum Mechanics, Can It Be Consistent with Locality?

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe; Sestito, Angela

2011-07-01

We single out an alternative, strict interpretation of the Einstein-Podolsky-Rosen criterion of reality, and identify the implied extensions of quantum correlations. Then we prove that the theorem of Bell, and the non-locality theorems without inequalities, fail if the new extensions are adopted. Therefore, these theorems can be interpreted as arguments against the wide interpretation of the criterion of reality rather than as a violation of locality.

Comment on 'All quantum observables in a hidden-variable model must commute simultaneously'

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

Nagata, Koji

Malley discussed [Phys. Rev. A 69, 022118 (2004)] that all quantum observables in a hidden-variable model for quantum events must commute simultaneously. In this comment, we discuss that Malley's theorem is indeed valid for the hidden-variable theoretical assumptions, which were introduced by Kochen and Specker. However, we give an example that the local hidden-variable (LHV) model for quantum events preserves noncommutativity of quantum observables. It turns out that Malley's theorem is not related to the LHV model for quantum events, in general.

Faithful quantum broadcast beyond the no-go theorem

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Deng, Yun; Chen, Xiu-Bo; Yang, Yi-Xian; Li, Hong-Heng

2013-05-01

The main superiority of the quantum remote preparation over quantum teleportation lies the classical resource saving. This situation may be changed from the following constructions. Our purpose in this paper is to find some special differences between these two quantum tasks besides the classical resource costs. Some novel schemes show that the first one is useful to simultaneously broadcast arbitrary quantum states, while the second one cannot because of the quantum no-cloning theorem. Moreover, these broadcast schemes may be adapted to satisfying the different receivers' requirements or distributing the classical information, which are important in various quantum applications such as the quantum secret distribution or the quantum network communication.

Quantum Nonlocality and Reality

NASA Astrophysics Data System (ADS)

Bell, Mary; Gao, Shan

2016-09-01

Preface; Part I. John Stewart Bell: The Physicist: 1. John Bell: the Irish connection Andrew Whitaker; 2. Recollections of John Bell Michael Nauenberg; 3. John Bell: recollections of a great scientist and a great man Gian-Carlo Ghirardi; Part II. Bell's Theorem: 4. What did Bell really prove? Jean Bricmont; 5. The assumptions of Bell's proof Roderich Tumulka; 6. Bell on Bell's theorem: the changing face of nonlocality Harvey R. Brown and Christopher G. Timpson; 7. Experimental tests of Bell inequalities Marco Genovese; 8. Bell's theorem without inequalities: on the inception and scope of the GHZ theorem Olival Freire, Jr and Osvaldo Pessoa, Jr; 9. Strengthening Bell's theorem: removing the hidden-variable assumption Henry P. Stapp; Part III. Nonlocality: Illusions or Reality?: 10. Is any theory compatible with the quantum predictions necessarily nonlocal? Bernard d'Espagnat; 11. Local causality, probability and explanation Richard A. Healey; 12. Bell inequality and many-worlds interpretation Lev Vaidman; 13. Quantum solipsism and non-locality Travis Norsen; 14. Lessons of Bell's theorem: nonlocality, yes; action at a distance, not necessarily Wayne C. Myrvold; 15. Bell non-locality, Hardy's paradox and hyperplane dependence Gordon N. Fleming; 16. Some thoughts on quantum nonlocality and its apparent incompatibility with relativity Shan Gao; 17. A reasonable thing that just might work Daniel Rohrlich; 18. Weak values and quantum nonlocality Yakir Aharonov and Eliahu Cohen; Part IV. Nonlocal Realistic Theories: 19. Local beables and the foundations of physics Tim Maudlin; 20. John Bell's varying interpretations of quantum mechanics: memories and comments H. Dieter Zeh; 21. Some personal reflections on quantum non-locality and the contributions of John Bell Basil J. Hiley; 22. Bell on Bohm Sheldon Goldstein; 23. Interactions and inequality Philip Pearle; 24. Gravitation and the noise needed in objective reduction models Stephen L. Adler; 25. Towards an objective physics of Bell non-locality: palatial twistor theory Roger Penrose; 26. Measurement and macroscopicity: overcoming conceptual imprecision in quantum measurement theory Gregg Jaeger; Index.

The Misapplication of Probability Theory in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Racicot, Ronald

2014-03-01

This article is a revision of two papers submitted to the APS in the past two and a half years. In these papers, arguments and proofs are summarized for the following: (1) The wrong conclusion by EPR that Quantum Mechanics is incomplete, perhaps requiring the addition of ``hidden variables'' for completion. Theorems that assume such ``hidden variables,'' such as Bell's theorem, are also wrong. (2) Quantum entanglement is not a realizable physical phenomenon and is based entirely on assuming a probability superposition model for quantum spin. Such a model directly violates conservation of angular momentum. (3) Simultaneous multiple-paths followed by a quantum particle traveling through space also cannot possibly exist. Besides violating Noether's theorem, the multiple-paths theory is based solely on probability calculations. Probability calculations by themselves cannot possibly represent simultaneous physically real events. None of the reviews of the submitted papers actually refuted the arguments and evidence that was presented. These analyses should therefore be carefully evaluated since the conclusions reached have such important impact in quantum mechanics and quantum information theory.

Quantization of Chirikov Map and Quantum KAM Theorem.

NASA Astrophysics Data System (ADS)

Shi, Kang-Jie

KAM theorem is one of the most important theorems in classical nonlinear dynamics and chaos. To extend KAM theorem to the regime of quantum mechanics, we first study the quantum Chirikov map, whose classical counterpart provides a good example of KAM theorem. Under resonance condition 2pihbar = 1/N, we obtain the eigenstates of the evolution operator of this system. We find that the wave functions in the coherent state representation (CSR) are very similar to the classical trajectories. In particular, some of these wave functions have wall-like structure at the locations of classical KAM curves. We also find that a local average is necessary for a Wigner function to approach its classical limit in the phase space. We then study the general problem theoretically. Under similar conditions for establishing the classical KAM theorem, we obtain a quantum extension of KAM theorem. By constructing successive unitary transformations, we can greatly reduce the perturbation part of a near-integrable Hamiltonian system in a region associated with a Diophantine number {rm W}_{o}. This reduction is restricted only by the magnitude of hbar.. We can summarize our results as follows: In the CSR of a nearly integrable quantum system, associated with a Diophantine number {rm W}_ {o}, there is a band near the corresponding KAM torus of the classical limit of the system. In this band, a Gaussian wave packet moves quasi-periodically (and remain close to the KAM torus) for a long time, with possible diffusion in both the size and the shape of its wave packet. The upper bound of the tunnelling rate out of this band for the wave packet can be made much smaller than any given power of hbar, if the original perturbation is sufficiently small (but independent of hbar). When hbarto 0, we reproduce the classical KAM theorem. For most near-integrable systems the eigenstate wave function in the above band can either have a wall -like structure or have a vanishing amplitude. These conclusions agree with the numerical results of the quantum Chirikov map.

Generalized entropy production fluctuation theorems for quantum systems

NASA Astrophysics Data System (ADS)

Rana, Shubhashis; Lahiri, Sourabh; Jayannavar, A. M.

2013-02-01

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.

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

Generalization of the Ehrenfest theorem to quantum systems with periodical boundary conditions

NASA Astrophysics Data System (ADS)

Sanin, Andrey L.; Bagmanov, Andrey T.

2005-04-01

A generalization of Ehrenfest's theorem is discussed. For this purpose the quantum systems with periodical boundary conditions are being revised. The relations for time derivations of mean coordinate and momentum are derived once again. In comparison with Ehrenfest's theorem and its conventional quantities, the additional local terms occur which are caused boundaries. Because of this, the obtained new relations can be named as generalized. An example for using these relations is given.

Making Sense of Bell's Theorem and Quantum Nonlocality

NASA Astrophysics Data System (ADS)

Boughn, Stephen

2017-05-01

Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum mechanics and by inference nature herself are nonlocal in the sense that a measurement on a system by an observer at one location has an immediate effect on a distant entangled system (one with which the original system has previously interacted). Einstein was repulsed by such "spooky action at a distance" and was led to question whether quantum mechanics could provide a complete description of physical reality. In this paper I argue that quantum mechanics does not require spooky action at a distance of any kind and yet it is entirely reasonable to question the assumption that quantum mechanics can provide a complete description of physical reality. The magic of entangled quantum states has little to do with entanglement and everything to do with superposition, a property of all quantum systems and a foundational tenet of quantum mechanics.

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.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering.

PubMed

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-08-26

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell's nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR's original scenario is "steering", i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.

Quantum States and Generalized Observables: A Simple Proof of Gleason's Theorem

NASA Astrophysics Data System (ADS)

Busch, P.

2003-09-01

A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple proof of the result, analogous to Gleason’s theorem, that any quantum state is given by a density operator. As a corollary we obtain a vonNeumann type argument against noncontextual hidden variables. It follows that on an individual interpretation of quantum mechanics the values of effects are appropriately understood as propensities.

Private algebras in quantum information and infinite-dimensional complementarity

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

Crann, Jason, E-mail: jason-crann@carleton.ca; Laboratoire de Mathématiques Paul Painlevé–UMR CNRS 8524, UFR de Mathématiques, Université Lille 1–Sciences et Technologies, 59655 Villeneuve d’Ascq Cédex; Kribs, David W., E-mail: dkribs@uoguelph.ca

We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.

Bertrand's theorem and virial theorem in fractional classical mechanics

NASA Astrophysics Data System (ADS)

Yu, Rui-Yan; Wang, Towe

2017-09-01

Fractional classical mechanics is the classical counterpart of fractional quantum mechanics. The central force problem in this theory is investigated. Bertrand's theorem is generalized, and virial theorem is revisited, both in three spatial dimensions. In order to produce stable, closed, non-circular orbits, the inverse-square law and the Hooke's law should be modified in fractional classical mechanics.

Autonomous quantum to classical transitions and the generalized imaging theorem

NASA Astrophysics Data System (ADS)

Briggs, John S.; Feagin, James M.

2016-03-01

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. Here we prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Currently, the quantum to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

A quantum framework for likelihood ratios

NASA Astrophysics Data System (ADS)

Bond, Rachael L.; He, Yang-Hui; Ormerod, Thomas C.

The ability to calculate precise likelihood ratios is fundamental to science, from Quantum Information Theory through to Quantum State Estimation. However, there is no assumption-free statistical methodology to achieve this. For instance, in the absence of data relating to covariate overlap, the widely used Bayes’ theorem either defaults to the marginal probability driven “naive Bayes’ classifier”, or requires the use of compensatory expectation-maximization techniques. This paper takes an information-theoretic approach in developing a new statistical formula for the calculation of likelihood ratios based on the principles of quantum entanglement, and demonstrates that Bayes’ theorem is a special case of a more general quantum mechanical expression.

Exact Dynamics via Poisson Process: a unifying Monte Carlo paradigm

NASA Astrophysics Data System (ADS)

Gubernatis, James

2014-03-01

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

From the necessary to the possible: the genesis of the spin-statistics theorem

NASA Astrophysics Data System (ADS)

Blum, Alexander

2014-12-01

The spin-statistics theorem, which relates the intrinsic angular momentum of a single particle to the type of quantum statistics obeyed by a system of many such particles, is one of the central theorems in quantum field theory and the physics of elementary particles. It was first formulated in 1939/40 by Wolfgang Pauli and his assistant Markus Fierz. This paper discusses the developments that led up to this first formulation, starting from early attempts in the late 1920s to explain why charged matter particles obey Fermi-Dirac statistics, while photons obey Bose-Einstein statistics. It is demonstrated how several important developments paved the way from such general philosophical musings to a general (and provable) theorem, most notably the use of quantum field theory, the discovery of new elementary particles, and the generalization of the notion of spin. It is also discussed how the attempts to prove a spin-statistics connection were driven by Pauli from formal to more physical arguments, culminating in Pauli's 1940 proof. This proof was a major success for the beleaguered theory of quantum field theory and the methods Pauli employed proved essential for the renaissance of quantum field theory and the development of renormalization techniques in the late 1940s.

What is Quantum Mechanics? A Minimal Formulation

NASA Astrophysics Data System (ADS)

Friedberg, R.; Hohenberg, P. C.

2018-03-01

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called "microscopic theory", applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen-Specker-Bell theorem and Gleason's theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

PubMed Central

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-01-01

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox. PMID:27562658

Sharp Contradiction for Local-Hidden-State Model in Quantum Steering

NASA Astrophysics Data System (ADS)

Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Pati, Arun Kumar

2016-08-01

In quantum theory, no-go theorems are important as they rule out the existence of a particular physical model under consideration. For instance, the Greenberger-Horne-Zeilinger (GHZ) theorem serves as a no-go theorem for the nonexistence of local hidden variable models by presenting a full contradiction for the multipartite GHZ states. However, the elegant GHZ argument for Bell’s nonlocality does not go through for bipartite Einstein-Podolsky-Rosen (EPR) state. Recent study on quantum nonlocality has shown that the more precise description of EPR’s original scenario is “steering”, i.e., the nonexistence of local hidden state models. Here, we present a simple GHZ-like contradiction for any bipartite pure entangled state, thus proving a no-go theorem for the nonexistence of local hidden state models in the EPR paradox. This also indicates that the very simple steering paradox presented here is indeed the closest form to the original spirit of the EPR paradox.

Quantum Experimental Data in Psychology and Economics

NASA Astrophysics Data System (ADS)

Aerts, Diederik; D'Hooghe, Bart; Haven, Emmanuel

2010-12-01

We prove a theorem which shows that a collection of experimental data of probabilistic weights related to decisions with respect to situations and their disjunction cannot be modeled within a classical probabilistic weight structure in case the experimental data contain the effect referred to as the ‘disjunction effect’ in psychology. We identify different experimental situations in psychology, more specifically in concept theory and in decision theory, and in economics (namely situations where Savage’s Sure-Thing Principle is violated) where the disjunction effect appears and we point out the common nature of the effect. We analyze how our theorem constitutes a no-go theorem for classical probabilistic weight structures for common experimental data when the disjunction effect is affecting the values of these data. We put forward a simple geometric criterion that reveals the non classicality of the considered probabilistic weights and we illustrate our geometrical criterion by means of experimentally measured membership weights of items with respect to pairs of concepts and their disjunctions. The violation of the classical probabilistic weight structure is very analogous to the violation of the well-known Bell inequalities studied in quantum mechanics. The no-go theorem we prove in the present article with respect to the collection of experimental data we consider has a status analogous to the well known no-go theorems for hidden variable theories in quantum mechanics with respect to experimental data obtained in quantum laboratories. Our analysis puts forward a strong argument in favor of the validity of using the quantum formalism for modeling the considered psychological experimental data as considered in this paper.

Fluctuation theorems in feedback-controlled open quantum systems: Quantum coherence and absolute irreversibility

NASA Astrophysics Data System (ADS)

Murashita, Yûto; Gong, Zongping; Ashida, Yuto; Ueda, Masahito

2017-10-01

The thermodynamics of quantum coherence has attracted growing attention recently, where the thermodynamic advantage of quantum superposition is characterized in terms of quantum thermodynamics. We investigate the thermodynamic effects of quantum coherent driving in the context of the fluctuation theorem. We adopt a quantum-trajectory approach to investigate open quantum systems under feedback control. In these systems, the measurement backaction in the forward process plays a key role, and therefore the corresponding time-reversed quantum measurement and postselection must be considered in the backward process, in sharp contrast to the classical case. The state reduction associated with quantum measurement, in general, creates a zero-probability region in the space of quantum trajectories of the forward process, which causes singularly strong irreversibility with divergent entropy production (i.e., absolute irreversibility) and hence makes the ordinary fluctuation theorem break down. In the classical case, the error-free measurement ordinarily leads to absolute irreversibility, because the measurement restricts classical paths to the region compatible with the measurement outcome. In contrast, in open quantum systems, absolute irreversibility is suppressed even in the presence of the projective measurement due to those quantum rare events that go through the classically forbidden region with the aid of quantum coherent driving. This suppression of absolute irreversibility exemplifies the thermodynamic advantage of quantum coherent driving. Absolute irreversibility is shown to emerge in the absence of coherent driving after the measurement, especially in systems under time-delayed feedback control. We show that absolute irreversibility is mitigated by increasing the duration of quantum coherent driving or decreasing the delay time of feedback control.

Quantum interval-valued probability: Contextuality and the Born rule

NASA Astrophysics Data System (ADS)

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

2018-05-01

We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and the Born rule. While foundational results such as the Kochen-Specker and Gleason theorems are valid in the context of infinite precision, they fail to hold in general in a world with limited resources. Here we employ an interval-valued framework to establish bounds on the validity of those theorems in realistic experimental environments. In this way, not only can we quantify the idea of finite-precision measurement within our theory, but we can also suggest a possible resolution of the Meyer-Mermin debate on the impact of finite-precision measurement on the Kochen-Specker theorem.

A Perron-Frobenius type of theorem for quantum operations

NASA Astrophysics Data System (ADS)

Lagro, Matthew

Quantum random walks are a generalization of classical Markovian random walks to a quantum mechanical or quantum computing setting. Quantum walks have promising applications but are complicated by quantum decoherence. We prove that the long-time limiting behavior of the class of quantum operations which are the convex combination of norm one operators is governed by the eigenvectors with norm one eigenvalues which are shared by the operators. This class includes all operations formed by a coherent operation with positive probability of orthogonal measurement at each step. We also prove that any operation that has range contained in a low enough dimension subspace of the space of density operators has limiting behavior isomorphic to an associated Markov chain. A particular class of such operations are coherent operations followed by an orthogonal measurement. Applications of the convergence theorems to quantum walks are given.

Recurrence theorems: A unified account

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

Wallace, David, E-mail: david.wallace@balliol.ox.ac.uk

I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.

Slowly changing potential problems in Quantum Mechanics: Adiabatic theorems, ergodic theorems, and scattering

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

Fishman, S., E-mail: fishman@physics.technion.ac.il; Soffer, A., E-mail: soffer@math.rutgers.edu

2016-07-15

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.

Quantum stochastic thermodynamic on harmonic networks

DOE PAGES

Deffner, Sebastian

2016-01-04

Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Furthermore, their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

Quantum stochastic thermodynamic on harmonic networks

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

Deffner, Sebastian

Fluctuation theorems are symmetry relations for the probability to observe an amount of entropy production in a finite-time process. In a recent paper Pigeon et al (2016 New. J. Phys. 18 013009) derived fluctuation theorems for harmonic networks by means of the large deviation theory. Furthermore, their novel approach is illustrated with various examples of experimentally relevant systems. As a main result, however, Pigeon et al provide new insight how to consistently formulate quantum stochastic thermodynamics, and provide new and robust tools for the study of the thermodynamics of quantum harmonic networks.

Quantum computing without wavefunctions: time-dependent density functional theory for universal quantum computation.

PubMed

Tempel, David G; Aspuru-Guzik, Alán

2012-01-01

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.

Autonomous quantum to classical transitions and the generalized imaging theorem

DOE PAGES

Briggs, John S.; Feagin, James M.

2016-03-16

The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic distances from a microscopic reaction zone. We prove the generalized imaging theorem which shows that the spatial wave function of any multi-particle quantum system, propagating over distances and times large on an atomic scale but still microscopic, and subject to deterministic external fields and particle interactions, becomes proportional to the initial momentum wave function where the position and momentum coordinates define a classical trajectory. Now, the quantummore » to classical transition is considered to occur via decoherence caused by stochastic interaction with an environment. The imaging theorem arises from unitary Schrödinger propagation and so is valid without any environmental interaction. It implies that a simultaneous measurement of both position and momentum will define a unique classical trajectory, whereas a less complete measurement of say position alone can lead to quantum interference effects.« less

Pulsed Rabi oscillations in quantum two-level systems: beyond the area theorem

NASA Astrophysics Data System (ADS)

Fischer, Kevin A.; Hanschke, Lukas; Kremser, Malte; Finley, Jonathan J.; Müller, Kai; Vučković, Jelena

2018-01-01

The area theorem states that when a short optical pulse drives a quantum two-level system, it undergoes Rabi oscillations in the probability of scattering a single photon. In this work, we investigate the breakdown of the area theorem as both the pulse length becomes non-negligible and for certain pulse areas. Using simple quantum trajectories, we provide an analytic approximation to the photon emission dynamics of a two-level system. Our model provides an intuitive way to understand re-excitation, which elucidates the mechanism behind the two-photon emission events that can spoil single-photon emission. We experimentally measure the emission statistics from a semiconductor quantum dot, acting as a two-level system, and show good agreement with our simple model for short pulses. Additionally, the model clearly explains our recent results (Fischer and Hanschke 2017 et al Nat. Phys.) showing dominant two-photon emission from a two-level system for pulses with interaction areas equal to an even multiple of π.

Comments on Musha's theorem that an evanescent photon in the microtubule is a superluminal particle.

PubMed

Hari, Syamala D

2014-07-01

Takaaki Musha's research of high performance quantum computation in living systems is motivated by the theories of Penrose and Hameroff that microtubules in the brain function as quantum computers, and by those of Jibu and Yasue that the quantum states of microtubules depend upon boson condensates of evanescent photons. His work is based on the assumption that the evanescent photons described by Jibu et al. are superluminal and that they are tachyons defined and discussed by well-known physicists such as Sudarshan, Feinberg and Recami. Musha gives a brief justification for the assumption and sometimes calls it a theorem. However, the assumption is not valid because Jibu et al. stated that the evanescent photons have transmission speed smaller than that of light and that their mass is real and momentum is imaginary whereas a tachyon's mass is imaginary and momentum is real. We show here that Musha's proof of the "theorem" has errors and hence his theorem/assumption is not valid. This article is not meant to further discuss any biological aspects of the brain but only to comment on the consistency of the quantum-physical aspects of earlier work by Musha et al. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

Differentiability of correlations in realistic quantum mechanics

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

Cabrera, Alejandro; Faria, Edson de; Pujals, Enrique

2015-09-15

We prove a version of Bell’s theorem in which the locality assumption is weakened. We start by assuming theoretical quantum mechanics and weak forms of relativistic causality and of realism (essentially the fact that observable values are well defined independently of whether or not they are measured). Under these hypotheses, we show that only one of the correlation functions that can be formulated in the framework of the usual Bell theorem is unknown. We prove that this unknown function must be differentiable at certain angular configuration points that include the origin. We also prove that, if this correlation is assumedmore » to be twice differentiable at the origin, then we arrive at a version of Bell’s theorem. On the one hand, we are showing that any realistic theory of quantum mechanics which incorporates the kinematic aspects of relativity must lead to this type of rough correlation function that is once but not twice differentiable. On the other hand, this study brings us a single degree of differentiability away from a relativistic von Neumann no hidden variables theorem.« less

Gleason-Busch theorem for sequential measurements

NASA Astrophysics Data System (ADS)

Flatt, Kieran; Barnett, Stephen M.; Croke, Sarah

2017-12-01

Gleason's theorem is a statement that, given some reasonable assumptions, the Born rule used to calculate probabilities in quantum mechanics is essentially unique [A. M. Gleason, Indiana Univ. Math. J. 6, 885 (1957), 10.1512/iumj.1957.6.56050]. We show that Gleason's theorem contains within it also the structure of sequential measurements, and along with this the state update rule. We give a small set of axioms, which are physically motivated and analogous to those in Busch's proof of Gleason's theorem [P. Busch, Phys. Rev. Lett. 91, 120403 (2003), 10.1103/PhysRevLett.91.120403], from which the familiar Kraus operator form follows. An axiomatic approach has practical relevance as well as fundamental interest, in making clear those assumptions which underlie the security of quantum communication protocols. Interestingly, the two-time formalism is seen to arise naturally in this approach.

From statistical proofs of the Kochen-Specker theorem to noise-robust noncontextuality inequalities

NASA Astrophysics Data System (ADS)

Kunjwal, Ravi; Spekkens, Robert W.

2018-05-01

The Kochen-Specker theorem rules out models of quantum theory wherein projective measurements are assigned outcomes deterministically and independently of context. This notion of noncontextuality is not applicable to experimental measurements because these are never free of noise and thus never truly projective. For nonprojective measurements, therefore, one must drop the requirement that an outcome be assigned deterministically in the model and merely require that it be assigned a distribution over outcomes in a manner that is context-independent. By demanding context independence in the representation of preparations as well, one obtains a generalized principle of noncontextuality that also supports a quantum no-go theorem. Several recent works have shown how to derive inequalities on experimental data which, if violated, demonstrate the impossibility of finding a generalized-noncontextual model of this data. That is, these inequalities do not presume quantum theory and, in particular, they make sense without requiring an operational analog of the quantum notion of projectiveness. We here describe a technique for deriving such inequalities starting from arbitrary proofs of the Kochen-Specker theorem. It extends significantly previous techniques that worked only for logical proofs, which are based on sets of projective measurements that fail to admit of any deterministic noncontextual assignment, to the case of statistical proofs, which are based on sets of projective measurements that d o admit of some deterministic noncontextual assignments, but not enough to explain the quantum statistics.

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

NASA Astrophysics Data System (ADS)

Bachmann, Sven; De Roeck, Wojciech; Fraas, Martin

2018-03-01

The adiabatic theorem refers to a setup where an evolution equation contains a time-dependent parameter whose change is very slow, measured by a vanishing parameter ɛ. Under suitable assumptions the solution of the time-inhomogenous equation stays close to an instantaneous fixpoint. In the present paper, we prove an adiabatic theorem with an error bound that is independent of the number of degrees of freedom. Our setup is that of quantum spin systems where the manifold of ground states is separated from the rest of the spectrum by a spectral gap. One important application is the proof of the validity of linear response theory for such extended, genuinely interacting systems. In general, this is a long-standing mathematical problem, which can be solved in the present particular case of a gapped system, relevant e.g. for the integer quantum Hall effect.

Bell's theorem, the measurement problem, Newton's self-gravitation and its connections to violations of the discrete symmetries C, P, T

NASA Astrophysics Data System (ADS)

Hiesmayr, Beatrix C.

2015-07-01

About 50 years ago John St. Bell published his famous Bell theorem that initiated a new field in physics. This contribution discusses how discrete symmetries relate to the big open questions of quantum mechanics, in particular: (i) how correlations stronger than those predicted by theories sharing randomness (Bell's theorem) relate to the violation of the CP symmetry and the P symmetry; and its relation to the security of quantum cryptography, (ii) how the measurement problem (“why do we observe no tables in superposition?”) can be polled in weakly decaying systems, (iii) how strongly and weakly interacting quantum systems are affected by Newton's self gravitation. These presented preliminary results show that the meson-antimeson systems and the hyperon- antihyperon systems are a unique laboratory to tackle deep fundamental questions and to contribute to the understand what impact the violation of discrete symmetries has.

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.

Non Locality Proofs in Quantum Mechanics Analyzed by Ordinary Mathematical Logic

NASA Astrophysics Data System (ADS)

Nisticò, Giuseppe

2014-10-01

The so-called non-locality theorems aim to show that Quantum Mechanics is not consistent with the Locality Principle. Their proofs require, besides the standard postulates of Quantum Theory, further conditions, as for instance the Criterion of Reality, which cannot be formulated in the language of Standard Quantum Theory; this difficulty makes the proofs not verifiable according to usual logico-mathematical methods, and therefore it is a source of the controversial debate about the real implications of these theorems. The present work addresses this difficulty for Bell-type and Stapp's arguments of non-locality. We supplement the formalism of Quantum Mechanics with formal statements inferred from the further conditions in the two different cases. Then an analysis of the two arguments is performed according to ordinary mathematical logic.

Relation between ``no broadcasting'' for noncommuting states and ``no local broadcasting'' for quantum correlations

NASA Astrophysics Data System (ADS)

Luo, Shunlong; Li, Nan; Cao, Xuelian

2009-05-01

The no-broadcasting theorem, first established by Barnum [Phys. Rev. Lett. 76, 2818 (1996)], states that a set of quantum states can be broadcast if and only if it constitutes a commuting family. Quite recently, Piani [Phys. Rev. Lett. 100, 090502 (2008)] showed, by using an ingenious and sophisticated method, that the correlations in a single bipartite state can be locally broadcast if and only if the state is effectively a classical one (i.e., the correlations therein are classical). In this Brief Report, under the condition of nondegenerate spectrum, we provide an alternative and significantly simpler proof of the latter result based on the original no-broadcasting theorem and the monotonicity of the quantum relative entropy. This derivation motivates us to conjecture the equivalence between these two elegant yet formally different no-broadcasting theorems and indicates a subtle and fundamental issue concerning spectral degeneracy which also lies at the heart of the conflict between the von Neumann projection postulate and the Lüders ansatz for quantum measurements. This relation not only offers operational interpretations for commutativity and classicality but also illustrates the basic significance of noncommutativity in characterizing quantumness from the informational perspective.

John S. Bell's concept of local causality

NASA Astrophysics Data System (ADS)

Norsen, Travis

2011-12-01

John Stewart Bell's famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many workers assert that Bell's theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with ``hidden'' variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently--as establishing an ``essential conflict'' between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell's own views more widely known and to explain Bell's little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell's formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.

John S. Bell's concept of local causality

NASA Astrophysics Data System (ADS)

Norsen, Travis

2011-12-01

John Stewart Bell's famous theorem is widely regarded as one of the most important developments in the foundations of physics. Yet even as we approach the 50th anniversary of Bell's discovery, its meaning and implications remain controversial. Many workers assert that Bell's theorem refutes the possibility suggested by Einstein, Podolsky, and Rosen (EPR) of supplementing ordinary quantum theory with "hidden" variables that might restore determinism and/or some notion of an observer-independent reality. But Bell himself interpreted the theorem very differently—as establishing an "essential conflict" between the well-tested empirical predictions of quantum theory and relativistic local causality. Our goal is to make Bell's own views more widely known and to explain Bell's little-known formulation of the concept of relativistic local causality on which his theorem rests. We also show precisely how Bell's formulation of local causality can be used to derive an empirically testable Bell-type inequality and to recapitulate the EPR argument.

Fluctuation Theorem for Many-Body Pure Quantum States.

PubMed

Iyoda, Eiki; Kaneko, Kazuya; Sagawa, Takahiro

2017-09-08

We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.

Quantum steganography with large payload based on entanglement swapping of χ-type entangled states

NASA Astrophysics Data System (ADS)

Qu, Zhi-Guo; Chen, Xiu-Bo; Luo, Ming-Xing; Niu, Xin-Xin; Yang, Yi-Xian

2011-04-01

In this paper, we firstly propose a new simple method to calculate entanglement swapping of χ-type entangled states, and then present a novel quantum steganography protocol with large payload. The new protocol adopts entanglement swapping to build up the hidden channel within quantum secure direct communication with χ-type entangled states for securely transmitting secret messages. Comparing with the previous quantum steganographies, the capacity of the hidden channel is much higher, which is increased to eight bits. Meanwhile, due to the quantum uncertainty theorem and the no-cloning theorem its imperceptibility is proved to be great in the analysis, and its security is also analyzed in detail, which is proved that intercept-resend attack, measurement-resend attack, ancilla attack, man-in-the-middle attack or even Dos(Denial of Service) attack couldn't threaten it. As a result, the protocol can be applied in various fields of quantum communication.

Experimental violation of local causality in a quantum network.

PubMed

Carvacho, Gonzalo; Andreoli, Francesco; Santodonato, Luca; Bentivegna, Marco; Chaves, Rafael; Sciarrino, Fabio

2017-03-16

Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.

No-go theorem for passive single-rail linear optical quantum computing.

PubMed

Wu, Lian-Ao; Walther, Philip; Lidar, Daniel A

2013-01-01

Photonic quantum systems are among the most promising architectures for quantum computers. It is well known that for dual-rail photons effective non-linearities and near-deterministic non-trivial two-qubit gates can be achieved via the measurement process and by introducing ancillary photons. While in principle this opens a legitimate path to scalable linear optical quantum computing, the technical requirements are still very challenging and thus other optical encodings are being actively investigated. One of the alternatives is to use single-rail encoded photons, where entangled states can be deterministically generated. Here we prove that even for such systems universal optical quantum computing using only passive optical elements such as beam splitters and phase shifters is not possible. This no-go theorem proves that photon bunching cannot be passively suppressed even when extra ancilla modes and arbitrary number of photons are used. Our result provides useful guidance for the design of optical quantum computers.

Experimental violation of local causality in a quantum network

PubMed Central

Carvacho, Gonzalo; Andreoli, Francesco; Santodonato, Luca; Bentivegna, Marco; Chaves, Rafael; Sciarrino, Fabio

2017-01-01

Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols. PMID:28300068

Fluctuation Theorem for Many-Body Pure Quantum States

NASA Astrophysics Data System (ADS)

Iyoda, Eiki; Kaneko, Kazuya; Sagawa, Takahiro

2017-09-01

We prove the second law of thermodynamics and the nonequilibrium fluctuation theorem for pure quantum states. The entire system obeys reversible unitary dynamics, where the initial state of the heat bath is not the canonical distribution but is a single energy eigenstate that satisfies the eigenstate-thermalization hypothesis. Our result is mathematically rigorous and based on the Lieb-Robinson bound, which gives the upper bound of the velocity of information propagation in many-body quantum systems. The entanglement entropy of a subsystem is shown connected to thermodynamic heat, highlighting the foundation of the information-thermodynamics link. We confirmed our theory by numerical simulation of hard-core bosons, and observed dynamical crossover from thermal fluctuations to bare quantum fluctuations. Our result reveals a universal scenario that the second law emerges from quantum mechanics, and can be experimentally tested by artificial isolated quantum systems such as ultracold atoms.

Experimental violation of local causality in a quantum network

NASA Astrophysics Data System (ADS)

Carvacho, Gonzalo; Andreoli, Francesco; Santodonato, Luca; Bentivegna, Marco; Chaves, Rafael; Sciarrino, Fabio

2017-03-01

Bell's theorem plays a crucial role in quantum information processing and thus several experimental investigations of Bell inequalities violations have been carried out over the years. Despite their fundamental relevance, however, previous experiments did not consider an ingredient of relevance for quantum networks: the fact that correlations between distant parties are mediated by several, typically independent sources. Here, using a photonic setup, we investigate a quantum network consisting of three spatially separated nodes whose correlations are mediated by two distinct sources. This scenario allows for the emergence of the so-called non-bilocal correlations, incompatible with any local model involving two independent hidden variables. We experimentally witness the emergence of this kind of quantum correlations by violating a Bell-like inequality under the fair-sampling assumption. Our results provide a proof-of-principle experiment of generalizations of Bell's theorem for networks, which could represent a potential resource for quantum communication protocols.

Proposal for founding mistrustful quantum cryptography on coin tossing

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

Kent, Adrian; Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ,

2003-07-01

A significant branch of classical cryptography deals with the problems which arise when mistrustful parties need to generate, process, or exchange information. As Kilian showed a while ago, mistrustful classical cryptography can be founded on a single protocol, oblivious transfer, from which general secure multiparty computations can be built. The scope of mistrustful quantum cryptography is limited by no-go theorems, which rule out, inter alia, unconditionally secure quantum protocols for oblivious transfer or general secure two-party computations. These theorems apply even to protocols which take relativistic signaling constraints into account. The best that can be hoped for, in general, aremore » quantum protocols which are computationally secure against quantum attack. Here a method is described for building a classically certified bit commitment, and hence every other mistrustful cryptographic task, from a secure coin-tossing protocol. No security proof is attempted, but reasons are sketched why these protocols might resist quantum computational attack.« less

Markov Property of the Conformal Field Theory Vacuum and the a Theorem.

PubMed

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

2017-06-30

We use strong subadditivity of entanglement entropy, Lorentz invariance, and the Markov property of the vacuum state of a conformal field theory to give new proof of the irreversibility of the renormalization group in d=4 space-time dimensions-the a theorem. This extends the proofs of the c and F theorems in dimensions d=2 and d=3 based on vacuum entanglement entropy, and gives a unified picture of all known irreversibility theorems in relativistic quantum field theory.

Optimal no-go theorem on hidden-variable predictions of effect expectations

NASA Astrophysics Data System (ADS)

Blass, Andreas; Gurevich, Yuri

2018-03-01

No-go theorems prove that, under reasonable assumptions, classical hidden-variable theories cannot reproduce the predictions of quantum mechanics. Traditional no-go theorems proved that hidden-variable theories cannot predict correctly the values of observables. Recent expectation no-go theorems prove that hidden-variable theories cannot predict the expectations of observables. We prove the strongest expectation-focused no-go theorem to date. It is optimal in the sense that the natural weakenings of the assumptions and the natural strengthenings of the conclusion make the theorem fail. The literature on expectation no-go theorems strongly suggests that the expectation-focused approach is more general than the value-focused one. We establish that the expectation approach is not more general.

Realization of a Quantum Random Generator Certified with the Kochen-Specker Theorem

NASA Astrophysics Data System (ADS)

Kulikov, Anatoly; Jerger, Markus; Potočnik, Anton; Wallraff, Andreas; Fedorov, Arkady

2017-12-01

Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.

Realization of a Quantum Random Generator Certified with the Kochen-Specker Theorem.

PubMed

Kulikov, Anatoly; Jerger, Markus; Potočnik, Anton; Wallraff, Andreas; Fedorov, Arkady

2017-12-15

Random numbers are required for a variety of applications from secure communications to Monte Carlo simulation. Yet randomness is an asymptotic property, and no output string generated by a physical device can be strictly proven to be random. We report an experimental realization of a quantum random number generator (QRNG) with randomness certified by quantum contextuality and the Kochen-Specker theorem. The certification is not performed in a device-independent way but through a rigorous theoretical proof of each outcome being value indefinite even in the presence of experimental imperfections. The analysis of the generated data confirms the incomputable nature of our QRNG.

Not-Post-Peierls compatibility under noisy channels

NASA Astrophysics Data System (ADS)

Ducuara, Andrés F.; Susa, Cristian E.; Reina, John H.

2017-06-01

The Pusey-Barrett-Rudolph (PBR) theorem deals with the realism of the quantum states. It establishes that every pure quantum state is real, in the context of quantum ontological models. Specifically, by guaranteeing the property of not-Post-Peierls (\

High-dimensional quantum cloning and applications to quantum hacking

PubMed Central

Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W.; Karimi, Ebrahim

2017-01-01

Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography. PMID:28168219

High-dimensional quantum cloning and applications to quantum hacking.

PubMed

Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W; Karimi, Ebrahim

2017-02-01

Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.

Bell's Theorem and Einstein's `Spooky Actions' from a Simple Thought Experiment

NASA Astrophysics Data System (ADS)

Kuttner, Fred; Rosenblum, Bruce

2010-02-01

In 1964 John Bell proved a theorem2 allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they do. Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at any level. And a simple, semi-classical derivation of the quantum theory result can be given for physics students. These entanglement phenomena are today applied in industrial laboratories and are increasingly discussed in the popular literature. Unfortunately, they are also misappropriated by the purveyors of pseudoscience, something physicists have a responsibility to address.3 Students can be intrigued by the quantum strangeness physics has encountered at a boundary of our discipline.

A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics

NASA Technical Reports Server (NTRS)

Gingold, H.

1991-01-01

A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.

Graph State-Based Quantum Secret Sharing with the Chinese Remainder Theorem

NASA Astrophysics Data System (ADS)

Guo, Ying; Luo, Peng; Wang, Yijun

2016-11-01

Quantum secret sharing (QSS) is a significant quantum cryptography technology in the literature. Dividing an initial secret into several sub-secrets which are then transferred to other legal participants so that it can be securely recovered in a collaboration fashion. In this paper, we develop a quantum route selection based on the encoded quantum graph state, thus enabling the practical QSS scheme in the small-scale complex quantum network. Legal participants are conveniently designated with the quantum route selection using the entanglement of the encoded graph states. Each participant holds a vertex of the graph state so that legal participants are selected through performing operations on specific vertices. The Chinese remainder theorem (CRT) strengthens the security of the recovering process of the initial secret among the legal participants. The security is ensured by the entanglement of the encoded graph states that are cooperatively prepared and shared by legal users beforehand with the sub-secrets embedded in the CRT over finite fields.

Sanov and central limit theorems for output statistics of quantum Markov chains

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

Horssen, Merlijn van, E-mail: merlijn.vanhorssen@nottingham.ac.uk; Guţă, Mădălin, E-mail: madalin.guta@nottingham.ac.uk

2015-02-15

In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Suchmore » higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.« less

Entropic no-disturbance as a physical principle

NASA Astrophysics Data System (ADS)

Jia, Zhih-Ahn; Zhai, Rui; Yu, Bai-Chu; Wu, Yu-Chun; Guo, Guang-Can

2018-05-01

The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism; the essence of the theorem is the lack of a joint probability distribution for some experiment settings. We exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such kind of entropic realism either. The entropic form of Gleason's no-disturbance principle is developed and characterized by the intersection of several entropic cones. Entropic contextuality and entropic nonlocality are investigated in depth in this framework as well. We show how one can construct monogamy relations using entropic cone and basic Shannon-type inequalities. The general criterion for several entropic tests to be monogamous is also developed; using the criterion, we demonstrate that entropic nonlocal correlations, entropic contextuality tests, and entropic nonlocality and entropic contextuality are monogamous. Finally, we analyze the entropic monogamy relations for the multiparty and many-test case, which may play a crucial role in quantum network communication.

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.

Mean energy of some interacting bosonic systems derived by virtue of the generalized Hellmann-Feynman theorem

NASA Astrophysics Data System (ADS)

Fan, Hong-yi; Xu, Xue-xiang

2009-06-01

By virtue of the generalized Hellmann-Feynman theorem [H. Y. Fan and B. Z. Chen, Phys. Lett. A 203, 95 (1995)], we derive the mean energy of some interacting bosonic systems for some Hamiltonian models without proceeding with diagonalizing the Hamiltonians. Our work extends the field of applications of the Hellmann-Feynman theorem and may enrich the theory of quantum statistics.

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.

Mathematical and physical meaning of the Bell inequalities

NASA Astrophysics Data System (ADS)

Santos, Emilio

2016-09-01

It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values \\{0,1\\}. A hidden variables model may be defined as a mapping between a set of quantum projection operators and a set of random variables. The model is noncontextual if there is a joint probability distribution. The Bell inequalities are necessary conditions for its existence. The inequalities are most relevant when measurements are performed at space-like separation, thus showing a conflict between quantum mechanics and local realism (Bell's theorem). The relations of the Bell inequalities with contextuality, the Kochen-Specker theorem, and quantum entanglement are briefly discussed.

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.

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One-Dimensional Bose Gases

DOE PAGES

Brandino, G. P.; Caux, J. -S.; Konik, R. M.

2015-12-16

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking,more » we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.« less

Why are para-hydrogen clusters superfluid? A quantum theorem of corresponding states study.

PubMed

Sevryuk, Mikhail B; Toennies, J Peter; Ceperley, David M

2010-08-14

The quantum theorem of corresponding states is applied to N=13 and N=26 cold quantum fluid clusters to establish where para-hydrogen clusters lie in relation to more and less quantum delocalized systems. Path integral Monte Carlo calculations of the energies, densities, radial and pair distributions, and superfluid fractions are reported at T=0.5 K for a Lennard-Jones (LJ) (12,6) potential using six different de Boer parameters including the accepted value for hydrogen. The results indicate that the hydrogen clusters are on the borderline to being a nonsuperfluid solid but that the molecules are sufficiently delocalized to be superfluid. A general phase diagram for the total and kinetic energies of LJ (12,6) clusters encompassing all sizes from N=2 to N=infinity and for the entire range of de Boer parameters is presented. Finally the limiting de Boer parameters for quantum delocalization induced unbinding ("quantum unbinding") are estimated and the new results are found to agree with previous calculations for the bulk and smaller clusters.

Teaching the Jahn-Teller Theorem: A Simple Exercise That Illustrates How the Magnitude of Distortion Depends on the Number of Electrons and Their Occupation of the Degenerate Energy Level

ERIC Educational Resources Information Center

Johansson, Adam Johannes

2013-01-01

Teaching the Jahn-Teller theorem offers several challenges. For many students, the first encounter comes in coordination chemistry, which can be difficult due to the already complicated nature of transition-metal complexes. Moreover, a deep understanding of the Jahn-Teller theorem requires that one is well acquainted with quantum mechanics and…

Weyl consistency conditions in non-relativistic quantum field theory

DOE PAGES

Pal, Sridip; Grinstein, Benjamín

2016-12-05

Weyl consistency conditions have been used in unitary relativistic quantum field theory to impose constraints on the renormalization group flow of certain quantities. We classify the Weyl anomalies and their renormalization scheme ambiguities for generic non-relativistic theories in 2 + 1 dimensions with anisotropic scaling exponent z = 2; the extension to other values of z are discussed as well. We give the consistency conditions among these anomalies. As an application we find several candidates for a C-theorem. Here, we comment on possible candidates for a C-theorem in higher dimensions.

Quantum-field-theoretical approach to phase–space techniques: Symmetric Wick theorem and multitime Wigner representation

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

Plimak, L.I., E-mail: Lev.Plimak@mbi-berlin.de; Olsen, M.K.

2014-12-15

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. Analogs of Wick’s theorem for the Weyl ordering are verified. Using the Bose–Hubbard chain as an example, we show how these may be applied to constructing a mapping of the system in question to phase space. Regularisation issues and the reordering problem for the Heisenberg operators are addressed.

Quantum Markov Semigroups with Unbounded Generator and Time Evolution of the Support Projection of a State

NASA Astrophysics Data System (ADS)

Gliouez, Souhir; Hachicha, Skander; Nasroui, Ikbel

We characterize the support projection of a state evolving under the action of a quantum Markov semigroup with unbounded generator represented in the generalized GKSL form and a quantum version of the classical Lévy-Austin-Ornstein theorem.

Continuous-time quantum walks on star graphs

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

Salimi, S.

2009-06-15

In this paper, we investigate continuous-time quantum walk on star graphs. It is shown that quantum central limit theorem for a continuous-time quantum walk on star graphs for N-fold star power graph, which are invariant under the quantum component of adjacency matrix, converges to continuous-time quantum walk on K{sub 2} graphs (complete graph with two vertices) and the probability of observing walk tends to the uniform distribution.

Hidden Variable Theories and Quantum Nonlocality

ERIC Educational Resources Information Center

Boozer, A. D.

2009-01-01

We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of…

Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

NASA Astrophysics Data System (ADS)

Cho, Gil Young; Hsieh, Chang-Tse; Ryu, Shinsei

2017-11-01

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

Sharpening the second law of thermodynamics with the quantum Bayes theorem.

PubMed

Gharibyan, Hrant; Tegmark, Max

2014-09-01

We prove a generalization of the classic Groenewold-Lindblad entropy inequality, combining decoherence and the quantum Bayes theorem into a simple unified picture where decoherence increases entropy while observation decreases it. This provides a rigorous quantum-mechanical version of the second law of thermodynamics, governing how the entropy of a system (the entropy of its density matrix, partial-traced over the environment and conditioned on what is known) evolves under general decoherence and observation. The powerful tool of spectral majorization enables both simple alternative proofs of the classic Lindblad and Holevo inequalities without using strong subadditivity, and also novel inequalities for decoherence and observation that hold not only for von Neumann entropy, but also for arbitrary concave entropies.

How to (properly) strengthen Bell's theorem using counterfactuals

NASA Astrophysics Data System (ADS)

Bigaj, Tomasz

Bell's theorem in its standard version demonstrates that the joint assumptions of the hidden-variable hypothesis and the principle of local causation lead to a conflict with quantum-mechanical predictions. In his latest counterfactual strengthening of Bell's theorem, Stapp attempts to prove that the locality assumption itself contradicts the quantum-mechanical predictions in the Hardy case. His method relies on constructing a complex, non-truth functional formula which consists of statements about measurements and outcomes in some region R, and whose truth value depends on the selection of a measurement setting in a space-like separated location L. Stapp argues that this fact shows that the information about the measurement selection made in L has to be present in R. I give detailed reasons why this conclusion can and should be resisted. Next I correct and formalize an informal argument by Shimony and Stein showing that the locality condition coupled with Einstein's criterion of reality is inconsistent with quantum-mechanical predictions. I discuss the possibility of avoiding the inconsistency by rejecting Einstein's criterion rather than the locality assumption.

From the Kochen-Specker theorem to noncontextuality inequalities without assuming determinism.

PubMed

Kunjwal, Ravi; Spekkens, Robert W

2015-09-11

The Kochen-Specker theorem demonstrates that it is not possible to reproduce the predictions of quantum theory in terms of a hidden variable model where the hidden variables assign a value to every projector deterministically and noncontextually. A noncontextual value assignment to a projector is one that does not depend on which other projectors-the context-are measured together with it. Using a generalization of the notion of noncontextuality that applies to both measurements and preparations, we propose a scheme for deriving inequalities that test whether a given set of experimental statistics is consistent with a noncontextual model. Unlike previous inequalities inspired by the Kochen-Specker theorem, we do not assume that the value assignments are deterministic and therefore in the face of a violation of our inequality, the possibility of salvaging noncontextuality by abandoning determinism is no longer an option. Our approach is operational in the sense that it does not presume quantum theory: a violation of our inequality implies the impossibility of a noncontextual model for any operational theory that can account for the experimental observations, including any successor to quantum theory.

Communication, Correlation and Complementarity

NASA Astrophysics Data System (ADS)

Schumacher, Benjamin Wade

1990-01-01

In quantum communication, a sender prepares a quantum system in a state corresponding to his message and conveys it to a receiver, who performs a measurement on it. The receiver acquires information about the message based on the outcome of his measurement. Since the state of a single quantum system is not always completely determinable from measurement, quantum mechanics limits the information capacity of such channels. According to a theorem of Kholevo, the amount of information conveyed by the channel can be no greater than the entropy of the ensemble of possible physical signals. The connection between information and entropy allows general theorems to be proved regarding the energy requirements of communication. For example, it can be shown that one particular quantum coding scheme, called thermal coding, uses energy with maximum efficiency. A close analogy between communication and quantum correlation can be made using Everett's notion of relative states. Kholevo's theorem can be used to prove that the mutual information of a pair of observables on different systems is bounded by the entropy of the state of each system. This confirms and extends an old conjecture of Everett. The complementarity of quantum observables can be described by information-theoretic uncertainty relations, several of which have been previously derived. These relations imply limits on the degree to which different messages can be coded in complementary observables of a single channel. Complementarity also restricts the amount of information that can be recovered from a given channel using a given decoding observable. Information inequalities can be derived which are analogous to the well-known Bell inequalities for correlated quantum systems. These inequalities are satisfied for local hidden variable theories but are violated by quantum systems, even where the correlation is weak. These information inequalities are metric inequalities for an "information distance", and their structure can be made exactly analogous to that of the familiar covariance Bell inequalities by introducing a "covariance distance". Similar inequalities derived for successive measurements on a single system are also violated in quantum mechanics.

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

Quantum properties of supersymmetric theories regularized by higher covariant derivatives

NASA Astrophysics Data System (ADS)

Stepanyantz, Konstantin

2018-02-01

We investigate quantum corrections in \\mathscr{N} = 1 non-Abelian supersymmetric gauge theories, regularized by higher covariant derivatives. In particular, by the help of the Slavnov-Taylor identities we prove that the vertices with two ghost legs and one leg of the quantum gauge superfield are finite in all orders. This non-renormalization theorem is confirmed by an explicit one-loop calculation. By the help of this theorem we rewrite the exact NSVZ β-function in the form of the relation between the β-function and the anomalous dimensions of the matter superfields, of the quantum gauge superfield, and of the Faddeev-Popov ghosts. Such a relation has simple qualitative interpretation and allows suggesting a prescription producing the NSVZ scheme in all loops for the theories regularized by higher derivatives. This prescription is verified by the explicit three-loop calculation for the terms quartic in the Yukawa couplings.

Path integrals, supersymmetric quantum mechanics, and the Atiyah-Singer index theorem for twisted Dirac

NASA Astrophysics Data System (ADS)

Fine, Dana S.; Sawin, Stephen

2017-01-01

Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.

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

Beigi, Salman

Sandwiched (quantum) α-Rényi divergence has been recently defined in the independent works of Wilde et al. [“Strong converse for the classical capacity of entanglement-breaking channels,” preprint http://arxiv.org/abs/arXiv:1306.1586 (2013)] and Müller-Lennert et al. [“On quantum Rényi entropies: a new definition, some properties and several conjectures,” preprint http://arxiv.org/abs/arXiv:1306.3142v1 (2013)]. This new quantum divergence has already found applications in quantum information theory. Here we further investigate properties of this new quantum divergence. In particular, we show that sandwiched α-Rényi divergence satisfies the data processing inequality for all values of α > 1. Moreover we prove that α-Holevo information, a variant of Holevo informationmore » defined in terms of sandwiched α-Rényi divergence, is super-additive. Our results are based on Hölder's inequality, the Riesz-Thorin theorem and ideas from the theory of complex interpolation. We also employ Sion's minimax theorem.« less

Quantum Groups, Property (T), and Weak Mixing

NASA Astrophysics Data System (ADS)

Brannan, Michael; Kerr, David

2018-06-01

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having almost invariant vectors. This is a generalization of a theorem of Bekka and Valette from the group setting and was previously established in the case of low dual by Daws, Skalski, and Viselter. Our approach uses spectral techniques and is completely different from those of Bekka-Valette and Daws-Skalski-Viselter. By a separate argument we furthermore extend the result to second countable nonunimodular locally compact quantum groups, which are shown in particular not to have property (T), generalizing a theorem of Fima from the discrete setting. We also obtain quantum group versions of characterizations of property (T) of Kerr and Pichot in terms of the Baire category theory of weak mixing representations and of Connes and Weiss in terms of the prevalence of strongly ergodic actions.

Sandwiched Rényi divergence satisfies data processing inequality

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

Beigi, Salman

2013-12-15

Sandwiched (quantum) α-Rényi divergence has been recently defined in the independent works of Wilde et al. [“Strong converse for the classical capacity of entanglement-breaking channels,” preprint http://arxiv.org/abs/arXiv:1306.1586 (2013)] and Müller-Lennert et al. [“On quantum Rényi entropies: a new definition, some properties and several conjectures,” preprint http://arxiv.org/abs/arXiv:1306.3142v1 (2013)]. This new quantum divergence has already found applications in quantum information theory. Here we further investigate properties of this new quantum divergence. In particular, we show that sandwiched α-Rényi divergence satisfies the data processing inequality for all values of α > 1. Moreover we prove that α-Holevo information, a variant of Holevo informationmore » defined in terms of sandwiched α-Rényi divergence, is super-additive. Our results are based on Hölder's inequality, the Riesz-Thorin theorem and ideas from the theory of complex interpolation. We also employ Sion's minimax theorem.« less

No-go theorem for iterations of unknown quantum gates

NASA Astrophysics Data System (ADS)

Soleimanifar, Mehdi; Karimipour, Vahid

2016-01-01

We propose a no-go theorem by proving the impossibility of constructing a deterministic quantum circuit that iterates a unitary oracle by calling it only once. Different schemes are provided to bypass this result and to approximately realize the iteration. The optimal scheme is also studied. An interesting observation is that for a large number of iterations, a trivial strategy like using the identity channel has the optimal performance, and preprocessing, postprocessing, or using resources like entanglement does not help at all. Intriguingly, the number of iterations, when being large enough, does not affect the performance of the proposed schemes.

Quantum calculus of classical vortex images, integrable models and quantum states

NASA Astrophysics Data System (ADS)

Pashaev, Oktay K.

2016-10-01

From two circle theorem described in terms of q-periodic functions, in the limit q→1 we have derived the strip theorem and the stream function for N vortex problem. For regular N-vortex polygon we find compact expression for the velocity of uniform rotation and show that it represents a nonlinear oscillator. We describe q-dispersive extensions of the linear and nonlinear Schrodinger equations, as well as the q-semiclassical expansions in terms of Bernoulli and Euler polynomials. Different kind of q-analytic functions are introduced, including the pq-analytic and the golden analytic functions.

Inelastic light and electron scattering in parabolic quantum dots in magnetic field: Implications of generalized Kohn's theorem

NASA Astrophysics Data System (ADS)

Kushwaha, Manvir S.

2016-03-01

We investigate a one-component, quasi-zero-dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron energy loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in diverse fields such as quantum computing and medical imaging.

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates.

PubMed

Mitri, F G

2015-09-01

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam's path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque. Copyright © 2015 Elsevier B.V. All rights reserved.

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

Lindgren, Ingvar; Salomonson, Sten

The locality theorem in density-functional theory (DFT) states that the functional derivative of the Hohenberg-Kohn universal functional can be expressed as a local multiplicative potential function, and this is the basis of DFT and of the successful Kohn-Sham model. Nesbet has in several papers [Phys. Rev. A 58, R12 (1998); ibid.65, 010502 (2001); Adv. Quant. Chem, 43, 1 (2003)] claimed that this theorem is in conflict with fundamental quantum physics, and as a consequence that the Hohenberg-Kohn theory cannot be generally valid. We have commented upon these works [Comment, Phys. Rev. A 67, 056501 (2003)] and recently extended the argumentsmore » [Adv. Quantum Chem. 43, 95 (2003)]. We have shown that there is no such conflict and that the locality theorem is inherently exact. In the present work we have furthermore verified this numerically by constructing a local Kohn-Sham potential for the 1s2s{sup 3}S state of helium that generates the many-body electron density and shown that the corresponding 2s Kohn-Sham orbital eigenvalue agrees with the ionization energy to nine digits. Similar result is obtained with the Hartree-Fock density. Therefore, in addition to verifying the locality theorem, this result also confirms the so-called ionization-potential theorem.« less

Quantum identities for the action

NASA Astrophysics Data System (ADS)

Gozzi, E.

2018-04-01

In this paper we derive various identities involving the action functional which enters the path-integral formulation of quantum mechanics. They provide some kind of generalisations of the Ehrenfest theorem giving correlations between powers of the action and its functional derivatives.

Fully Quantum Fluctuation Theorems

NASA Astrophysics Data System (ADS)

Åberg, Johan

2018-02-01

Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce "conditional" fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

NASA Astrophysics Data System (ADS)

Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

2008-11-01

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Role of quantum coherence in the thermodynamics of energy transfer

NASA Astrophysics Data System (ADS)

Henao, Ivan; Serra, Roberto M.

2018-06-01

Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot body to the cold one), posing an apparent challenge to the second law of thermodynamics. Such an "anomalous" heat current was observed in a recent experiment (K. Micadei et al., arXiv:1711.03323), by employing two spin systems initially quantum correlated. Nevertheless, the precise relationship between this intriguing phenomenon and the initial conditions that allow it is not fully evident. Here, we address energy transfer in a wider perspective, identifying a nonclassical contribution that applies to the reversion of the heat flow as well as to more general forms of energy exchange. We derive three theorems that describe the energy transfer between two microscopic systems, for arbitrary initial bipartite states. Using these theorems, we obtain an analytical bound showing that certain type of quantum coherence can optimize such a process, outperforming incoherent states. This genuine quantum advantage is corroborated through a characterization of the energy transfer between two qubits. For this system, it is shown that a large enough amount of coherence is necessary and sufficient to revert the thermodynamic arrow of time. As a second crucial consequence of the presented theorems, we introduce a class of nonequilibrium states that only allow unidirectional energy flow. In this way, we broaden the set where the standard Clausius statement of the second law applies.

Statistical Mechanics and Applications in Condensed Matter

NASA Astrophysics Data System (ADS)

Di Castro, Carlo; Raimondi, Roberto

2015-08-01

Preface; 1. Thermodynamics: a brief overview; 2. Kinetics; 3. From Boltzmann to Gibbs; 4. More ensembles; 5. The thermodynamic limit and its thermodynamic stability; 6. Density matrix and quantum statistical mechanics; 7. The quantum gases; 8. Mean-field theories and critical phenomena; 9. Second quantization and Hartree-Fock approximation; 10. Linear response and fluctuation-dissipation theorem in quantum systems: equilibrium and small deviations; 11. Brownian motion and transport in disordered systems; 12. Fermi liquids; 13. The Landau theory of the second order phase transitions; 14. The Landau-Wilson model for critical phenomena; 15. Superfluidity and superconductivity; 16. The scaling theory; 17. The renormalization group approach; 18. Thermal Green functions; 19. The microscopic foundations of Fermi liquids; 20. The Luttinger liquid; 21. Quantum interference effects in disordered electron systems; Appendix A. The central limit theorem; Appendix B. Some useful properties of the Euler Gamma function; Appendix C. Proof of the second theorem of Yang and Lee; Appendix D. The most probable distribution for the quantum gases; Appendix E. Fermi-Dirac and Bose-Einstein integrals; Appendix F. The Fermi gas in a uniform magnetic field: Landau diamagnetism; Appendix G. Ising and gas-lattice models; Appendix H. Sum over discrete Matsubara frequencies; Appendix I. Hydrodynamics of the two-fluid model of superfluidity; Appendix J. The Cooper problem in the theory of superconductivity; Appendix K. Superconductive fluctuations phenomena; Appendix L. Diagrammatic aspects of the exact solution of the Tomonaga Luttinger model; Appendix M. Details on the theory of the disordered Fermi liquid; References; Author index; Index.

Monte Carlo simulation of quantum Zeno effect in the brain

NASA Astrophysics Data System (ADS)

Georgiev, Danko

2015-12-01

Environmental decoherence appears to be the biggest obstacle for successful construction of quantum mind theories. Nevertheless, the quantum physicist Henry Stapp promoted the view that the mind could utilize quantum Zeno effect to influence brain dynamics and that the efficacy of such mental efforts would not be undermined by environmental decoherence of the brain. To address the physical plausibility of Stapp's claim, we modeled the brain using quantum tunneling of an electron in a multiple-well structure such as the voltage sensor in neuronal ion channels and performed Monte Carlo simulations of quantum Zeno effect exerted by the mind upon the brain in the presence or absence of environmental decoherence. The simulations unambiguously showed that the quantum Zeno effect breaks down for timescales greater than the brain decoherence time. To generalize the Monte Carlo simulation results for any n-level quantum system, we further analyzed the change of brain entropy due to the mind probing actions and proved a theorem according to which local projections cannot decrease the von Neumann entropy of the unconditional brain density matrix. The latter theorem establishes that Stapp's model is physically implausible but leaves a door open for future development of quantum mind theories provided the brain has a decoherence-free subspace.

Adiabatic evolution of decoherence-free subspaces and its shortcuts

NASA Astrophysics Data System (ADS)

Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.

2017-10-01

The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.

Software-defined network abstractions and configuration interfaces for building programmable quantum networks

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

Dasari, Venkat; Sadlier, Ronald J; Geerhart, Mr. Billy

Well-defined and stable quantum networks are essential to realize functional quantum applications. Quantum networks are complex and must use both quantum and classical channels to support quantum applications like QKD, teleportation, and superdense coding. In particular, the no-cloning theorem prevents the reliable copying of quantum signals such that the quantum and classical channels must be highly coordinated using robust and extensible methods. We develop new network abstractions and interfaces for building programmable quantum networks. Our approach leverages new OpenFlow data structures and table type patterns to build programmable quantum networks and to support quantum applications.

Unconditionally secure multi-party quantum commitment scheme

NASA Astrophysics Data System (ADS)

Wang, Ming-Qiang; Wang, Xue; Zhan, Tao

2018-02-01

A new unconditionally secure multi-party quantum commitment is proposed in this paper by encoding the committed message to the phase of a quantum state. Multi-party means that there are more than one recipient in our scheme. We show that our quantum commitment scheme is unconditional hiding and binding, and hiding is perfect. Our technique is based on the interference of phase-encoded coherent states of light. Its security proof relies on the no-cloning theorem of quantum theory and the properties of quantum information.

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'.

Explaining quantum correlations through evolution of causal models

NASA Astrophysics Data System (ADS)

Harper, Robin; Chapman, Robert J.; Ferrie, Christopher; Granade, Christopher; Kueng, Richard; Naoumenko, Daniel; Flammia, Steven T.; Peruzzo, Alberto

2017-04-01

We propose a framework for the systematic and quantitative generalization of Bell's theorem using causal networks. We first consider the multiobjective optimization problem of matching observed data while minimizing the causal effect of nonlocal variables and prove an inequality for the optimal region that both strengthens and generalizes Bell's theorem. To solve the optimization problem (rather than simply bound it), we develop a genetic algorithm treating as individuals causal networks. By applying our algorithm to a photonic Bell experiment, we demonstrate the trade-off between the quantitative relaxation of one or more local causality assumptions and the ability of data to match quantum correlations.

The generalized second law implies a quantum singularity theorem

NASA Astrophysics Data System (ADS)

Wall, Aron C.

2013-08-01

The generalized second law can be used to prove a singularity theorem, by generalizing the notion of a trapped surface to quantum situations. Like Penrose’s original singularity theorem, it implies that spacetime is null-geodesically incomplete inside black holes, and to the past of spatially infinite Friedmann-Robertson-Walker cosmologies. If space is finite instead, the generalized second law requires that there only be a finite amount of entropy producing processes in the past, unless there is a reversal of the arrow of time. In asymptotically flat spacetime, the generalized second law also rules out traversable wormholes, negative masses, and other forms of faster-than-light travel between asymptotic regions, as well as closed timelike curves. Furthermore it is impossible to form baby universes which eventually become independent of the mother universe, or to restart inflation. Since the semiclassical approximation is used only in regions with low curvature, it is argued that the results may hold in full quantum gravity. The introduction describes the second law and its time-reverse, in ordinary and generalized thermodynamics, using either the fine-grained or the coarse-grained entropy. (The fine-grained version is used in all results except those relating to the arrow of time.)

Quantum walks with an anisotropic coin II: scattering theory

NASA Astrophysics Data System (ADS)

Richard, S.; Suzuki, A.; de Aldecoa, R. Tiedra

2018-05-01

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. Our analysis is based on an abstract framework for the scattering theory of unitary operators in a two-Hilbert spaces setting, which is of independent interest.

Generalization of the Bogoliubov-Zubarev Theorem for Dynamic Pressure to the Case of Compressibility

NASA Astrophysics Data System (ADS)

Rudoi, Yu. G.

2018-01-01

We present the motivation, formulation, and modified proof of the Bogoliubov-Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann-Feynman theorem in the framework of the quantum description of a physical object.

One-range addition theorems for derivatives of Slater-type orbitals.

PubMed

Guseinov, Israfil

2004-06-01

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of psi(alpha)-ETOs (Guseinov II (2003) J Mol Model 9:190-194), where alpha=1, 0, -1, -2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron-nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

Generalized Bloch theorem for complex periodic potentials: A powerful application to quantum transport calculations

NASA Astrophysics Data System (ADS)

Zhang, X.-G.; Varga, Kalman; Pantelides, Sokrates T.

2007-07-01

Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations but have not so far been adapted for quantum transport problems with open boundary conditions. Here, we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method are demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data.

Open Quantum Random Walks on the Half-Line: The Karlin-McGregor Formula, Path Counting and Foster's Theorem

NASA Astrophysics Data System (ADS)

Jacq, Thomas S.; Lardizabal, Carlos F.

2017-11-01

In this work we consider open quantum random walks on the non-negative integers. By considering orthogonal matrix polynomials we are able to describe transition probability expressions for classes of walks via a matrix version of the Karlin-McGregor formula. We focus on absorbing boundary conditions and, for simpler classes of examples, we consider path counting and the corresponding combinatorial tools. A non-commutative version of the gambler's ruin is studied by obtaining the probability of reaching a certain fortune and the mean time to reach a fortune or ruin in terms of generating functions. In the case of the Hadamard coin, a counting technique for boundary restricted paths in a lattice is also presented. We discuss an open quantum version of Foster's Theorem for the expected return time together with applications.

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

Flego, S.P.; Plastino, A.; Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca

We explore intriguing links connecting Hellmann-Feynman's theorem to a thermodynamics information-optimizing principle based on Fisher's information measure. - Highlights: > We link a purely quantum mechanical result, the Hellmann-Feynman theorem, with Jaynes' information theoretical reciprocity relations. > These relations involve the coefficients of a series expansion of the potential function. > We suggest the existence of a Legendre transform structure behind Schroedinger's equation, akin to the one characterizing thermodynamics.

Steady states of OQBM: Central Limit Theorem, Gaussian and non-Gaussian behavior

NASA Astrophysics Data System (ADS)

Petruccione, Francesco; Sinayskiy, Ilya

Open Quantum Brownian Motion (OQBM) describes a Brownian particle with an additional internal quantum degree of freedom. Originally, it was introduced as a scaling limit of Open Quantum Walks (OQWs). Recently, it was noted, that for the model of free OQBM with a two-level system as an internal degree of freedom and decoherent coupling to a dissipative environment, one could use weak external driving of the internal degree of freedom to manipulate the steady-state position of the walker. This observation establishes a useful connection between controllable parameters of the OQBM, e.g. driving strengths and magnitude of detuning, and its steady state properties. Although OQWs satisfy a central limit theorem (CLT), it is known, that OQBM, in general, does not. The aim of this work is to derive steady states for some particular OQBMs and observe possible transitions from Gaussian to non-Gaussian behavior depending on the choice of quantum coin and as a function of diffusion coefficient and dissipation strength.

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).

Software-defined network abstractions and configuration interfaces for building programmable quantum networks

NASA Astrophysics Data System (ADS)

Dasari, Venkat R.; Sadlier, Ronald J.; Geerhart, Billy E.; Snow, Nikolai A.; Williams, Brian P.; Humble, Travis S.

2017-05-01

Well-defined and stable quantum networks are essential to realize functional quantum communication applications. Quantum networks are complex and must use both quantum and classical channels to support quantum applications like QKD, teleportation, and superdense coding. In particular, the no-cloning theorem prevents the reliable copying of quantum signals such that the quantum and classical channels must be highly coordinated using robust and extensible methods. In this paper, we describe new network abstractions and interfaces for building programmable quantum networks. Our approach leverages new OpenFlow data structures and table type patterns to build programmable quantum networks and to support quantum applications.

Linear and nonlinear spectroscopy from quantum master equations.

PubMed

Fetherolf, Jonathan H; Berkelbach, Timothy C

2017-12-28

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Linear and nonlinear spectroscopy from quantum master equations

NASA Astrophysics Data System (ADS)

Fetherolf, Jonathan H.; Berkelbach, Timothy C.

2017-12-01

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

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

Koenig, Robert; Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125; Mitchison, Graeme

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result include Renner's 'exponential' approximation by 'almost-product' states, a theorem which deals with certain triples of representations of the unitary group, and the result of D'Cruz et al. [e-print quant-ph/0606139;Phys. Rev. Lett. 98, 160406 (2007)] for infinite-dimensional systems. We show how these theorems follow from a single, general de Finetti theorem for representations of symmetry groups, each instance corresponding to a particular choicemore » of symmetry group and representation of that group. This gives some insight into the nature of the set of approximating states and leads to some new results, including an exponential theorem for infinite-dimensional systems.« less

Recoverability in quantum information theory

NASA Astrophysics Data System (ADS)

Wilde, Mark

The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.

A short walk in quantum probability

NASA Astrophysics Data System (ADS)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.

Quantum State Tomography of a Fiber-Based Source of Polarization-Entangled Photon Pairs

DTIC Science & Technology

2007-12-20

Processing 175−179 (IEEE, Bangalore, 1984). 4. A. K. Ekert, “ Quantum cryptography based on Bell’s theorem ,” Phys. Rev. Lett. 67, 661–663 (1991). 5...NUMBERS Quantum State Tomography of a Fiber- Based Source of MURI Center for Photonic Quantum Information Systems: AROIARDA Program Polarization...Computer Society Press, Los Alamitos, 1996). 7. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “ Quantum cryptography ,” Rev. Mod. Phys. 74, 145

Bell's theorem and quantum mechanics

NASA Astrophysics Data System (ADS)

Rosen, Nathan

1994-02-01

Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor

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.

Quantum chaos in nuclear physics

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

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

Transient quantum fluctuation theorems and generalized measurements

NASA Astrophysics Data System (ADS)

Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter

2014-01-01

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol. We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.

Transient quantum fluctuation theorems and generalized measurements

NASA Astrophysics Data System (ADS)

Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter

2014-05-01

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol.We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.

Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes

DOE PAGES

Remmen, Grant N.; Bao, Ning; Pollack, Jason

2016-07-11

We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throatmore » separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.« less

Entanglement conservation, ER=EPR, and a new classical area theorem for wormholes

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

Remmen, Grant N.; Bao, Ning; Pollack, Jason

We consider the question of entanglement conservation in the context of the ER=EPR correspondence equating quantum entanglement with wormholes. In quantum mechanics, the entanglement between a system and its complement is conserved under unitary operations that act independently on each; ER=EPR suggests that an analogous statement should hold for wormholes. We accordingly prove a new area theorem in general relativity: for a collection of dynamical wormholes and black holes in a spacetime satisfying the null curvature condition, the maximin area for a subset of the horizons (giving the largest area attained by the minimal cross section of the multi-wormhole throatmore » separating the subset from its complement) is invariant under classical time evolution along the outermost apparent horizons. The evolution can be completely general, including horizon mergers and the addition of classical matter satisfying the null energy condition. In conclusion, this theorem is the gravitational dual of entanglement conservation and thus constitutes an explicit characterization of the ER=EPR duality in the classical limit.« less

A Cameron-Storvick Theorem for Analytic Feynman Integrals on Product Abstract Wiener Space and Applications

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

Choi, Jae Gil, E-mail: jgchoi@dankook.ac.kr; Chang, Seung Jun, E-mail: sejchang@dankook.ac.kr

In this paper we derive a Cameron-Storvick theorem for the analytic Feynman integral of functionals on product abstract Wiener space B{sup 2}. We then apply our result to obtain an evaluation formula for the analytic Feynman integral of unbounded functionals on B{sup 2}. We also present meaningful examples involving functionals which arise naturally in quantum mechanics.

Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states

PubMed Central

Haw, Jing Yan; Zhao, Jie; Dias, Josephine; Assad, Syed M.; Bradshaw, Mark; Blandino, Rémi; Symul, Thomas; Ralph, Timothy C.; Lam, Ping Koy

2016-01-01

The no-cloning theorem states that an unknown quantum state cannot be cloned exactly and deterministically due to the linearity of quantum mechanics. Associated with this theorem is the quantitative no-cloning limit that sets an upper bound to the quality of the generated clones. However, this limit can be circumvented by abandoning determinism and using probabilistic methods. Here, we report an experimental demonstration of probabilistic cloning of arbitrary coherent states that clearly surpasses the no-cloning limit. Our scheme is based on a hybrid linear amplifier that combines an ideal deterministic linear amplifier with a heralded measurement-based noiseless amplifier. We demonstrate the production of up to five clones with the fidelity of each clone clearly exceeding the corresponding no-cloning limit. Moreover, since successful cloning events are heralded, our scheme has the potential to be adopted in quantum repeater, teleportation and computing applications. PMID:27782135

Testing subleading multiple soft graviton theorem for CHY prescription

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2018-01-01

In arXiv:1707.06803 we derived the subleading multiple soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. In this paper we verify this explicitly using the CHY formula for tree level scattering amplitudes of arbitrary number of gravitons in Einstein gravity. We pay special care to fix the signs of the amplitudes and resolve an apparent discrepancy between our general results in arXiv:1707.06803 and previous results on soft graviton theorem from CHY formula.

Classical-Quantum Correspondence by Means of Probability Densities

NASA Technical Reports Server (NTRS)

Vegas, Gabino Torres; Morales-Guzman, J. D.

1996-01-01

Within the frame of the recently introduced phase space representation of non relativistic quantum mechanics, we propose a Lagrangian from which the phase space Schrodinger equation can be derived. From that Lagrangian, the associated conservation equations, according to Noether's theorem, are obtained. This shows that one can analyze quantum systems completely in phase space as it is done in coordinate space, without additional complications.

The spectral theorem for quaternionic unbounded normal operators based on the S-spectrum

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

Alpay, Daniel, E-mail: dany@math.bgu.ac.il; Kimsey, David P., E-mail: dpkimsey@gmail.com; Colombo, Fabrizio, E-mail: fabrizio.colombo@polimi.it

In this paper we prove the spectral theorem for quaternionic unbounded normal operators using the notion of S-spectrum. The proof technique consists of first establishing a spectral theorem for quaternionic bounded normal operators and then using a transformation which maps a quaternionic unbounded normal operator to a quaternionic bounded normal operator. With this paper we complete the foundation of spectral analysis of quaternionic operators. The S-spectrum has been introduced to define the quaternionic functional calculus but it turns out to be the correct object also for the spectral theorem for quaternionic normal operators. The lack of a suitable notion ofmore » spectrum was a major obstruction to fully understand the spectral theorem for quaternionic normal operators. A prime motivation for studying the spectral theorem for quaternionic unbounded normal operators is given by the subclass of unbounded anti-self adjoint quaternionic operators which play a crucial role in the quaternionic quantum mechanics.« less

Quantum Theory from Observer's Mathematics Point of View

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

Khots, Dmitriy; Khots, Boris

2010-05-04

This work considers the linear (time-dependent) Schrodinger equation, quantum theory of two-slit interference, wave-particle duality for single photons, and the uncertainty principle in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics, see [1]. Certain theoretical results and communications pertaining to these theorems are also provided.

Completeness of the Coulomb Wave Functions in Quantum Mechanics

ERIC Educational Resources Information Center

Mukunda, N.

1978-01-01

Gives an explicit and elementary proof that the radial energy eigenfunctions for the hydrogen atom in quantum mechanics, bound and scattering states included, form a complete set. The proof uses some properties of the confluent hypergeometric functions and the Cauchy residue theorem from analytic function theory. (Author/GA)

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.

Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state.

PubMed

Gieseler, Jan; Quidant, Romain; Dellago, Christoph; Novotny, Lukas

2014-05-01

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for understanding irreversibility and the second law in fundamental chemical and biological processes that are actively driven, thus operating far from thermal equilibrium. Here, we apply the framework of fluctuation theorems to investigate the important case of a system relaxing from a non-equilibrium state towards equilibrium. Using a vacuum-trapped nanoparticle, we demonstrate experimentally the validity of a fluctuation theorem for the relative entropy change occurring during relaxation from a non-equilibrium steady state. The platform established here allows non-equilibrium fluctuation theorems to be studied experimentally for arbitrary steady states and can be extended to investigate quantum fluctuation theorems as well as systems that do not obey detailed balance.

A short walk in quantum probability.

PubMed

Hudson, Robin

2018-04-28

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Quantum many-body adiabaticity, topological Thouless pump and driven impurity in a one-dimensional quantum fluid

NASA Astrophysics Data System (ADS)

Lychkovskiy, Oleg; Gamayun, Oleksandr; Cheianov, Vadim

2018-02-01

The quantum adiabatic theorem states that a driven system can be kept arbitrarily close to the instantaneous eigenstate of its Hamiltonian if the latter varies in time slowly enough. When it comes to applying the adiabatic theorem in practice, the key question to be answered is how slow slowly enough is. This question can be an intricate one, especially for many-body systems, where the limits of slow driving and large system size may not commute. Recently we have shown how the quantum adiabaticity in many-body systems is related to the generalized orthogonality catastrophe [arXiv 1611.00663, to appear in Phys. Rev. Lett.]. We have proven a rigorous inequality relating these two phenomena and applied it to establish conditions for the quantized transport in the topological Thouless pump. In the present contribution we (i) review these developments and (ii) apply the inequality to establish the conditions for adiabaticity in a one-dimensional system consisting of a quantum fluid and an impurity particle pulled through the fluid by an external force. The latter analysis is vital for the correct quantitative description of the phenomenon of quasi-Bloch oscillations in a one-dimensional translation invariant impurity-fluid system.

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.

Tests of alternative quantum theories with neutrons

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

Sponar, S.; Durstberger-Rennhofer, K.; Badurek, G.

2014-12-04

According to Bell’s theorem, every theory based on local realism is at variance with certain predictions of quantum mechanics. A theory that maintains realism but abandons reliance on locality, which has been proposed by Leggett, is incompatible with experimentally observable quantum correlations. In our experiment correlation measurements of spin-energy entangled single-neutrons violate a Leggett-type inequality by more than 7.6 standard deviations. The experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.

Bit-Oriented Quantum Public-Key Cryptosystem Based on Bell States

NASA Astrophysics Data System (ADS)

Wu, WanQing; Cai, QingYu; Zhang, HuanGuo; Liang, XiaoYan

2018-02-01

Quantum public key encryption system provides information confidentiality using quantum mechanics. This paper presents a quantum public key cryptosystem (Q P K C) based on the Bell states. By H o l e v o's theorem, the presented scheme provides the security of the secret key using one-wayness during the QPKC. While the QPKC scheme is information theoretic security under chosen plaintext attack (C P A). Finally some important features of presented QPKC scheme can be compared with other QPKC scheme.

Extracontextuality and extravalence in quantum mechanics.

PubMed

Auffèves, Alexia; Grangier, Philippe

2018-07-13

We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Bit-Oriented Quantum Public-Key Cryptosystem Based on Bell States

NASA Astrophysics Data System (ADS)

Wu, WanQing; Cai, QingYu; Zhang, HuanGuo; Liang, XiaoYan

2018-06-01

Quantum public key encryption system provides information confidentiality using quantum mechanics. This paper presents a quantum public key cryptosystem ( Q P K C) based on the Bell states. By H o l e v o' s theorem, the presented scheme provides the security of the secret key using one-wayness during the QPKC. While the QPKC scheme is information theoretic security under chosen plaintext attack ( C P A). Finally some important features of presented QPKC scheme can be compared with other QPKC scheme.

Quantum work statistics of charged Dirac particles in time-dependent fields

DOE PAGES

Deffner, Sebastian; Saxena, Avadh

2015-09-28

The quantum Jarzynski equality is an important theorem of modern quantum thermodynamics. We show that the Jarzynski equality readily generalizes to relativistic quantum mechanics described by the Dirac equation. After establishing the conceptual framework we solve a pedagogical, yet experimentally relevant, system analytically. As a main result we obtain the exact quantum work distributions for charged particles traveling through a time-dependent vector potential evolving under Schrödinger as well as under Dirac dynamics, and for which the Jarzynski equality is verified. Thus, special emphasis is put on the conceptual and technical subtleties arising from relativistic quantum mechanics.

The faithful remote preparation of general quantum states

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing; Deng, Yun; Chen, Xiu-Bo; Yang, Yi-Xian

2013-01-01

This paper is to establish a theoretical framework for faithful and deterministic remote state preparation, which is related to the classical Hurwitz theorem. And then based on the new theory various schemes with different characteristics are presented. Moreover, the permutation group and the partially quantum resources have also discussed for faithful schemes.

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

Bosonization in Space-Time

NASA Astrophysics Data System (ADS)

Stone, Michael

The following sections are included: * Introduction * Free Fermi Fields * Free Bosons * The Bosonization Rules * A Quantum Pythagoras Theorem * Appendix 1A. Complex Coordinates * Appendix IB. Conformal Symmetry * References

No-go theorem for boson condensation in topologically ordered quantum liquids

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

Neupert, Titus; He, Huan; Keyserlingk, Curt von

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

No-go theorem for boson condensation in topologically ordered quantum liquids

DOE PAGES

Neupert, Titus; He, Huan; Keyserlingk, Curt von; ...

2016-12-07

Certain phase transitions between topological quantum field theories (TQFTs) are driven by the condensation of bosonic anyons. However, as bosons in a TQFT are themselves nontrivial collective excitations, there can be topological obstructions that prevent them from condensing. Here we formulate such an obstruction in the form of a no-go theorem. We use it to show that no condensation is possible in SO(3) k TQFTs with odd k. We further show that a 'layered' theory obtained by tensoring SO(3) k TQFT with itself any integer number of times does not admit condensation transitions either. Furthermore, this includes (as the casemore » k = 3) the noncondensability of any number of layers of the Fibonacci TQFT.« less

Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems

NASA Astrophysics Data System (ADS)

Laloë, F.

2001-06-01

This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: They are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except for very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrödinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) may be a potential source for conflicts; various attitudes that are possible to avoid this problem are discussed in this text. After a brief historical introduction, recalling how the very special status of the state vector has emerged in quantum mechanics, various conceptual difficulties are introduced and discussed. The Einstein-Podolsky-Rosen (EPR) theorem is presented with the help of a botanical parable, in a way that emphasizes how deeply the EPR reasoning is rooted into what is often called "scientific method." In another section the Greenberger-Horne-Zeilinger argument, the Hardy impossibilities, as well as the Bell-Kochen-Specker theorem are introduced in simple terms. The final two sections attempt to give a summary of the present situation: One section discusses nonlocality and entanglement as we see it presently, with brief mention of recent experiments; the last section contains a (nonexhaustive) list of various attitudes that are found among physicists, and that are helpful to alleviate the conceptual difficulties of quantum mechanics.

A No-Go Theorem for the Continuum Limit of a Periodic Quantum Spin Chain

NASA Astrophysics Data System (ADS)

Jones, Vaughan F. R.

2018-01-01

We show that the Hilbert space formed from a block spin renormalization construction of a cyclic quantum spin chain (based on the Temperley-Lieb algebra) does not support a chiral conformal field theory whose Hamiltonian generates translation on the circle as a continuous limit of the rotations on the lattice.

Averaging in SU(2) open quantum random walk

NASA Astrophysics Data System (ADS)

Clement, Ampadu

2014-03-01

We study the average position and the symmetry of the distribution in the SU(2) open quantum random walk (OQRW). We show that the average position in the central limit theorem (CLT) is non-uniform compared with the average position in the non-CLT. The symmetry of distribution is shown to be even in the CLT.

Quantum technology past, present, future: quantum energetics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Choi, Sang H.

2017-04-01

Since the development of quantum physics in the early part of the 1900s, this field of study has made remarkable contributions to our civilization. Some of these advances include lasers, light-emitting diodes (LED), sensors, spectroscopy, quantum dots, quantum gravity and quantum entanglements. In 1998, the NASA Langley Research Center established a quantum technology committee to monitor the progress in this area and initiated research to determine the potential of quantum technology for future NASA missions. The areas of interest in quantum technology at NASA included fundamental quantum-optics materials associated with quantum dots and quantum wells, device-oriented photonic crystals, smart optics, quantum conductors, quantum information and computing, teleportation theorem, and quantum energetics. A brief review of the work performed, the progress made in advancing these technologies, and the potential NASA applications of quantum technology will be presented.

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

Experimental Test of Compatibility-Loophole-Free Contextuality with Spatially Separated Entangled Qutrits.

PubMed

Hu, Xiao-Min; Chen, Jiang-Shan; Liu, Bi-Heng; Guo, Yu; Huang, Yun-Feng; Zhou, Zong-Quan; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can

2016-10-21

The physical impact and the testability of the Kochen-Specker (KS) theorem is debated because of the fact that perfect compatibility in a single quantum system cannot be achieved in practical experiments with finite precision. Here, we follow the proposal of A. Cabello and M. T. Cunha [Phys. Rev. Lett. 106, 190401 (2011)], and present a compatibility-loophole-free experimental violation of an inequality of noncontextual theories by two spatially separated entangled qutrits. A maximally entangled qutrit-qutrit state with a fidelity as high as 0.975±0.001 is prepared and distributed to separated spaces, and these two photons are then measured locally, providing the compatibility requirement. The results show that the inequality for noncontextual theory is violated by 31 standard deviations. Our experiments pave the way to close the debate about the testability of the KS theorem. In addition, the method to generate high-fidelity and high-dimension entangled states will provide significant advantages in high-dimension quantum encoding and quantum communication.

H-theorem and Maxwell demon in quantum physics

NASA Astrophysics Data System (ADS)

Kirsanov, N. S.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.; Blatter, G.; Lesovik, G. B.

2018-02-01

The Second Law of Thermodynamics states that temporal evolution of an isolated system occurs with non-diminishing entropy. In quantum realm, this holds for energy-isolated systems the evolution of which is described by the so-called unital quantum channel. The entropy of a system evolving in a non-unital quantum channel can, in principle, decrease. We formulate a general criterion of unitality for the evolution of a quantum system, enabling a simple and rigorous approach for finding and identifying the processes accompanied by decreasing entropy in energy-isolated systems. We discuss two examples illustrating our findings, the quantum Maxwell demon and heating-cooling process within a two-qubit system.

Typical Local Measurements in Generalized Probabilistic Theories: Emergence of Quantum Bipartite Correlations

NASA Astrophysics Data System (ADS)

Kleinmann, Matthias; Osborne, Tobias J.; Scholz, Volkher B.; Werner, Albert H.

2013-01-01

What singles out quantum mechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalization of Dvoretzky’s theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

Classical noise, quantum noise and secure communication

NASA Astrophysics Data System (ADS)

Tannous, C.; Langlois, J.

2016-01-01

Secure communication based on message encryption might be performed by combining the message with controlled noise (called pseudo-noise) as performed in spread-spectrum communication used presently in Wi-Fi and smartphone telecommunication systems. Quantum communication based on entanglement is another route for securing communications as demonstrated by several important experiments described in this work. The central role played by the photon in unifying the description of classical and quantum noise as major ingredients of secure communication systems is highlighted and described on the basis of the classical and quantum fluctuation dissipation theorems.

Some conservative estimates in quantum cryptography

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

Molotkov, S. N.

2006-08-15

Relationship is established between the security of the BB84 quantum key distribution protocol and the forward and converse coding theorems for quantum communication channels. The upper bound Q{sub c} {approx} 11% on the bit error rate compatible with secure key distribution is determined by solving the transcendental equation H(Q{sub c})=C-bar({rho})/2, where {rho} is the density matrix of the input ensemble, C-bar({rho}) is the classical capacity of a noiseless quantum channel, and H(Q) is the capacity of a classical binary symmetric channel with error rate Q.

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

More, R.M.

A new statistical model (the quantum-statistical model (QSM)) was recently introduced by Kalitkin and Kuzmina for the calculation of thermodynamic properties of compressed matter. This paper examines the QSM and gives (i) a numerical QSM calculation of pressure and energy for aluminum and comparison to existing augmented-plane-wave data; (ii) display of separate kinetic, exchange, and quantum pressure terms; (iii) a study of electron density at the nucleus; (iv) a study of the effects of the Kirzhnitz-Weizsacker parameter controlling the gradient terms; (v) an analytic expansion for very high densities; and (vi) rigorous pressure theorems including a general version of themore » virial theorem which applies to an arbitrary microscopic volume. It is concluded that the QSM represents the most accurate and consistent theory of the Thomas-Fermi type.« less

Black holes, information, and the universal coefficient theorem

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

Patrascu, Andrei T.

2016-07-15

General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

Memory-built-in quantum cloning in a hybrid solid-state spin register

NASA Astrophysics Data System (ADS)

Wang, W.-B.; Zu, C.; He, L.; Zhang, W.-G.; Duan, L.-M.

2015-07-01

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude. The realization of a cloning machine with built-in quantum memory provides a key step for application of quantum cloning in quantum information science.

Memory-built-in quantum cloning in a hybrid solid-state spin register.

PubMed

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

2015-07-16

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude. The realization of a cloning machine with built-in quantum memory provides a key step for application of quantum cloning in quantum information science.

Work Measurement as a Generalized Quantum Measurement

NASA Astrophysics Data System (ADS)

Roncaglia, Augusto J.; Cerisola, Federico; Paz, Juan Pablo

2014-12-01

We present a new method to measure the work w performed on a driven quantum system and to sample its probability distribution P (w ). The method is based on a simple fact that remained unnoticed until now: Work on a quantum system can be measured by performing a generalized quantum measurement at a single time. Such measurement, which technically speaking is denoted as a positive operator valued measure reduces to an ordinary projective measurement on an enlarged system. This observation not only demystifies work measurement but also suggests a new quantum algorithm to efficiently sample the distribution P (w ). This can be used, in combination with fluctuation theorems, to estimate free energies of quantum states on a quantum computer.

Extended Quantum Field Theory, Index Theory, and the Parity Anomaly

NASA Astrophysics Data System (ADS)

Müller, Lukas; Szabo, Richard J.

2018-06-01

We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of a geometric cobordism bicategory which incorporates general background fields in a stack, and together with the theory of symmetric monoidal bicategories we use it to provide the concrete forms of invertible extended quantum field theories which capture anomalies in both the path integral and Hamiltonian frameworks. Specialising this situation by using the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and Melrose, we obtain a new Hamiltonian perspective on the parity anomaly. We compute explicitly the 2-cocycle of the projective representation of the gauge symmetry on the quantum state space, which is defined in a parity-symmetric way by suitably augmenting the standard chiral fermionic Fock spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that naturally appear in the index theorem. We describe the significance of our constructions for the bulk-boundary correspondence in a large class of time-reversal invariant gauge-gravity symmetry-protected topological phases of quantum matter with gapless charged boundary fermions, including the standard topological insulator in 3 + 1 dimensions.

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".

Generalized reciprocity theorem for semiconductor devices

NASA Technical Reports Server (NTRS)

Misiakos, K.; Lindholm, F. A.

1985-01-01

A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.

Resolution of the EPR Paradox for Fermion Spin Correlations

NASA Astrophysics Data System (ADS)

Close, Robert

2011-10-01

The EPR paradox addresses the question of whether a physical system can have a definite state independent of its measurement. Bell's Theorem places limits on correlations between local measurements of particles whose properties are established prior to measurement. Experimental violation of Bell's theorem has been regarded as evidence against the existence of a definite state prior to measurement. We model fermions as having a spatial distribution of spin values, so that a Stern-Gerlach device samples the spin distribution differently at different orientations. The computed correlations agree with quantum mechanical predictions and experimental observations. Bell's Theorem is not applicable because for any sampling of angles, different points on the sphere have different density of states.

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Noncommutative gauge theory for Poisson manifolds

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Wess, Julius

2000-09-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface

ERIC Educational Resources Information Center

Fernandez, Francisco M.

2010-01-01

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…

Bell Nonlocality, Signal Locality and Unpredictability (or What Bohr Could Have Told Einstein at Solvay Had He Known About Bell Experiments)

NASA Astrophysics Data System (ADS)

Cavalcanti, Eric G.; Wiseman, Howard M.

2012-10-01

The 1964 theorem of John Bell shows that no model that reproduces the predictions of quantum mechanics can simultaneously satisfy the assumptions of locality and determinism. On the other hand, the assumptions of signal locality plus predictability are also sufficient to derive Bell inequalities. This simple theorem, previously noted but published only relatively recently by Masanes, Acin and Gisin, has fundamental implications not entirely appreciated. Firstly, nothing can be concluded about the ontological assumptions of locality or determinism independently of each other—it is possible to reproduce quantum mechanics with deterministic models that violate locality as well as indeterministic models that satisfy locality. On the other hand, the operational assumption of signal locality is an empirically testable (and well-tested) consequence of relativity. Thus Bell inequality violations imply that we can trust that some events are fundamentally unpredictable, even if we cannot trust that they are indeterministic. This result grounds the quantum-mechanical prohibition of arbitrarily accurate predictions on the assumption of no superluminal signalling, regardless of any postulates of quantum mechanics. It also sheds a new light on an early stage of the historical debate between Einstein and Bohr.

An Estimation of the Logarithmic Timescale in Ergodic Dynamics

NASA Astrophysics Data System (ADS)

Gomez, Ignacio S.

An estimation of the logarithmic timescale in quantum systems having an ergodic dynamics in the semiclassical limit, is presented. The estimation is based on an extension of the Krieger’s finite generator theorem for discretized σ-algebras and using the time rescaling property of the Kolmogorov-Sinai entropy. The results are in agreement with those obtained in the literature but with a simpler mathematics and within the context of the ergodic theory. Moreover, some consequences of the Poincaré’s recurrence theorem are also explored.

Subleading soft theorem for multiple soft gravitons

NASA Astrophysics Data System (ADS)

Chakrabarti, Subhroneel; Kashyap, Sitender Pratap; Sahoo, Biswajit; Sen, Ashoke; Verma, Mritunjay

2017-12-01

We derive the subleading soft graviton theorem in a generic quantum theory of gravity for arbitrary number of soft external gravitons and arbitrary number of finite energy external states carrying arbitrary mass and spin. Our results are valid to all orders in perturbation theory when the number of non-compact space-time dimensions is six or more, but only for tree amplitudes for five or less non-compact space-time dimensions due to enhanced contribution to loop amplitudes from the infrared region.

Memory-built-in quantum cloning in a hybrid solid-state spin register

PubMed Central

Wang, W.-B.; Zu, C.; He, L.; Zhang, W.-G.; Duan, L.-M.

2015-01-01

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude. The realization of a cloning machine with built-in quantum memory provides a key step for application of quantum cloning in quantum information science. PMID:26178617

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

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stabilitymore » parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.« less

Quantum mechanics: The Bayesian theory generalized to the space of Hermitian matrices

NASA Astrophysics Data System (ADS)

Benavoli, Alessio; Facchini, Alessandro; Zaffalon, Marco

2016-10-01

We consider the problem of gambling on a quantum experiment and enforce rational behavior by a few rules. These rules yield, in the classical case, the Bayesian theory of probability via duality theorems. In our quantum setting, they yield the Bayesian theory generalized to the space of Hermitian matrices. This very theory is quantum mechanics: in fact, we derive all its four postulates from the generalized Bayesian theory. This implies that quantum mechanics is self-consistent. It also leads us to reinterpret the main operations in quantum mechanics as probability rules: Bayes' rule (measurement), marginalization (partial tracing), independence (tensor product). To say it with a slogan, we obtain that quantum mechanics is the Bayesian theory in the complex numbers.

Single-Photon-Triggered Quantum Phase Transition

NASA Astrophysics Data System (ADS)

Lü, Xin-You; Zheng, Li-Li; Zhu, Gui-Lei; Wu, Ying

2018-06-01

We propose a hybrid quantum model combining cavity QED and optomechanics, which allows the occurrence of an equilibrium superradiant quantum phase transition (QPT) triggered by a single photon. This single-photon-triggered QPT exists in the cases of both ignoring and including the so-called A2 term; i.e., it is immune to the no-go theorem. It originally comes from the photon-dependent quantum criticality featured by the proposed hybrid quantum model. Moreover, a reversed superradiant QPT is induced by the competition between the introduced A2 term and the optomechanical interaction. This work offers an approach to manipulate QPT with a single photon, which should inspire the exploration of single-photon quantum-criticality physics and the engineering of new single-photon quantum devices.

The generalization of the Mermin-Wagner theorem and the possibility of long-range order in the isotropic discrete one-dimensional quantum Heisenberg model

NASA Astrophysics Data System (ADS)

Rudoy, Yu. G.; Kotelnikova, O. A.

2012-10-01

The problem of existence of long-range order in the isotropic quantum Heisenberg model on the D=1 lattice is reconsidered in view of the possibility of sufficiently slow decaying exchange interaction with infinite effective radius. It is shown that the macrosopic arguments given by Landau and Lifshitz and then supported microscopically by Mermin and Wagner fail for this case so that the non-zero spontaneous magnetization may yet exist. This result was anticipated by Thouless on the grounds of phenomenological analysis, and we give its microscopic foundation, which amounts to the generalization of Mermin-Wagner theorem for the case of the infinite second moment of the exchange interaction. Two well known in lattice statistics models - i.e., Kac-I and Kac-II - illustrate our results.

Significant-Loophole-Free Test of Bell's Theorem with Entangled Photons.

PubMed

Giustina, Marissa; Versteegh, Marijn A M; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Pruneri, Valerio; Mitchell, Morgan W; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E; Shalm, Lynden K; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton

2015-12-18

Local realism is the worldview in which physical properties of objects exist independently of measurement and where physical influences cannot travel faster than the speed of light. Bell's theorem states that this worldview is incompatible with the predictions of quantum mechanics, as is expressed in Bell's inequalities. Previous experiments convincingly supported the quantum predictions. Yet, every experiment requires assumptions that provide loopholes for a local realist explanation. Here, we report a Bell test that closes the most significant of these loopholes simultaneously. Using a well-optimized source of entangled photons, rapid setting generation, and highly efficient superconducting detectors, we observe a violation of a Bell inequality with high statistical significance. The purely statistical probability of our results to occur under local realism does not exceed 3.74×10^{-31}, corresponding to an 11.5 standard deviation effect.

Breakdown of the Wigner-Mattis theorem in semiconductor carbon-nanotube quantum dots

NASA Astrophysics Data System (ADS)

Rontani, Massimo; Secchi, Andrea; Manghi, Franca

2009-03-01

The Wigner-Mattis theorem states the ground state of two bound electrons, in the absence of the magnetic field, is always a spin-singlet. We predict the opposite result --a triplet- for two electrons in a quantum dot defined in a semiconductor carbon nanotube. The claim is supported by extensive many-body calculations based on the accurate configuration interaction code DONRODRIGO (www.s3.infm.t/donrodrigo). The crux of the matter is the peculiar two-valley structure of low-energy states, which encodes a pseudo-spin degree of freedom. The spin polarization of the ground state corresponds to a pseudo-spin singlet, which is selected by the inter-valley short-range Coulomb interaction. Single-electron excitation spectra and STM wave function images may validate this scenario, as shown by our numerical simulations.

Quantum Spin Stabilized Magnetic Levitation

NASA Astrophysics Data System (ADS)

Rusconi, C. C.; Pöchhacker, V.; Kustura, K.; Cirac, J. I.; Romero-Isart, O.

2017-10-01

We theoretically show that, despite Earnshaw's theorem, a nonrotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely, the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein-de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that, in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.

Quantum Spin Stabilized Magnetic Levitation.

PubMed

Rusconi, C C; Pöchhacker, V; Kustura, K; Cirac, J I; Romero-Isart, O

2017-10-20

We theoretically show that, despite Earnshaw's theorem, a nonrotating single magnetic domain nanoparticle can be stably levitated in an external static magnetic field. The stabilization relies on the quantum spin origin of magnetization, namely, the gyromagnetic effect. We predict the existence of two stable phases related to the Einstein-de Haas effect and the Larmor precession. At a stable point, we derive a quadratic Hamiltonian that describes the quantum fluctuations of the degrees of freedom of the system. We show that, in the absence of thermal fluctuations, the quantum state of the nanomagnet at the equilibrium point contains entanglement and squeezing.

The new electromagnetic tetrads, infinite tetrad nesting and the non-trivial emergence of complex numbers in real theories of gravitation

NASA Astrophysics Data System (ADS)

Garat, Alcides

How complex numbers get into play in a non-trivial way in real theories of gravitation is relevant since in a unified structure they should be able to relate in a natural way with quantum theories. For a long time this issue has been lingering on both relativistic formulations and quantum theories. We will analyze this fundamental subject under the light of new group isomorphism theorems linking local internal groups of transformations and local groups of spacetime transformations. The bridge between these two kinds of transformations is represented by new tetrads introduced previously. It is precisely through these local tetrad structures that we will provide a non-trivial answer to this old issue. These new tetrads have two fundamental building components, the skeletons and the gauge vectors. It is these constructive elements that provide the mathematical support that allows to prove group isomorphism theorems. In addition to this, we will prove a unique new property, the infinite tetrad nesting, alternating the nesting with non-Abelian tetrads in the construction of the tetrad gauge vectors. As an application we will demonstrate an alternative proof of a new group isomorphism theorem.

A Meinardus Theorem with Multiple Singularities

NASA Astrophysics Data System (ADS)

Granovsky, Boris L.; Stark, Dudley

2012-09-01

Meinardus proved a general theorem about the asymptotics of the number of weighted partitions, when the Dirichlet generating function for weights has a single pole on the positive real axis. Continuing (Granovsky et al., Adv. Appl. Math. 41:307-328, 2008), we derive asymptotics for the numbers of three basic types of decomposable combinatorial structures (or, equivalently, ideal gas models in statistical mechanics) of size n, when their Dirichlet generating functions have multiple simple poles on the positive real axis. Examples to which our theorem applies include ones related to vector partitions and quantum field theory. Our asymptotic formula for the number of weighted partitions disproves the belief accepted in the physics literature that the main term in the asymptotics is determined by the rightmost pole.

A Geometrical Approach to Bell's Theorem

NASA Technical Reports Server (NTRS)

Rubincam, David Parry

2000-01-01

Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.

The (virtual) conceptual necessity of quantum probabilities in cognitive psychology.

PubMed

Blutner, Reinhard; beim Graben, Peter

2013-06-01

We propose a way in which Pothos & Busemeyer (P&B) could strengthen their position. Taking a dynamic stance, we consider cognitive tests as functions that transfer a given input state into the state after testing. Under very general conditions, it can be shown that testable properties in cognition form an orthomodular lattice. Gleason's theorem then yields the conceptual necessity of quantum probabilities (QP).

A Survey of Quantum Programming Languages: History, Methods, and Tools

DTIC Science & Technology

2008-01-01

and entanglement , to achieve computational solutions to certain problems in less time (fewer computational cycles) than is possible using classical...superposition of quantum bits, entanglement , destructive measurement, and the no-cloning theorem. These differences must be thoroughly understood and even...computers using well-known languages such as C, C++, Java, and rapid prototyping languages such as Maple, Mathematica, and Matlab . A good on-line

Rapid Communication: Quasi-gedanken experiment challenging the no-signalling theorem

NASA Astrophysics Data System (ADS)

Kalamidas, Demetrios A.

2018-01-01

Kennedy ( Philos. Sci. 62, 4 (1995)) has argued that the various quantum mechanical no-signalling proofs formulated thus far share a common mathematical framework, are circular in nature, and do not preclude the construction of empirically testable schemes wherein superluminal exchange of information can occur. In light of this thesis, we present a potentially feasible quantum-optical scheme that purports to enable superluminal signalling.

Quantum Enhanced Imaging by Entangled States

DTIC Science & Technology

2009-07-01

classes of entangled states. In tripartite systems two classes of genuine tripartite entanglement have been discovered, namely, the Greenberger -Horne...D. M. Greenberger , M. Horne and A. Zeilinger, in Bell’s Theorem, Quantum Theory, and Concepts of the Universe, ed. M. Kafatos (Kluwer, Dordrecht 1989...Gallium Indium Arsenide Phosphide (a III-V compound semiconductor) GHZ: Greenberger -Horne-Zeilinger (a class of entangled states) GLAD: General

An Identity-Based Anti-Quantum Privacy-Preserving Blind Authentication in Wireless Sensor Networks.

PubMed

Zhu, Hongfei; Tan, Yu-An; Zhu, Liehuang; Wang, Xianmin; Zhang, Quanxin; Li, Yuanzhang

2018-05-22

With the development of wireless sensor networks, IoT devices are crucial for the Smart City; these devices change people's lives such as e-payment and e-voting systems. However, in these two systems, the state-of-art authentication protocols based on traditional number theory cannot defeat a quantum computer attack. In order to protect user privacy and guarantee trustworthy of big data, we propose a new identity-based blind signature scheme based on number theorem research unit lattice, this scheme mainly uses a rejection sampling theorem instead of constructing a trapdoor. Meanwhile, this scheme does not depend on complex public key infrastructure and can resist quantum computer attack. Then we design an e-payment protocol using the proposed scheme. Furthermore, we prove our scheme is secure in the random oracle, and satisfies confidentiality, integrity, and non-repudiation. Finally, we demonstrate that the proposed scheme outperforms the other traditional existing identity-based blind signature schemes in signing speed and verification speed, outperforms the other lattice-based blind signature in signing speed, verification speed, and signing secret key size.

Diagrammar in classical scalar field theory

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

Cattaruzza, E., E-mail: Enrico.Cattaruzza@gmail.com; Gozzi, E., E-mail: gozzi@ts.infn.it; INFN, Sezione di Trieste

2011-09-15

In this paper we analyze perturbatively a g{phi}{sup 4}classical field theory with and without temperature. In order to do that, we make use of a path-integral approach developed some time ago for classical theories. It turns out that the diagrams appearing at the classical level are many more than at the quantum level due to the presence of extra auxiliary fields in the classical formalism. We shall show that a universal supersymmetry present in the classical path-integral mentioned above is responsible for the cancelation of various diagrams. The same supersymmetry allows the introduction of super-fields and super-diagrams which considerably simplifymore » the calculations and make the classical perturbative calculations almost 'identical' formally to the quantum ones. Using the super-diagrams technique, we develop the classical perturbation theory up to third order. We conclude the paper with a perturbative check of the fluctuation-dissipation theorem. - Highlights: > We provide the Feynman diagrams of perturbation theory for a classical field theory. > We give a super-formalism which links the quantum diagrams to the classical ones. > We check perturbatively the fluctuation-dissipation theorem.« less

An Identity-Based Anti-Quantum Privacy-Preserving Blind Authentication in Wireless Sensor Networks

PubMed Central

Zhu, Hongfei; Tan, Yu-an; Zhu, Liehuang; Wang, Xianmin; Zhang, Quanxin; Li, Yuanzhang

2018-01-01

With the development of wireless sensor networks, IoT devices are crucial for the Smart City; these devices change people’s lives such as e-payment and e-voting systems. However, in these two systems, the state-of-art authentication protocols based on traditional number theory cannot defeat a quantum computer attack. In order to protect user privacy and guarantee trustworthy of big data, we propose a new identity-based blind signature scheme based on number theorem research unit lattice, this scheme mainly uses a rejection sampling theorem instead of constructing a trapdoor. Meanwhile, this scheme does not depend on complex public key infrastructure and can resist quantum computer attack. Then we design an e-payment protocol using the proposed scheme. Furthermore, we prove our scheme is secure in the random oracle, and satisfies confidentiality, integrity, and non-repudiation. Finally, we demonstrate that the proposed scheme outperforms the other traditional existing identity-based blind signature schemes in signing speed and verification speed, outperforms the other lattice-based blind signature in signing speed, verification speed, and signing secret key size. PMID:29789475

Functional determinants, index theorems, and exact quantum black hole entropy

NASA Astrophysics Data System (ADS)

Murthy, Sameer; Reys, Valentin

2015-12-01

The exact quantum entropy of BPS black holes can be evaluated using localization in supergravity. An important ingredient in this program, that has been lacking so far, is the one-loop effect arising from the quadratic fluctuations of the exact deformation (the QV operator). We compute the fluctuation determinant for vector multiplets and hyper multiplets around Q-invariant off-shell configurations in four-dimensional N=2 supergravity with AdS 2 × S 2 boundary conditions, using the Atiyah-Bott fixed-point index theorem and a subsequent zeta function regularization. Our results extend the large-charge on-shell entropy computations in the literature to a regime of finite charges. Based on our results, we present an exact formula for the quantum entropy of BPS black holes in N=2 supergravity. We explain cancellations concerning 1/8 -BPS black holes in N=8 supergravity that were observed in arXiv:1111.1161. We also make comments about the interpretation of a logarithmic term in the topological string partition function in the low energy supergravity theory.

A significant-loophole-free test of Bell's theorem with entangled photons

NASA Astrophysics Data System (ADS)

Giustina, Marissa; Versteegh, Marijn A. M.; Wengerowsky, Sören; Handsteiner, Johannes; Hochrainer, Armin; Phelan, Kevin; Steinlechner, Fabian; Kofler, Johannes; Larsson, Jan-Åke; Abellán, Carlos; Amaya, Waldimar; Mitchell, Morgan W.; Beyer, Jörn; Gerrits, Thomas; Lita, Adriana E.; Shalm, Lynden K.; Nam, Sae Woo; Scheidl, Thomas; Ursin, Rupert; Wittmann, Bernhard; Zeilinger, Anton

2017-10-01

John Bell's theorem of 1964 states that local elements of physical reality, existing independent of measurement, are inconsistent with the predictions of quantum mechanics (Bell, J. S. (1964), Physics (College. Park. Md). Specifically, correlations between measurement results from distant entangled systems would be smaller than predicted by quantum physics. This is expressed in Bell's inequalities. Employing modifications of Bell's inequalities, many experiments have been performed that convincingly support the quantum predictions. Yet, all experiments rely on assumptions, which provide loopholes for a local realist explanation of the measurement. Here we report an experiment with polarization-entangled photons that simultaneously closes the most significant of these loopholes. We use a highly efficient source of entangled photons, distributed these over a distance of 58.5 meters, and implemented rapid random setting generation and high-efficiency detection to observe a violation of a Bell inequality with high statistical significance. The merely statistical probability of our results to occur under local realism is less than 3.74×10-31, corresponding to an 11.5 standard deviation effect.

Quantum approach to classical statistical mechanics.

PubMed

Somma, R D; Batista, C D; Ortiz, G

2007-07-20

We present a new approach to study the thermodynamic properties of d-dimensional classical systems by reducing the problem to the computation of ground state properties of a d-dimensional quantum model. This classical-to-quantum mapping allows us to extend the scope of standard optimization methods by unifying them under a general framework. The quantum annealing method is naturally extended to simulate classical systems at finite temperatures. We derive the rates to assure convergence to the optimal thermodynamic state using the adiabatic theorem of quantum mechanics. For simulated and quantum annealing, we obtain the asymptotic rates of T(t) approximately (pN)/(k(B)logt) and gamma(t) approximately (Nt)(-c/N), for the temperature and magnetic field, respectively. Other annealing strategies are also discussed.

Much Polyphony but Little Harmony: Otto Sackur's Groping for a Quantum Theory of Gases

NASA Astrophysics Data System (ADS)

Badino, Massimiliano; Friedrich, Bretislav

2013-09-01

The endeavor of Otto Sackur (1880-1914) was driven, on the one hand, by his interest in Nernst's heat theorem, statistical mechanics, and the problem of chemical equilibrium and, on the other hand, by his goal to shed light on classical mechanics from the quantum vantage point. Inspired by the interplay between classical physics and quantum theory, Sackur chanced to expound his personal take on the role of the quantum in the changing landscape of physics in the turbulent 1910s. We tell the story of this enthusiastic practitioner of the old quantum theory and early contributor to quantum statistical mechanics, whose scientific ontogenesis provides a telling clue about the phylogeny of his contemporaries.

Nonlocality, no-signalling, and Bellʼs theorem investigated by Weyl conformal differential geometry

NASA Astrophysics Data System (ADS)

De Martini, Francesco; Santamato, Enrico

2014-12-01

The principles and methods of conformal quantum geometrodynamics based on Weyl differential geometry are presented. The theory applied to the case of the relativistic single quantum spin-\\frac{1}{2} leads to a novel and unconventional derivation of the Dirac equation. The further extension of the theory to the case of two-spins-\\frac{1}{2} in the EPR entangled state and to the related violation of Bell inequalities leads, by an exact non-relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.

Geometry and physics of pseudodifferential operators on manifolds

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Napolitano, George M.

2016-09-01

A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: existence theorem for the function that generalizes the phase; analogue of Taylor's theorem; torsion and curvature terms in the symbolic calculus; the two kinds of derivative acting on smooth sections of the cotangent bundle of the Riemannian manifold; the concept of symbol as an equivalence class. Physical motivations and applications are then outlined, with emphasis on Green functions of quantum field theory and Parker's evaluation of Hawking radiation.

Richard P. Feynman and the Feynman Diagrams

Science.gov Websites

available in full-text and on the Web. Documents: A Theorem and Its Application to Finite Tampers, DOE Fermi-Thomas Theory; DOE Technical Report, April 28, 1947 Mathematical Formulation of the Quantum Theory

Chiral Luttinger liquids and a generalized Luttinger's theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Daniel; Zaletel, Michael; Moore, Joel

2014-03-01

We use bosonic field theories and the infinite system density matrix renormalization group (iDMRG) method to study infinite strips of fractional quantum Hall (FQH) states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge mode exponents and momenta without finite-size errors. We analyze states in the first and second level of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid (χLL) theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the non-chiral case. We prove a generalized Luttinger's theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in 1D.

Chiral Luttinger liquids and a generalized Luttinger theorem in fractional quantum Hall edges via finite-entanglement scaling

NASA Astrophysics Data System (ADS)

Varjas, Dániel; Zaletel, Michael P.; Moore, Joel E.

2013-10-01

We use bosonic field theories and the infinite system density matrix renormalization group method to study infinite strips of fractional quantum Hall states starting from microscopic Hamiltonians. Finite-entanglement scaling allows us to accurately measure chiral central charge, edge-mode exponents, and momenta without finite-size errors. We analyze states in the first and second levels of the standard hierarchy and compare our results to predictions of the chiral Luttinger liquid theory. The results confirm the universality of scaling exponents in chiral edges and demonstrate that renormalization is subject to universal relations in the nonchiral case. We prove a generalized Luttinger theorem involving all singularities in the momentum-resolved density, which naturally arises when mapping Landau levels on a cylinder to a fermion chain and deepens our understanding of non-Fermi liquids in one dimension.

Are field quanta real objects? Some remarks on the ontology of quantum field theory

NASA Astrophysics Data System (ADS)

Bigaj, Tomasz

2018-05-01

One of the key philosophical questions regarding quantum field theory is whether it should be given a particle or field interpretation. The particle interpretation of QFT is commonly viewed as being undermined by the well-known no-go results, such as the Malament, Reeh-Schlieder and Hegerfeldt theorems. These theorems all focus on the localizability problem within the relativistic framework. In this paper I would like to go back to the basics and ask the simple-minded question of how the notion of quanta appears in the standard procedure of field quantization, starting with the elementary case of the finite numbers of harmonic oscillators, and proceeding to the more realistic scenario of continuous fields with infinitely many degrees of freedom. I will try to argue that the way the standard formalism introduces the talk of field quanta does not justify treating them as particle-like objects with well-defined properties.

Boolean approach to dichotomic quantum measurement theories

NASA Astrophysics Data System (ADS)

Nagata, K.; Nakamura, T.; Batle, J.; Abdalla, S.; Farouk, A.

2017-02-01

Recently, a new measurement theory based on truth values was proposed by Nagata and Nakamura [Int. J. Theor. Phys. 55, 3616 (2016)], that is, a theory where the results of measurements are either 0 or 1. The standard measurement theory accepts a hidden variable model for a single Pauli observable. Hence, we can introduce a classical probability space for the measurement theory in this particular case. Additionally, we discuss in the present contribution the fact that projective measurement theories (the results of which are either +1 or -1) imply the Bell, Kochen, and Specker (BKS) paradox for a single Pauli observable. To justify our assertion, we present the BKS theorem in almost all the two-dimensional states by using a projective measurement theory. As an example, we present the BKS theorem in two-dimensions with white noise. Our discussion provides new insight into the quantum measurement problem by using this measurement theory based on the truth values.

Finite-size analysis of continuous-variable measurement-device-independent quantum key distribution

NASA Astrophysics Data System (ADS)

Zhang, Xueying; Zhang, Yichen; Zhao, Yijia; Wang, Xiangyu; Yu, Song; Guo, Hong

2017-10-01

We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.

High-speed quantum networking by ship

NASA Astrophysics Data System (ADS)

Devitt, Simon J.; Greentree, Andrew D.; Stephens, Ashley M.; van Meter, Rodney

2016-11-01

Networked entanglement is an essential component for a plethora of quantum computation and communication protocols. Direct transmission of quantum signals over long distances is prevented by fibre attenuation and the no-cloning theorem, motivating the development of quantum repeaters, designed to purify entanglement, extending its range. Quantum repeaters have been demonstrated over short distances, but error-corrected, global repeater networks with high bandwidth require new technology. Here we show that error corrected quantum memories installed in cargo containers and carried by ship can provide a exible connection between local networks, enabling low-latency, high-fidelity quantum communication across global distances at higher bandwidths than previously proposed. With demonstrations of technology with sufficient fidelity to enable topological error-correction, implementation of the quantum memories is within reach, and bandwidth increases with improvements in fabrication. Our approach to quantum networking avoids technological restrictions of repeater deployment, providing an alternate path to a worldwide Quantum Internet.

High-speed quantum networking by ship

PubMed Central

Devitt, Simon J.; Greentree, Andrew D.; Stephens, Ashley M.; Van Meter, Rodney

2016-01-01

Networked entanglement is an essential component for a plethora of quantum computation and communication protocols. Direct transmission of quantum signals over long distances is prevented by fibre attenuation and the no-cloning theorem, motivating the development of quantum repeaters, designed to purify entanglement, extending its range. Quantum repeaters have been demonstrated over short distances, but error-corrected, global repeater networks with high bandwidth require new technology. Here we show that error corrected quantum memories installed in cargo containers and carried by ship can provide a exible connection between local networks, enabling low-latency, high-fidelity quantum communication across global distances at higher bandwidths than previously proposed. With demonstrations of technology with sufficient fidelity to enable topological error-correction, implementation of the quantum memories is within reach, and bandwidth increases with improvements in fabrication. Our approach to quantum networking avoids technological restrictions of repeater deployment, providing an alternate path to a worldwide Quantum Internet. PMID:27805001

High-speed quantum networking by ship.

PubMed

Devitt, Simon J; Greentree, Andrew D; Stephens, Ashley M; Van Meter, Rodney

2016-11-02

Networked entanglement is an essential component for a plethora of quantum computation and communication protocols. Direct transmission of quantum signals over long distances is prevented by fibre attenuation and the no-cloning theorem, motivating the development of quantum repeaters, designed to purify entanglement, extending its range. Quantum repeaters have been demonstrated over short distances, but error-corrected, global repeater networks with high bandwidth require new technology. Here we show that error corrected quantum memories installed in cargo containers and carried by ship can provide a exible connection between local networks, enabling low-latency, high-fidelity quantum communication across global distances at higher bandwidths than previously proposed. With demonstrations of technology with sufficient fidelity to enable topological error-correction, implementation of the quantum memories is within reach, and bandwidth increases with improvements in fabrication. Our approach to quantum networking avoids technological restrictions of repeater deployment, providing an alternate path to a worldwide Quantum Internet.

Superadiabatic Controlled Evolutions and Universal Quantum Computation.

PubMed

Santos, Alan C; Sarandy, Marcelo S

2015-10-29

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts.

Superadiabatic Controlled Evolutions and Universal Quantum Computation

PubMed Central

Santos, Alan C.; Sarandy, Marcelo S.

2015-01-01

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided by the superadiabatic theory, constitute a valuable tool to speed up the adiabatic quantum behavior. Here, we propose a superadiabatic route to implement universal quantum computation. Our method is based on the realization of piecewise controlled superadiabatic evolutions. Remarkably, they can be obtained by simple time-independent counter-diabatic Hamiltonians. In particular, we discuss the implementation of fast rotation gates and arbitrary n-qubit controlled gates, which can be used to design different sets of universal quantum gates. Concerning the energy cost of the superadiabatic implementation, we show that it is dictated by the quantum speed limit, providing an upper bound for the corresponding adiabatic counterparts. PMID:26511064

Black holes are almost optimal quantum cloners

NASA Astrophysics Data System (ADS)

Adami, Christoph; Ver Steeg, Greg

2015-06-01

If black holes were able to clone quantum states, a number of paradoxes in black hole physics would disappear. However, the linearity of quantum mechanics forbids exact cloning of quantum states. Here we show that black holes indeed clone incoming quantum states with a fidelity that depends on the black hole’s absorption coefficient, without violating the no-cloning theorem because the clones are only approximate. Perfectly reflecting black holes are optimal universal ‘quantum cloning machines’ and operate on the principle of stimulated emission, exactly as their quantum optical counterparts. In the limit of perfect absorption, the fidelity of clones is only equal to what can be obtained via quantum state estimation methods. But for any absorption probability less than one, the cloning fidelity is nearly optimal as long as ω /T≥slant 10, a common parameter for modest-sized black holes.

The Generalized Hellmann-Feynman Theorem Approach to Quantum Effects of Mesoscopic Complicated Coupling Circuit at Finite Temperature

NASA Astrophysics Data System (ADS)

Wang, Xiu-Xia

2016-02-01

By employing the generalized Hellmann-Feynman theorem, the quantization of mesoscopic complicated coupling circuit is proposed. The ensemble average energy, the energy fluctuation and the energy distribution are investigated at finite temperature. It is shown that the generalized Hellmann-Feynman theorem plays the key role in quantizing a mesoscopic complicated coupling circuit at finite temperature, and when the temperature is lower than the specific temperature, the value of (\\vartriangle {hat {H}})2 is almost zero and the values of e and (\\vartriangle hat {{H}})2are basically constant, but while the temperature rises to the specific temperature, both of them move upward rapidly. The energy fluctuation of the system becomes larger when the coupling inductance is larger or the coupling capacitance is smaller.

Subleading soft graviton theorem for loop amplitudes

NASA Astrophysics Data System (ADS)

Sen, Ashoke

2017-11-01

Superstring field theory gives expressions for heterotic and type II string loop amplitudes that are free from ultraviolet and infrared divergences when the number of non-compact space-time dimensions is five or more. We prove the subleading soft graviton theorem in these theories to all orders in perturbation theory for S-matrix elements of arbitrary number of finite energy external states but only one external soft graviton. We also prove the leading soft graviton theorem for arbitrary number of finite energy external states and arbitrary number of soft gravitons. Since our analysis is based on general properties of one particle irreducible effective action, the results are valid in any theory of quantum gravity that gives finite result for the S-matrix order by order in perturbation theory without violating general coordinate invariance.

Counterfactual attack on counterfactual quantum key distribution

NASA Astrophysics Data System (ADS)

Zhang, Sheng; Wnang, Jian; Tang, Chao Jing

2012-05-01

It is interesting that counterfactual quantum cryptography protocols allow two remotely separated parties to share a secret key without transmitting any signal particles. Generally, these protocols, expected to provide security advantages, base their security on a translated no-cloning theorem. Therefore, they potentially exhibit unconditional security in theory. In this letter, we propose a new Trojan horse attack, by which an eavesdropper Eve can gain full information about the key without being noticed, to real implementations of a counterfactual quantum cryptography system. Most importantly, the presented attack is available even if the system has negligible imperfections. Therefore, it shows that the present realization of counterfactual quantum key distribution is vulnerable.

Memory-built-in quantum cloning in a hybrid solid-state spin register

NASA Astrophysics Data System (ADS)

Wang, Weibin; Zu, Chong; He, Li; Zhang, Wengang; Duan, Luming

2015-05-01

As a way to circumvent the quantum no-cloning theorem, approximate quantum cloning protocols have received wide attention with remarkable applications. Copying of quantum states to memory qubits provides an important strategy for eavesdropping in quantum cryptography. We report an experiment that realizes cloning of quantum states from an electron spin to a nuclear spin in a hybrid solid-state spin register with near-optimal fidelity. The nuclear spin provides an ideal memory qubit at room temperature, which stores the cloned quantum states for a millisecond under ambient conditions, exceeding the lifetime of the original quantum state carried by the electron spin by orders of magnitude, and making it an ideal memory qubit. Our experiment is based on control of an individual nitrogen vacancy (NV) center in the diamond, which is a diamond defect that attracts strong interest in recent years with great potential for implementation of quantum information protocols.

The super-indeterminism in orthodox quantum mechanics does not implicate the reality of experimenter free will

NASA Astrophysics Data System (ADS)

Walleczek, J.

2016-03-01

The concept of ‘super-indeterminism’ captures the notion that the free choice assumption of orthodox quantum mechanics necessitates only the following requirement: an agent's free-choice performance in the selection of measurement settings must not represent an exception to the rule of irreducible quantum indeterminism in the physical universe (i.e, “universal indeterminism”). Any additional metaphysical speculation, such as to whether quantum indeterminism, i.e., intrinsic randomness, implicates the reality of experimenter “freedom”, “free will”, or “free choice”, is redundant in relation to the predictive success of orthodox quantum mechanics. Accordingly, super-indeterminism views as redundant also, from a technical standpoint, whether an affirmative or a negative answer is claimed in reference to universal indeterminism as a necessary precondition for experimenter freedom. Super-indeterminism accounts, for example, for the circular reasoning which is implicit in the free will theorem by Conway and Kochen [1,2]. The concept of super-indeterminism is of great assistance in clarifying the often misunderstood meaning of the concept of “free variables” as used by John Bell [3]. The present work argues that Bell sought an operational, effective free will theorem, one based upon the notion of “determinism without predetermination”, i.e., one wherein “free variables” represent universally uncomputable variables. In conclusion, the standard interpretation of quantum theory does not answer, and does not need to answer in order to ensure the predictive success of orthodox theory, the question of whether either incompatibilism or compatibilism is valid in relation to free-will metaphysics and to the free-will phenomenology of experimenter agents in quantum mechanics.

Self-adjointness of deformed unbounded operators

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

Much, Albert

2015-09-15

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.

Seaworthy Quantum Key Distribution Design and Validation (SEAKEY)

DTIC Science & Technology

2015-08-07

absorption and scattering using MODTRAN [ Berk et al.]. Thus, channel efficiency is expressed as follows: G=GT×exp[−αL], (10) where exp[−αL] is...34 New Journal of Physics 13, 013003 (2011). [Scarani et al.] Valerio Scarani, Helle Bechmann-Pasquinucci, Nicolas J . Cerf, Miloslav Dušek, Norbert...050303 (2005). [Renner and Cirac] R. Renner and J . I. Cirac, de Finetti representation theorem for infinite-dimensional quantum systems and

Matching factorization theorems with an inverse-error weighting

NASA Astrophysics Data System (ADS)

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; Pisano, Cristian; Signori, Andrea

2018-06-01

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections to the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H0 boson and Drell-Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins-Soper-Sterman subtraction scheme. It is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.

Matching factorization theorems with an inverse-error weighting

DOE PAGES

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe; ...

2018-04-03

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

Matching factorization theorems with an inverse-error weighting

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

Echevarria, Miguel G.; Kasemets, Tomas; Lansberg, Jean-Philippe

We propose a new fast method to match factorization theorems applicable in different kinematical regions, such as the transverse-momentum-dependent and the collinear factorization theorems in Quantum Chromodynamics. At variance with well-known approaches relying on their simple addition and subsequent subtraction of double-counted contributions, ours simply builds on their weighting using the theory uncertainties deduced from the factorization theorems themselves. This allows us to estimate the unknown complete matched cross section from an inverse-error-weighted average. The method is simple and provides an evaluation of the theoretical uncertainty of the matched cross section associated with the uncertainties from the power corrections tomore » the factorization theorems (additional uncertainties, such as the nonperturbative ones, should be added for a proper comparison with experimental data). Its usage is illustrated with several basic examples, such as Z boson, W boson, H 0 boson and Drell–Yan lepton-pair production in hadronic collisions, and compared to the state-of-the-art Collins–Soper–Sterman subtraction scheme. In conclusion, it is also not limited to the transverse-momentum spectrum, and can straightforwardly be extended to match any (un)polarized cross section differential in other variables, including multi-differential measurements.« less

Can different quantum state vectors correspond to the same physical state? An experimental test

NASA Astrophysics Data System (ADS)

Nigg, Daniel; Monz, Thomas; Schindler, Philipp; Martinez, Esteban A.; Hennrich, Markus; Blatt, Rainer; Pusey, Matthew F.; Rudolph, Terry; Barrett, Jonathan

2016-01-01

A century after the development of quantum theory, the interpretation of a quantum state is still discussed. If a physicist claims to have produced a system with a particular quantum state vector, does this represent directly a physical property of the system, or is the state vector merely a summary of the physicist’s information about the system? Assume that a state vector corresponds to a probability distribution over possible values of an unknown physical or ‘ontic’ state. Then, a recent no-go theorem shows that distinct state vectors with overlapping distributions lead to predictions different from quantum theory. We report an experimental test of these predictions using trapped ions. Within experimental error, the results confirm quantum theory. We analyse which kinds of models are ruled out.

Measurements of entanglement over a kilometric distance to test superluminal models of Quantum Mechanics: preliminary results.

NASA Astrophysics Data System (ADS)

Cocciaro, B.; Faetti, S.; Fronzoni, L.

2017-08-01

As shown in the EPR paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics is a non-local Theory. The Bell theorem and the successive experiments ruled out the possibility of explaining quantum correlations using only local hidden variables models. Some authors suggested that quantum correlations could be due to superluminal communications that propagate isotropically with velocity vt > c in a preferred reference frame. For finite values of vt and in some special cases, Quantum Mechanics and superluminal models lead to different predictions. So far, no deviations from the predictions of Quantum Mechanics have been detected and only lower bounds for the superluminal velocities vt have been established. Here we describe a new experiment that increases the maximum detectable superluminal velocities and we give some preliminary results.

Proof of the Spin Statistics Connection 2: Relativistic Theory

NASA Astrophysics Data System (ADS)

Santamato, Enrico; De Martini, Francesco

2017-12-01

The traditional standard theory of quantum mechanics is unable to solve the spin-statistics problem, i.e. to justify the utterly important "Pauli Exclusion Principle" but by the adoption of the complex standard relativistic quantum field theory. In a recent paper (Santamato and De Martini in Found Phys 45(7):858-873, 2015) we presented a proof of the spin-statistics problem in the nonrelativistic approximation on the basis of the "Conformal Quantum Geometrodynamics". In the present paper, by the same theory the proof of the spin-statistics theorem is extended to the relativistic domain in the general scenario of curved spacetime. The relativistic approach allows to formulate a manifestly step-by-step Weyl gauge invariant theory and to emphasize some fundamental aspects of group theory in the demonstration. No relativistic quantum field operators are used and the particle exchange properties are drawn from the conservation of the intrinsic helicity of elementary particles. It is therefore this property, not considered in the standard quantum mechanics, which determines the correct spin-statistics connection observed in Nature (Santamato and De Martini in Found Phys 45(7):858-873, 2015). The present proof of the spin-statistics theorem is simpler than the one presented in Santamato and De Martini (Found Phys 45(7):858-873, 2015), because it is based on symmetry group considerations only, without having recourse to frames attached to the particles. Second quantization and anticommuting operators are not necessary.

Exploring quantum thermodynamics in continuous measurement of superconducting qubits

NASA Astrophysics Data System (ADS)

Murch, Kater

The extension of thermodynamics into the realm of quantum mechanics, where quantum fluctuations dominate and systems need not occupy definite states, poses unique challenges. Superconducting quantum circuits offer exquisite control over the environment of simple quantum systems allowing the exploration of thermodynamics at the quantum level through measurement and feedback control. We use a superconducting transmon qubit that is resonantly coupled to a waveguide cavity as an effectively one-dimensional quantum emitter. By driving the emitter and detecting the fluorescence with a near-quantum-limited Josephson parametric amplifier, we track the evolution of the quantum state and characterize the work and heat along single quantum trajectories. By using quantum feedback control to compensate for heat exchanged with the emitter's environment we are able to extract the work statistics associated with the quantum evolution and examine fundamental fluctuation theorems in non-equilibrium thermodynamics. This work was supported by the Alfred P. Sloan Foundation, the National Science Foundation, and the Office of Naval Research.

Room-Temperature Quantum Cloning Machine with Full Coherent Phase Control in Nanodiamond

PubMed Central

Chang, Yan-Chun; Liu, Gang-Qin; Liu, Dong-Qi; Fan, Heng; Pan, Xin-Yu

2013-01-01

In contrast to the classical world, an unknown quantum state cannot be cloned ideally, as stated by the no-cloning theorem. However, it is expected that approximate or probabilistic quantum cloning will be necessary for different applications, and thus various quantum cloning machines have been designed. Phase quantum cloning is of particular interest because it can be used to attack the Bennett-Brassard 1984 (BB84) states used in quantum key distribution for secure communications. Here, we report the first room-temperature implementation of quantum phase cloning with a controllable phase in a solid-state system: the nitrogen-vacancy centre of a nanodiamond. The phase cloner works well for all qubits located on the equator of the Bloch sphere. The phase is controlled and can be measured with high accuracy, and the experimental results are consistent with theoretical expectations. This experiment provides a basis for phase-controllable quantum information devices. PMID:23511233

Quantum recurrence and fractional dynamic localization in ac-driven perfect state transfer Hamiltonians

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

Longhi, Stefano, E-mail: stefano.longhi@fisi.polimi.it

Quantum recurrence and dynamic localization are investigated in a class of ac-driven tight-binding Hamiltonians, the Krawtchouk quantum chain, which in the undriven case provides a paradigmatic Hamiltonian model that realizes perfect quantum state transfer and mirror inversion. The equivalence between the ac-driven single-particle Krawtchouk Hamiltonian H{sup -hat} (t) and the non-interacting ac-driven bosonic junction Hamiltonian enables to determine in a closed form the quasi energy spectrum of H{sup -hat} (t) and the conditions for exact wave packet reconstruction (dynamic localization). In particular, we show that quantum recurrence, which is predicted by the general quantum recurrence theorem, is exact for themore » Krawtchouk quantum chain in a dense range of the driving amplitude. Exact quantum recurrence provides perfect wave packet reconstruction at a frequency which is fractional than the driving frequency, a phenomenon that can be referred to as fractional dynamic localization.« less

Quantum Chemistry on Quantum Computers: A Polynomial-Time Quantum Algorithm for Constructing the Wave Functions of Open-Shell Molecules.

PubMed

Sugisaki, Kenji; Yamamoto, Satoru; Nakazawa, Shigeaki; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Takui, Takeji

2016-08-18

Quantum computers are capable to efficiently perform full configuration interaction (FCI) calculations of atoms and molecules by using the quantum phase estimation (QPE) algorithm. Because the success probability of the QPE depends on the overlap between approximate and exact wave functions, efficient methods to prepare accurate initial guess wave functions enough to have sufficiently large overlap with the exact ones are highly desired. Here, we propose a quantum algorithm to construct the wave function consisting of one configuration state function, which is suitable for the initial guess wave function in QPE-based FCI calculations of open-shell molecules, based on the addition theorem of angular momentum. The proposed quantum algorithm enables us to prepare the wave function consisting of an exponential number of Slater determinants only by a polynomial number of quantum operations.

Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels

NASA Astrophysics Data System (ADS)

De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio

2017-04-01

We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p →q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

Gaussian States Minimize the Output Entropy of One-Mode Quantum Gaussian Channels.

PubMed

De Palma, Giacomo; Trevisan, Dario; Giovannetti, Vittorio

2017-04-21

We prove the long-standing conjecture stating that Gaussian thermal input states minimize the output von Neumann entropy of one-mode phase-covariant quantum Gaussian channels among all the input states with a given entropy. Phase-covariant quantum Gaussian channels model the attenuation and the noise that affect any electromagnetic signal in the quantum regime. Our result is crucial to prove the converse theorems for both the triple trade-off region and the capacity region for broadcast communication of the Gaussian quantum-limited amplifier. Our result extends to the quantum regime the entropy power inequality that plays a key role in classical information theory. Our proof exploits a completely new technique based on the recent determination of the p→q norms of the quantum-limited amplifier [De Palma et al., arXiv:1610.09967]. This technique can be applied to any quantum channel.

Far-infrared response of spherical quantum dots: Dielectric effects and the generalized Kohn's theorem

NASA Astrophysics Data System (ADS)

Movilla, J. L.; Planelles, J.

2007-05-01

The influence of the dielectric environment on the far-infrared (FIR) absorption spectra of two-electron spherical quantum dots is theoretically studied. Effective mass and envelope function approaches with realistic steplike confining potentials are used. Special attention is paid to absorptions that are induced by the electron-electron interaction. High confining barriers make the FIR absorption coefficients almost independent of the quantum dot dielectric environment. Low barrier heights and strong dielectric mismatches preserve the strong fundamental (Kohn) mode but yield the cancellation of excited absorptions, thus monitoring dielectrically induced phase transitions from volume to surface states.

What Exactly is the Information Paradox?

NASA Astrophysics Data System (ADS)

Mathur, S. D.

The black hole information paradox tells us something important about the way quantum mechanics and gravity fit together. In these lectures I try to give a pedagogical review of the essential physics leading to the paradox, using mostly pictures. Hawking's argument is recast as a "theorem": if quantum gravity effects are confined to within a given length scale and the vacuum is assumed to be unique, then there will be information loss. We conclude with a brief summary of how quantum effects in string theory violate the first condition and make the interior of the hole a "fuzzball".

Bell's Theorem, Entaglement, Quantum Teleportation and All That

ScienceCinema

Leggett, Anthony

2018-04-19

One of the most surprising aspects of quantum mechanics is that under certain circumstances it does not allow individual physical systems, even when isolated, to possess properties in their own right. This feature, first clearly appreciated by John Bell in 1964, has in the last three decades been tested experimentally and found (in most people's opinion) to be spectacularly confirmed. More recently it has been realized that it permits various operations which are classically impossible, such as "teleportation" and secure-in-principle cryptography. This talk is a very basic introduction to the subject, which requires only elementary quantum mechanics.

Nonextensive kinetic theory and H-theorem in general relativity

NASA Astrophysics Data System (ADS)

Santos, A. P.; Silva, R.; Alcaniz, J. S.; Lima, J. A. S.

2017-11-01

The nonextensive kinetic theory for degenerate quantum gases is discussed in the general relativistic framework. By incorporating nonadditive modifications in the collisional term of the relativistic Boltzmann equation and entropy current, it is shown that Tsallis entropic framework satisfies a H-theorem in the presence of gravitational fields. Consistency with the 2nd law of thermodynamics is obtained only whether the entropic q-parameter lies in the interval q ∈ [ 0 , 2 ] . As occurs in the absence of gravitational fields, it is also proved that the local collisional equilibrium is described by the extended Bose-Einstein (Fermi-Dirac) q-distributions.

High-Dimensional Circular Quantum Secret Sharing Using Orbital Angular Momentum

NASA Astrophysics Data System (ADS)

Tang, Dawei; Wang, Tie-jun; Mi, Sichen; Geng, Xiao-Meng; Wang, Chuan

2016-11-01

Quantum secret sharing is to distribute secret message securely between multi-parties. Here exploiting orbital angular momentum (OAM) state of single photons as the information carrier, we propose a high-dimensional circular quantum secret sharing protocol which increases the channel capacity largely. In the proposed protocol, the secret message is split into two parts, and each encoded on the OAM state of single photons. The security of the protocol is guaranteed by the laws of non-cloning theorem. And the secret messages could not be recovered except that the two receivers collaborated with each other. Moreover, the proposed protocol could be extended into high-level quantum systems, and the enhanced security could be achieved.

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

Venkatesan, R.C., E-mail: ravi@systemsresearchcorp.com; Plastino, A., E-mail: plastino@fisica.unlp.edu.ar

The (i) reciprocity relations for the relative Fisher information (RFI, hereafter) and (ii) a generalized RFI–Euler theorem are self-consistently derived from the Hellmann–Feynman theorem. These new reciprocity relations generalize the RFI–Euler theorem and constitute the basis for building up a mathematical Legendre transform structure (LTS, hereafter), akin to that of thermodynamics, that underlies the RFI scenario. This demonstrates the possibility of translating the entire mathematical structure of thermodynamics into a RFI-based theoretical framework. Virial theorems play a prominent role in this endeavor, as a Schrödinger-like equation can be associated to the RFI. Lagrange multipliers are determined invoking the RFI–LTS linkmore » and the quantum mechanical virial theorem. An appropriate ansatz allows for the inference of probability density functions (pdf’s, hereafter) and energy-eigenvalues of the above mentioned Schrödinger-like equation. The energy-eigenvalues obtained here via inference are benchmarked against established theoretical and numerical results. A principled theoretical basis to reconstruct the RFI-framework from the FIM framework is established. Numerical examples for exemplary cases are provided. - Highlights: • Legendre transform structure for the RFI is obtained with the Hellmann–Feynman theorem. • Inference of the energy-eigenvalues of the SWE-like equation for the RFI is accomplished. • Basis for reconstruction of the RFI framework from the FIM-case is established. • Substantial qualitative and quantitative distinctions with prior studies are discussed.« less

A Viable Paradigm for Quantum Reality

NASA Astrophysics Data System (ADS)

Srivastava, Jagdish

2010-10-01

After a brief discussion of the EPR paradox, Bell's inequality, and Aspect's experiment, arguments will be presented in favor of the following statements: ``As it stands, Quantum mechanics is incomplete. There is further hidden structure, which would involve variables. No influence can move faster than light. The wave function is one whole thing and any change in its structure instantly influences its outcomes. Bell's theorem has not been applied correctly. There is a better paradigm.'' The said paradigm will be presented.

Novel Principles and the Charge-Symmetric Design of Dirac's Quantum Mechanics: I. Enhanced Eriksen's Theorem and the Universal Charge-Index Formalism for Dirac's Equation in (Strong) External Static Fields

NASA Astrophysics Data System (ADS)

Kononets, Yu. V.

2016-12-01

The presented enhanced version of Eriksen's theorem defines an universal transform of the Foldy-Wouthuysen type and in any external static electromagnetic field (ESEMF) reveals a discrete symmetry of Dirac's equation (DE), responsible for existence of a highly influential conserved quantum number—the charge index distinguishing two branches of DE spectrum. It launches the charge-index formalism (CIF) obeying the charge-index conservation law (CICL). Via its unique ability to manipulate each spectrum branch independently, the CIF creates a perfect charge-symmetric architecture of Dirac's quantum mechanics (DQM), which resolves all the riddles of the standard DE theory (SDET). Besides the abstract CIF algebra, the paper discusses: (1) the novel accurate charge-symmetric definition of the electric-current density; (2) DE in the true-particle representation, where electrons and positrons coexist on equal footing; (3) flawless "natural" scheme of second quantization; and (4) new physical grounds for the Fermi-Dirac statistics. As a fundamental quantum law, the CICL originates from the kinetic-energy sign conservation and leads to a novel single-particle physics in strong-field situations. Prohibiting Klein's tunneling (KT) in Klein's zone via the CICL, the precise CIF algebra defines a new class of weakly singular DE solutions, strictly confined in the coordinate space and experiencing the total reflection from the potential barrier.

Electron-exchange and quantum screening effects on the Thomson scattering process in quantum Fermi plasmas

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

Lee, Gyeong Won; Jung, Young-Dae; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180-3590

2013-06-15

The influence of the electron-exchange and quantum screening on the Thomson scattering process is investigated in degenerate quantum Fermi plasmas. The Thomson scattering cross section in quantum plasmas is obtained by the plasma dielectric function and fluctuation-dissipation theorem as a function of the electron-exchange parameter, Fermi energy, plasmon energy, and wave number. It is shown that the electron-exchange effect enhances the Thomson scattering cross section in quantum plasmas. It is also shown that the differential Thomson scattering cross section has a minimum at the scattering angle Θ=π/2. It is also found that the Thomson scattering cross section increases with anmore » increase of the Fermi energy. In addition, the Thomson scattering cross section is found to be decreased with increasing plasmon energy.« less

Quantum work and the thermodynamic cost of quantum measurements

DOE PAGES

Deffner, Sebastian; Paz, Juan Pablo; Zurek, Wojciech H.

2016-07-07

Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derivemore » a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. Lastly, a comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.« less

Quantum-coherent mixtures of causal relations

NASA Astrophysics Data System (ADS)

Maclean, Jean-Philippe W.; Ried, Katja; Spekkens, Robert W.; Resch, Kevin J.

2017-05-01

Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity.

Unforgeable Noise-Tolerant Quantum Tokens

NASA Astrophysics Data System (ADS)

Yao, Norman; Pastawski, Fernando; Jiang, Liang; Lukin, Mikhail; Cirac, Ignacio

2012-06-01

The realization of devices which harness the laws of quantum mechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of ``quantum money.'' A dishonest holder of a quantum bank-note will invariably fail in any forging attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence and operational imperfections abound. Thus, the development of secure ``quantum money''-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store and measure single qubit quantum memories, making their experimental realization accessible with current technologies.

Quantum-coherent mixtures of causal relations

PubMed Central

MacLean, Jean-Philippe W.; Ried, Katja; Spekkens, Robert W.; Resch, Kevin J.

2017-01-01

Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity. PMID:28485394

Quantum-coherent mixtures of causal relations.

PubMed

MacLean, Jean-Philippe W; Ried, Katja; Spekkens, Robert W; Resch, Kevin J

2017-05-09

Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity.

High-Power Collective Charging of a Solid-State Quantum Battery

NASA Astrophysics Data System (ADS)

Ferraro, Dario; Campisi, Michele; Andolina, Gian Marcello; Pellegrini, Vittorio; Polini, Marco

2018-03-01

Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like √{N } for N ≫1 .

Quantum Markov semigroups constructed from quantum Bernoulli noises

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

Wang, Caishi; Chen, Jinshu

2016-02-15

Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on Bernoulli functionals, which can describe a two-level quantum system with infinitely many sites. In this paper, we consider the problem to construct quantum Markov semigroups (QMSs) directly from QBNs. We first establish several new theorems concerning QBNs. In particular, we define the number operator acting on Bernoulli functionals by using the canonical orthonormal basis, prove its self-adjoint property, and describe precisely its connections with QBN in a mathematically rigorous way. We then show the possibility to construct QMS directly from QBN. This is done by combiningmore » the general results on QMS with our new results on QBN obtained here. Finally, we examine some properties of QMS constructed from QBN.« less

New strings for old Veneziano amplitudes. II. Group-theoretic treatment

NASA Astrophysics Data System (ADS)

Kholodenko, A. L.

2006-09-01

In this part of our four parts work we use theory of polynomial invariants of finite pseudo-reflection groups in order to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes and the generating function reproducing these amplitudes. We demonstrate that such generating function and amplitudes associated with it can be recovered with help of finite dimensional exactly solvableN=2 supersymmetric quantum mechanical model known earlier from works of Witten, Stone and others. Using the Lefschetz isomorphism theorem we replace traditional supersymmetric calculations by the group-theoretic thus solving the Veneziano model exactly using standard methods of representation theory. Mathematical correctness of our arguments relies on important theorems by Shepard and Todd, Serre and Solomon proven respectively in the early 50s and 60s and documented in the monograph by Bourbaki. Based on these theorems, we explain why the developed formalism leaves all known results of conformal field theories unchanged. We also explain why these theorems impose stringent requirements connecting analytical properties of scattering amplitudes with symmetries of space-time in which such amplitudes act.

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.

Lorentz-violating modification of Dirac theory based on spin-nondegenerate operators

NASA Astrophysics Data System (ADS)

Reis, J. A. A. S.; Schreck, M.

2017-04-01

The Standard Model extension (SME) parametrizes all possible Lorentz-violating contributions to the Standard Model and general relativity. It can be considered as an effective framework to describe possible quantum-gravity effects for energies much below the Planck energy. In the current paper, the spin-nondegenerate operators of the SME fermion sector are the focus. The propagators, energies, and solutions to the modified Dirac equation are obtained for several families of coefficients including nonminimal ones. The particle energies and spinors are computed at first order in Lorentz violation and, with the optical theorem, they are shown to be consistent with the propagators. The optical theorem is then also used to derive the matrices formed from a spinor and its Dirac conjugate at all orders in Lorentz violation. The results are the first explicit ones derived for the spin-nondegenerate operators. They will prove helpful for future phenomenological calculations in the SME that rely on the footing of quantum field theory.

Synchronization between uncertain nonidentical networks with quantum chaotic behavior

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2016-11-01

Synchronization between uncertain nonidentical networks with quantum chaotic behavior is researched. The identification laws of unknown parameters in state equations of network nodes, the adaptive laws of configuration matrix elements and outer coupling strengths are determined based on Lyapunov theorem. The conditions of realizing synchronization between uncertain nonidentical networks are discussed and obtained. Further, Jaynes-Cummings model in physics are taken as the nodes of two networks and simulation results show that the synchronization performance between networks is very stable.

Two-player quantum pseudotelepathy based on recent all-versus-nothing violations of local realism

NASA Astrophysics Data System (ADS)

Cabello, Adán

2006-02-01

We introduce two two-player quantum pseudotelepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell’s theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and Méthot’s claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light cone (quant-ph/0511047) is incorrect.

What Bell proved: A reply to Blaylock

NASA Astrophysics Data System (ADS)

Maudlin, Tim

2010-01-01

Blaylock argues that the derivation of Bell's inequality requires a hidden assumption, counterfactual definiteness, of which Bell was unaware. A careful analysis of Bell's argument shows that Bell presupposes only locality and the predictions of standard quantum mechanics. Counterfactual definiteness, insofar as it is required, is derived in the course of the argument rather than presumed. Bell's theorem has no direct bearing on the many worlds interpretation not because that interpretation denies counterfactual definiteness but because it does not recover the predictions of standard quantum mechanics.

Noncommutative Quantum Mechanics based on Representations of Exotic Galilei Group

NASA Astrophysics Data System (ADS)

Amorim, R. G. G.; Ulhoa, S. C.

2018-02-01

Using elements of symmetry, we constructed the Noncommutative Schrödinger Equation from a representation of Exotic Galilei Group. As a consequence, we derive the Ehrenfest theorem using noncommutative coordinates. We also have showed others features of quantum mechanics in such a manifold. As an important result, we find out that a linear potential in the noncommutative Schrödinger equation is completely analogous to the ordinary case. We also worked with harmonic and anharmonic oscillators, giving corrections in the energy for each one.

Entanglement bases and general structures of orthogonal complete bases

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

Zhong Zaizhe

2004-10-01

In quantum mechanics and quantum information, to establish the orthogonal bases is a useful means. The existence of unextendible product bases impels us to study the 'entanglement bases' problems. In this paper, the concepts of entanglement bases and exact-entanglement bases are defined, and a theorem about exact-entanglement bases is given. We discuss the general structures of the orthogonal complete bases. Two examples of applications are given. At last, we discuss the problem of transformation of the general structure forms.

Security of continuous-variable quantum key distribution against general attacks.

PubMed

Leverrier, Anthony; García-Patrón, Raúl; Renner, Renato; Cerf, Nicolas J

2013-01-18

We prove the security of Gaussian continuous-variable quantum key distribution with coherent states against arbitrary attacks in the finite-size regime. In contrast to previously known proofs of principle (based on the de Finetti theorem), our result is applicable in the practically relevant finite-size regime. This is achieved using a novel proof approach, which exploits phase-space symmetries of the protocols as well as the postselection technique introduced by Christandl, Koenig, and Renner [Phys. Rev. Lett. 102, 020504 (2009)].

Hybrid ququart-encoded quantum cryptography protected by Kochen-Specker contextuality

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

Cabello, Adan; Department of Physics, Stockholm University, S-10691 Stockholm; D'Ambrosio, Vincenzo

2011-09-15

Quantum cryptographic protocols based on complementarity are not secure against attacks in which complementarity is imitated with classical resources. The Kochen-Specker (KS) theorem provides protection against these attacks, without requiring entanglement or spatially separated composite systems. We analyze the maximum tolerated noise to guarantee the security of a KS-protected cryptographic scheme against these attacks and describe a photonic realization of this scheme using hybrid ququarts defined by the polarization and orbital angular momentum of single photons.

Topics in quantum cryptography, quantum error correction, and channel simulation

NASA Astrophysics Data System (ADS)

Luo, Zhicheng

In this thesis, we mainly investigate four different topics: efficiently implementable codes for quantum key expansion [51], quantum error-correcting codes based on privacy amplification [48], private classical capacity of quantum channels [44], and classical channel simulation with quantum side information [49, 50]. For the first topic, we propose an efficiently implementable quantum key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] quantum key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] quantum error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on tensor powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a quantum channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted quantum communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel simulation with quantum side information at the receiver. Our main theorem has two important corollaries: rate-distortion theory with quantum side information and common randomness distillation. Simple proofs of achievability of classical multi-terminal source coding problems can be made via a unified approach using the channel simulation theorem as building blocks. The fully quantum generalization of the problem is also conjectured with outer and inner bounds on the achievable rate pairs.

Stokes' theorem, gauge symmetry and the time-dependent Aharonov-Bohm effect

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

Macdougall, James, E-mail: jbm34@mail.fresnostate.edu; Singleton, Douglas, E-mail: dougs@csufresno.edu

2014-04-15

Stokes' theorem is investigated in the context of the time-dependent Aharonov-Bohm effect—the two-slit quantum interference experiment with a time varying solenoid between the slits. The time varying solenoid produces an electric field which leads to an additional phase shift which is found to exactly cancel the time-dependent part of the usual magnetic Aharonov-Bohm phase shift. This electric field arises from a combination of a non-single valued scalar potential and/or a 3-vector potential. The gauge transformation which leads to the scalar and 3-vector potentials for the electric field is non-single valued. This feature is connected with the non-simply connected topology ofmore » the Aharonov-Bohm set-up. The non-single valued nature of the gauge transformation function has interesting consequences for the 4-dimensional Stokes' theorem for the time-dependent Aharonov-Bohm effect. An experimental test of these conclusions is proposed.« less

Iterated Gate Teleportation and Blind Quantum Computation.

PubMed

Pérez-Delgado, Carlos A; Fitzsimons, Joseph F

2015-06-05

Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraint only holds in limited scenarios, and show how to overcome it using a novel method of iterated gate teleportations. This technique enables drastic reductions in the communication required for distributed quantum protocols, extending beyond the blind computation setting. Applied to blind quantum computation, this technique offers significant efficiency improvements, and in some scenarios offers an exponential reduction in communication requirements.

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality

NASA Astrophysics Data System (ADS)

Dong, Xi; Harlow, Daniel; Wall, Aron C.

2016-07-01

In this Letter we prove a simple theorem in quantum information theory, which implies that bulk operators in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A , provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local Couplings

NASA Astrophysics Data System (ADS)

Große, Johannes

2007-11-01

This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, in a second part the conformal anomaly of four dimensional supersymmetric quantum field theories coupled to classical N=1 supergravity is explored in a superfield formulation. The complete basis for the anomaly and consistency conditions, which arise from cohomological considerations, are given. Possible implications for an extension of Zamolodchikov's c-theorem to four dimensional supersymmetric quantum field theories are discussed.

Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality.

PubMed

Dong, Xi; Harlow, Daniel; Wall, Aron C

2016-07-08

In this Letter we prove a simple theorem in quantum information theory, which implies that bulk operators in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A, provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.

Continuous variable quantum cryptography using coherent states.

PubMed

Grosshans, Frédéric; Grangier, Philippe

2002-02-04

We propose several methods for quantum key distribution (QKD) based on the generation and transmission of random distributions of coherent or squeezed states, and we show that they are secure against individual eavesdropping attacks. These protocols require that the transmission of the optical line between Alice and Bob is larger than 50%, but they do not rely on "sub-shot-noise" features such as squeezing. Their security is a direct consequence of the no-cloning theorem, which limits the signal-to-noise ratio of possible quantum measurements on the transmission line. Our approach can also be used for evaluating various QKD protocols using light with Gaussian statistics.

Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

NASA Astrophysics Data System (ADS)

Rahmani, Faramarz; Golshani, Mehdi

2018-01-01

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.

The physical origins of the uncertainty theorem

NASA Astrophysics Data System (ADS)

Giese, Albrecht

2013-10-01

The uncertainty principle is an important element of quantum mechanics. It deals with certain pairs of physical parameters which cannot be determined to an arbitrary level of precision at the same time. According to the so-called Copenhagen interpretation of quantum mechanics, this uncertainty is an intrinsic property of the physical world. - This paper intends to show that there are good reasons for adopting a different view. According to the author, the uncertainty is not a property of the physical world but rather a limitation of our knowledge about the actual state of a physical process. This view conforms to the quantum theory of Louis de Broglie and to Albert Einstein's interpretation.

General no-go theorem for entanglement extraction

NASA Astrophysics Data System (ADS)

Simidzija, Petar; Jonsson, Robert H.; Martín-Martínez, Eduardo

2018-06-01

We study under what circumstances a separable bipartite system A-B can or cannot become entangled through local interactions with a bilocal entangled source S1-S2 . We obtain constraints on the general forms of the interaction Hamiltonians coupling A with S1 and B with S2 necessary for A and B to become entangled. We are able to generalize and provide nonperturbative insight on several previous no-go theorems of entanglement harvesting from quantum fields using these general results. We also discuss the role of communication in the process of entanglement extraction, establishing a distinction between genuine entanglement extraction and communication-assisted entanglement generation.

Quantum violation of an instrumental test

NASA Astrophysics Data System (ADS)

Chaves, Rafael; Carvacho, Gonzalo; Agresti, Iris; Di Giulio, Valerio; Aolita, Leandro; Giacomini, Sandro; Sciarrino, Fabio

2018-03-01

Inferring causal relations from experimental observations is of primal importance in science. Instrumental tests provide an essential tool for that aim, as they allow one to estimate causal dependencies even in the presence of unobserved common causes. In view of Bell's theorem, which implies that quantum mechanics is incompatible with our most basic notions of causality, it is of utmost importance to understand whether and how paradigmatic causal tools obtained in a classical setting can be carried over to the quantum realm. Here we show that quantum effects imply radically different predictions in the instrumental scenario. Among other results, we show that an instrumental test can be violated by entangled quantum states. Furthermore, we demonstrate such violation using a photonic set-up with active feed-forward of information, thus providing an experimental proof of this new form of non-classical behaviour. Our findings have fundamental implications in causal inference and may also lead to new applications of quantum technologies.

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".

Optimum testing of multiple hypotheses in quantum detection theory

NASA Technical Reports Server (NTRS)

Yuen, H. P.; Kennedy, R. S.; Lax, M.

1975-01-01

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Typical Werner states satisfying all linear Bell inequalities with dichotomic measurements

NASA Astrophysics Data System (ADS)

Luo, Ming-Xing

2018-04-01

Quantum entanglement as a special resource inspires various distinct applications in quantum information processing. Unfortunately, it is NP-hard to detect general quantum entanglement using Bell testing. Our goal is to investigate quantum entanglement with white noises that appear frequently in experiment and quantum simulations. Surprisingly, for almost all multipartite generalized Greenberger-Horne-Zeilinger states there are entangled noisy states that satisfy all linear Bell inequalities consisting of full correlations with dichotomic inputs and outputs of each local observer. This result shows generic undetectability of mixed entangled states in contrast to Gisin's theorem of pure bipartite entangled states in terms of Bell nonlocality. We further provide an accessible method to show a nontrivial set of noisy entanglement with small number of parties satisfying all general linear Bell inequalities. These results imply typical incompleteness of special Bell theory in explaining entanglement.

Ordering relations for quantum states

NASA Astrophysics Data System (ADS)

Durham, Ian

2015-03-01

It is often desirable to model physical states in an order-theoretic manner, e.g. as a partially ordered set. Classical states are known to possess a unique ordering relation corresponding to a neo-realist interpretation of these states. No such unique relation exists for quantum states. This lack of a unique ordering relation for quantum states turns out to be a manifestation of quantum contextuality vis-à-vis the Kochen-Specker theorem. It also turns out that this provides a link to certain large-scale thermodynamic processes. The suggestion that the ordering of quantum states leads to macroscopic thermodynamic processes is at least five decades old. The suggestion that the mechanism that drives the ordering is contextuality, is unique to this work. The argument is framed in the language of the theories of domains, categories, and topoi. Financial support provided by FQXi.

Convergence of a quantum normal form and a generalization of Cherry’s theorem

NASA Astrophysics Data System (ADS)

Barone, Fiorella; Graffi, Sandro

2012-01-01

We consider on L^2({ T}^2) the Schrödinger operator family H_\\varepsilon : \\varepsilon \\in { R} with the domain and action defined as follows: \\begin{eqnarray*} D(H_\\varepsilon )=H^1({ T}^2); \\quad H_\\varepsilon u=-i\\hbar \\omega \\cdot \

Generalized Galilean transformations and the measurement problem in the entropic dynamics approach to quantum theory

NASA Astrophysics Data System (ADS)

Johnson, David T.

Quantum mechanics is an extremely successful and accurate physical theory, yet since its inception, it has been afflicted with numerous conceptual difficulties. The primary subject of this thesis is the theory of entropic quantum dynamics (EQD), which seeks to avoid these conceptual problems by interpreting quantum theory from an informational perspective. We begin by reviewing Cox's work in describing probability theory as a means of rationally and consistently quantifying uncertainties. We then discuss how probabilities can be updated according to either Bayes' theorem or the extended method of maximum entropy (ME). After that discussion, we review the work of Caticha and Giffin that shows that Bayes' theorem is a special case of ME. This important result demonstrates that the ME method is the general method for updating probabilities. We then review some motivating difficulties in quantum mechanics before discussing Caticha's work in deriving quantum theory from the approach of entropic dynamics, which concludes our review. After entropic dynamics is introduced, we develop the concepts of symmetries and transformations from an informational perspective. The primary result is the formulation of a symmetry condition that any transformation must satisfy in order to qualify as a symmetry in EQD. We then proceed to apply this condition to the extended Galilean transformation. This transformation is of interest as it exhibits features of both special and general relativity. The transformation yields a gravitational potential that arises from an equivalence of information. We conclude the thesis with a discussion of the measurement problem in quantum mechanics. We discuss the difficulties that arise in the standard quantum mechanical approach to measurement before developing our theory of entropic measurement. In entropic dynamics, position is the only observable. We show how a theory built on this one observable can account for the multitude of measurements present in quantum theory. Furthermore, we show that the Born rule need not be postulated, but can be derived in EQD. Finally, we show how the wave function can be updated by the ME method as the phase is constructed purely in terms of probabilities.

Quantum Graphical Models and Belief Propagation

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

Leifer, M.S.; Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo Ont., N2L 2Y5; Poulin, D.

Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markovmore » Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley-Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described.« less

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings.

PubMed

Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

2017-12-15

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory-such as Hall's marriage problem-are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

Unforgeable noise-tolerant quantum tokens

PubMed Central

Pastawski, Fernando; Yao, Norman Y.; Jiang, Liang; Lukin, Mikhail D.; Cirac, J. Ignacio

2012-01-01

The realization of devices that harness the laws of quantum mechanics represents an exciting challenge at the interface of modern technology and fundamental science. An exemplary paragon of the power of such quantum primitives is the concept of “quantum money” [Wiesner S (1983) ACM SIGACT News 15:78–88]. A dishonest holder of a quantum bank note will invariably fail in any counterfeiting attempts; indeed, under assumptions of ideal measurements and decoherence-free memories such security is guaranteed by the no-cloning theorem. In any practical situation, however, noise, decoherence, and operational imperfections abound. Thus, the development of secure “quantum money”-type primitives capable of tolerating realistic infidelities is of both practical and fundamental importance. Here, we propose a novel class of such protocols and demonstrate their tolerance to noise; moreover, we prove their rigorous security by determining tight fidelity thresholds. Our proposed protocols require only the ability to prepare, store, and measure single quantum bit memories, making their experimental realization accessible with current technologies.

Quantum demolition filtering and optimal control of unstable systems.

PubMed

Belavkin, V P

2012-11-28

A brief account of the quantum information dynamics and dynamical programming methods for optimal control of quantum unstable systems is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme, we exploit the separation theorem of filtering and control aspects as in the usual case of quantum stable systems with non-demolition observation. This allows us to start with the Belavkin quantum filtering equation generalized to demolition observations and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to Hamiltonian terms in the filtering equation. An unstable controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

Quantum Experiments and Graphs: Multiparty States as Coherent Superpositions of Perfect Matchings

NASA Astrophysics Data System (ADS)

Krenn, Mario; Gu, Xuemei; Zeilinger, Anton

2017-12-01

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and graph theory. In these setups, the paths of photons are identified such that the photon-source information is never created. We find that each of these setups corresponds to an undirected graph, and every undirected graph corresponds to an experimental setup. Every term in the emerging quantum superposition corresponds to a perfect matching in the graph. Calculating the final quantum state is in the #P-complete complexity class, thus it cannot be done efficiently. To strengthen the link further, theorems from graph theory—such as Hall's marriage problem—are rephrased in the language of pair creation in quantum experiments. We show explicitly how this link allows one to answer questions about quantum experiments (such as which classes of entangled states can be created) with graph theoretical methods, and how to potentially simulate properties of graphs and networks with quantum experiments (such as critical exponents and phase transitions).

Exponential gain of randomness certified by quantum contextuality

NASA Astrophysics Data System (ADS)

Um, Mark; Zhang, Junhua; Wang, Ye; Wang, Pengfei; Kim, Kihwan

2017-04-01

We demonstrate the protocol of exponential gain of randomness certified by quantum contextuality in a trapped ion system. The genuine randomness can be produced by quantum principle and certified by quantum inequalities. Recently, randomness expansion protocols based on inequality of Bell-text and Kochen-Specker (KS) theorem, have been demonstrated. These schemes have been theoretically innovated to exponentially expand the randomness and amplify the randomness from weak initial random seed. Here, we report the experimental evidence of such exponential expansion of randomness. In the experiment, we use three states of a 138Ba + ion between a ground state and two quadrupole states. In the 138Ba + ion system, we do not have detection loophole and we apply a methods to rule out certain hidden variable models that obey a kind of extended noncontextuality.

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

The category of Yetter-Drinfel'd Hom-modules and the quantum Hom-Yang-Baxter equation

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

Chen, Yuanyuan; Zhang, Liangyun, E-mail: zlyun@njau.edu.cn

2014-03-15

In this paper, we introduce the category of Yetter-Drinfel'd Hom-modules which is a braided monoidal category and show that the category of Yetter-Drinfel'd Hom-modules is a full monoidal subcategory of the left center of left Hom-module category. Also we study the equivalent relationship between the category of Yetter-Drinfel'd Hom-modules and the category of Hom-modules over the Drinfel'd double. Finally, the Faddeev-Reshetikhin-Takhtajan (FRT) type theorem for the quantum Hom-Yang-Baxter equation is investigated.

Einstein and the Quantum: The Secret Life of EPR

NASA Astrophysics Data System (ADS)

Fine, Arthur

2006-05-01

Locality, separation and entanglement -- 1930s style. Starting with Solvay 1927, we'll explore the background to the 1935 paper by Einstein, Podolsky and Rosen: how it was composed, the actual argument and principles used, and how the paper was received by Schroedinger, and others. We'll also look at Bohr's response: the extent to which Bohr connects with what Einstein was after in EPR and the extent to which EPR marks a shift in Bohr's thinking about the quantum theory. Time permitting, we will contrast EPR with Bell's theorem.

Redundancy of constraints in the classical and quantum theories of gravitation.

NASA Technical Reports Server (NTRS)

Moncrief, V.

1972-01-01

It is shown that in Dirac's version of the quantum theory of gravitation, the Hamiltonian constraints are greatly redundant. If the Hamiltonian constraint condition is satisfied at one point on the underlying, closed three-dimensional manifold, then it is automatically satisfied at every point, provided only that the momentum constraints are everywhere satisfied. This permits one to replace the usual infinity of Hamiltonian constraints by a single condition which may be taken in the form of an integral over the manifold. Analogous theorems are given for the classical Einstein Hamilton-Jacobi equations.

Exact infinite-time statistics of the Loschmidt echo for a quantum quench.

PubMed

Campos Venuti, Lorenzo; Jacobson, N Tobias; Santra, Siddhartha; Zanardi, Paolo

2011-07-01

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this Letter we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasicritical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.

Security analysis on some experimental quantum key distribution systems with imperfect optical and electrical devices

NASA Astrophysics Data System (ADS)

Liang, Lin-Mei; Sun, Shi-Hai; Jiang, Mu-Sheng; Li, Chun-Yan

2014-10-01

In general, quantum key distribution (QKD) has been proved unconditionally secure for perfect devices due to quantum uncertainty principle, quantum noncloning theorem and quantum nondividing principle which means that a quantum cannot be divided further. However, the practical optical and electrical devices used in the system are imperfect, which can be exploited by the eavesdropper to partially or totally spy the secret key between the legitimate parties. In this article, we first briefly review the recent work on quantum hacking on some experimental QKD systems with respect to imperfect devices carried out internationally, then we will present our recent hacking works in details, including passive faraday mirror attack, partially random phase attack, wavelength-selected photon-number-splitting attack, frequency shift attack, and single-photon-detector attack. Those quantum attack reminds people to improve the security existed in practical QKD systems due to imperfect devices by simply adding countermeasure or adopting a totally different protocol such as measurement-device independent protocol to avoid quantum hacking on the imperfection of measurement devices [Lo, et al., Phys. Rev. Lett., 2012, 108: 130503].

Towards Quantum Cybernetics:. Optimal Feedback Control in Quantum Bio Informatics

NASA Astrophysics Data System (ADS)

Belavkin, V. P.

2009-02-01

A brief account of the quantum information dynamics and dynamical programming methods for the purpose of optimal control in quantum cybernetics with convex constraints and cońcave cost and bequest functions of the quantum state is given. Consideration is given to both open loop and feedback control schemes corresponding respectively to deterministic and stochastic semi-Markov dynamics of stable or unstable systems. For the quantum feedback control scheme with continuous observations we exploit the separation theorem of filtering and control aspects for quantum stochastic micro-dynamics of the total system. This allows to start with the Belavkin quantum filtering equation and derive the generalized Hamilton-Jacobi-Bellman equation using standard arguments of classical control theory. This is equivalent to a Hamilton-Jacobi equation with an extra linear dissipative term if the control is restricted to only Hamiltonian terms in the filtering equation. A controlled qubit is considered as an example throughout the development of the formalism. Finally, we discuss optimum observation strategies to obtain a pure quantum qubit state from a mixed one.

Coupled-oscillator theory of dispersion and Casimir-Polder interactions.

PubMed

Berman, P R; Ford, G W; Milonni, P W

2014-10-28

We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength. However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r(-4), a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called "remarkable formula" for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O'Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.

Nonlocality in Bohmian mechanics

NASA Astrophysics Data System (ADS)

Ghafar, Zati Amalina binti Mohd Abdul; Radiman, Shahidan bin; Siong, Ch'ng Han

2018-04-01

The Einstein-Podolsky-Rosen (EPR) paradox demonstrates that entangled particles can interact in such a way that it is possible to measure both their position and momentum instantaneously. The position or momentum of one particle can be determined by measuring another identical particle that exists in another space. This instantaneous action is actually called nonlocality. The nonlocality has been proved by Bell's theorem that states that all quantum theories must be nonlocal. The Bell's theorem gives a strong support to the hidden variable theory, i.e. Bohmian mechanics. Using nonlocality, we present that the velocity field of one particle can be obtained by measuring the velocity of other particles. The trajectory of these particles is perhaps surrealistic trajectory due to the nonlocality.

Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor’s Theorem

NASA Astrophysics Data System (ADS)

Yañez-Navarro, G.; Sun, Guo-Hua; Sun, Dong-Sheng; Chen, Chang-Yuan; Dong, Shi-Hai

2017-08-01

A few important integrals involving the product of two universal associated Legendre polynomials {P}{l\\prime}{m\\prime}(x), {P}{k\\prime}{n\\prime}(x) and x2a(1 - x2)-p-1, xb(1 ± x)-p-1 and xc(1 -x2)-p-1 (1 ± x) are evaluated using the operator form of Taylor’s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e. l‧ ≠ k‧ and m‧ ≠ n‧. Their selection rules are also given. We also verify the correctness of those integral formulas numerically. Supported by 20170938-SIP-IPN, Mexico

Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems.

PubMed

Guseinov, Israfil I; Görgün, Nurşen Seçkin

2011-06-01

The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.

Further evidence for the EPNT assumption

NASA Technical Reports Server (NTRS)

Greenberger, Daniel M.; Bernstein, Herbert J.; Horne, Michael; Zeilinger, Anton

1994-01-01

We recently proved a theorem extending the Greenberger-Horne-Zeilinger (GHZ) Theorem from multi-particle systems to two-particle systems. This proof depended upon an auxiliary assumption, the EPNT assumption (Emptiness of Paths Not Taken). According to this assumption, if there exists an Einstein-Rosen-Podolsky (EPR) element of reality that determines that a path is empty, then there can be no entity associated with the wave that travels this path (pilot-waves, empty waves, etc.) and reports information to the amplitude, when the paths recombine. We produce some further evidence in support of this assumption, which is certainly true in quantum theory. The alternative is that such a pilot-wave theory would have to violate EPR locality.

Higher-dimensional communication complexity problems: Classical protocols versus quantum ones based on Bell's theorem or prepare-transmit-measure schemes

NASA Astrophysics Data System (ADS)

Tavakoli, Armin; Żukowski, Marek

2017-04-01

Communication complexity problems (CCPs) are tasks in which separated parties attempt to compute a function whose inputs are distributed among the parties. Their communication is limited so that not all inputs can be sent. We show that broad classes of Bell inequalities can be mapped to CCPs and that a quantum violation of a Bell inequality is a necessary and sufficient condition for an enhancement of the related CCP beyond its classical limitation. However, one can implement CCPs by transmitting a quantum system, encoding no more information than is allowed in the CCP, and extracting information by performing measurements. We show that for a large class of Bell inequalities, the improvement of the CCP associated with a quantum violation of a Bell inequality can be no greater than the improvement obtained from quantum prepare-transmit-measure strategies.

Quantum Public Key Cryptosystem Based on Bell States

NASA Astrophysics Data System (ADS)

Wu, WanQing; Cai, QingYu; Zhang, HuanGuo; Liang, XiaoYan

2017-11-01

Classical public key cryptosystems ( P K C), such as R S A, E I G a m a l, E C C, are no longer secure in quantum algorithms, and quantum cryptography has become a novel research topic. In this paper we present a quantum asymmetrical cryptosystem i.e. quantum public key cryptosystem ( Q P K C) based on the Bell states. In particular, in the proposed QPKC the public key are given by the first n particles of Bell states and generalized Pauli operations. The corresponding secret key are the last n particles of Bell states and the inverse of generalized Pauli operations. The proposed QPKC encrypts the message using a public key and decrypts the ciphertext using a private key. By H o l e v o ' s theorem, we proved the security of the secret key and messages during the QPKC.

Postselection technique for quantum channels with applications to quantum cryptography.

PubMed

Christandl, Matthias; König, Robert; Renner, Renato

2009-01-16

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for an arbitrary input, it is sufficient to consider the case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained with help of the exponential de Finetti theorem.

Experimental ladder proof of Hardy's nonlocality for high-dimensional quantum systems

NASA Astrophysics Data System (ADS)

Chen, Lixiang; Zhang, Wuhong; Wu, Ziwen; Wang, Jikang; Fickler, Robert; Karimi, Ebrahim

2017-08-01

Recent years have witnessed a rapidly growing interest in high-dimensional quantum entanglement for fundamental studies as well as towards novel applications. Therefore, the ability to verify entanglement between physical qudits, d -dimensional quantum systems, is of crucial importance. To show nonclassicality, Hardy's paradox represents "the best version of Bell's theorem" without using inequalities. However, so far it has only been tested experimentally for bidimensional vector spaces. Here, we formulate a theoretical framework to demonstrate the ladder proof of Hardy's paradox for arbitrary high-dimensional systems. Furthermore, we experimentally demonstrate the ladder proof by taking advantage of the orbital angular momentum of high-dimensionally entangled photon pairs. We perform the ladder proof of Hardy's paradox for dimensions 3 and 4, both with the ladder up to the third step. Our paper paves the way towards a deeper understanding of the nature of high-dimensionally entangled quantum states and may find applications in quantum information science.

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.

Spin-adapted matrix product states and operators

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

Keller, Sebastian, E-mail: sebastian.keller@phys.chem.ethz.ch; Reiher, Markus, E-mail: markus.reiher@phys.chem.ethz.ch

Matrix product states (MPSs) and matrix product operators (MPOs) allow an alternative formulation of the density matrix renormalization group algorithm introduced by White. Here, we describe how non-abelian spin symmetry can be exploited in MPSs and MPOs by virtue of the Wigner–Eckart theorem at the example of the spin-adapted quantum chemical Hamiltonian operator.

A Symbiotic Relationship: The Observe-Orient-Decide-Act (OODA) Loop, Intuition, and Strategic Thought

DTIC Science & Technology

2013-03-01

Incompleteness Theorem (used in mathematics), and Heisenberg’s Uncertainty Principle as it pertains to the mathematical foundations of quantum ...subtlety which normal consciousness cannot even see…”46 It is in our PME system where we can create the time to develop the unconscious realms of the

Time-ordered exponential on the complex plane and Gell-Mann—Low formula as a mathematical theorem

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

Futakuchi, Shinichiro; Usui, Kouta

2016-04-15

The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann—Low formula under certain abstract conditions, in mathematically rigorous manner. We apply the abstract results to quantum electrodynamics with cutoffs.

Superconducting transitions in flat-band systems

DOE PAGES

Iglovikov, V. I.; Hébert, F.; Grémaud, B.; ...

2014-09-11

The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with unequal number of sites in each sublattice must have nonzero spin S at half-filling. Recently, there has been interest in Lieb geometries due to the possibility of novel topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using Determinant Quantum Montemore » Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems. Specifically, our results show unusual charge and charge transfer signatures within the flat band, and a reduction in pairing order at ρ = 2/3 and ρ = 4/3, the points at which the flat band is first occupied and then completely filled. Lastly, we compare our results to the case of flat bands in the Kagome lattice and demonstrate that the behavior observed in the two cases is rather different.« less

The photon identification loophole in EPRB experiments: computer models with single-wing selection

NASA Astrophysics Data System (ADS)

De Raedt, Hans; Michielsen, Kristel; Hess, Karl

2017-11-01

Recent Einstein-Podolsky-Rosen-Bohm experiments [M. Giustina et al. Phys. Rev. Lett. 115, 250401 (2015); L. K. Shalm et al. Phys. Rev. Lett. 115, 250402 (2015)] that claim to be loophole free are scrutinized. The combination of a digital computer and discrete-event simulation is used to construct a minimal but faithful model of the most perfected realization of these laboratory experiments. In contrast to prior simulations, all photon selections are strictly made, as they are in the actual experiments, at the local station and no other "post-selection" is involved. The simulation results demonstrate that a manifestly non-quantum model that identifies photons in the same local manner as in these experiments can produce correlations that are in excellent agreement with those of the quantum theoretical description of the corresponding thought experiment, in conflict with Bell's theorem which states that this is impossible. The failure of Bell's theorem is possible because of our recognition of the photon identification loophole. Such identification measurement-procedures are necessarily included in all actual experiments but are not included in the theory of Bell and his followers.

Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise.

PubMed

Leibovich, N; Dechant, A; Lutz, E; Barkai, E

2016-11-01

The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.

Coherence and measurement in quantum thermodynamics

PubMed Central

Kammerlander, P.; Anders, J.

2016-01-01

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed. PMID:26916503

Coherence and measurement in quantum thermodynamics.

PubMed

Kammerlander, P; Anders, J

2016-02-26

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

Coherence and measurement in quantum thermodynamics

NASA Astrophysics Data System (ADS)

Kammerlander, P.; Anders, J.

2016-02-01

Thermodynamics is a highly successful macroscopic theory widely used across the natural sciences and for the construction of everyday devices, from car engines to solar cells. With thermodynamics predating quantum theory, research now aims to uncover the thermodynamic laws that govern finite size systems which may in addition host quantum effects. Recent theoretical breakthroughs include the characterisation of the efficiency of quantum thermal engines, the extension of classical non-equilibrium fluctuation theorems to the quantum regime and a new thermodynamic resource theory has led to the discovery of a set of second laws for finite size systems. These results have substantially advanced our understanding of nanoscale thermodynamics, however putting a finger on what is genuinely quantum in quantum thermodynamics has remained a challenge. Here we identify information processing tasks, the so-called projections, that can only be formulated within the framework of quantum mechanics. We show that the physical realisation of such projections can come with a non-trivial thermodynamic work only for quantum states with coherences. This contrasts with information erasure, first investigated by Landauer, for which a thermodynamic work cost applies for classical and quantum erasure alike. Repercussions on quantum work fluctuation relations and thermodynamic single-shot approaches are also discussed.

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

Quantum plug n’ play: modular computation in the quantum regime

NASA Astrophysics Data System (ADS)

Thompson, Jayne; Modi, Kavan; Vedral, Vlatko; Gu, Mile

2018-01-01

Classical computation is modular. It exploits plug n’ play architectures which allow us to use pre-fabricated circuits without knowing their construction. This bestows advantages such as allowing parts of the computational process to be outsourced, and permitting individual circuit components to be exchanged and upgraded. Here, we introduce a formal framework to describe modularity in the quantum regime. We demonstrate a ‘no-go’ theorem, stipulating that it is not always possible to make use of quantum circuits without knowing their construction. This has significant consequences for quantum algorithms, forcing the circuit implementation of certain quantum algorithms to be rebuilt almost entirely from scratch after incremental changes in the problem—such as changing the number being factored in Shor’s algorithm. We develop a workaround capable of restoring modularity, and apply it to design a modular version of Shor’s algorithm that exhibits increased versatility and reduced complexity. In doing so we pave the way to a realistic framework whereby ‘quantum chips’ and remote servers can be invoked (or assembled) to implement various parts of a more complex quantum computation.

Reconstructing latent dynamical noise for better forecasting observables

NASA Astrophysics Data System (ADS)

Hirata, Yoshito

2018-03-01

I propose a method for reconstructing multi-dimensional dynamical noise inspired by the embedding theorem of Muldoon et al. [Dyn. Stab. Syst. 13, 175 (1998)] by regarding multiple predictions as different observables. Then, applying the embedding theorem by Stark et al. [J. Nonlinear Sci. 13, 519 (2003)] for a forced system, I produce time series forecast by supplying the reconstructed past dynamical noise as auxiliary information. I demonstrate the proposed method on toy models driven by auto-regressive models or independent Gaussian noise.

Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

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

Zhang, Xiao; Science and Technology on Electronic Information Control Laboratory, 610036, Chengdu, Sichuan; Wei, Chaozhen

2014-11-15

In this paper we use Dirac function to construct a fractional operator called fractional corresponding operator, which is the general form of momentum corresponding operator. Then we give a judging theorem for this operator and with this judging theorem we prove that R–L, G–L, Caputo, Riesz fractional derivative operator and fractional derivative operator based on generalized functions, which are the most popular ones, coincide with the fractional corresponding operator. As a typical application, we use the fractional corresponding operator to construct a new fractional quantization scheme and then derive a uniform fractional Schrödinger equation in form. Additionally, we find thatmore » the five forms of fractional Schrödinger equation belong to the particular cases. As another main result of this paper, we use fractional corresponding operator to generalize fractional quantization scheme by using Lévy path integral and use it to derive the corresponding general form of fractional Schrödinger equation, which consequently proves that these two quantization schemes are equivalent. Meanwhile, relations between the theory in fractional quantum mechanics and that in classic quantum mechanics are also discussed. As a physical example, we consider a particle in an infinite potential well. We give its wave functions and energy spectrums in two ways and find that both results are the same.« less

Quantum fluctuation theorems and power measurements

NASA Astrophysics Data System (ADS)

Prasanna Venkatesh, B.; Watanabe, Gentaro; Talkner, Peter

2015-07-01

Work in the paradigm of the quantum fluctuation theorems of Crooks and Jarzynski is determined by projective measurements of energy at the beginning and end of the force protocol. In analogy to classical systems, we consider an alternative definition of work given by the integral of the supplied power determined by integrating up the results of repeated measurements of the instantaneous power during the force protocol. We observe that such a definition of work, in spite of taking account of the process dependence, has different possible values and statistics from the work determined by the conventional two energy measurement approach (TEMA). In the limit of many projective measurements of power, the system’s dynamics is frozen in the power measurement basis due to the quantum Zeno effect leading to statistics only trivially dependent on the force protocol. In general the Jarzynski relation is not satisfied except for the case when the instantaneous power operator commutes with the total Hamiltonian at all times. We also consider properties of the joint statistics of power-based definition of work and TEMA work in protocols where both values are determined. This allows us to quantify their correlations. Relaxing the projective measurement condition, weak continuous measurements of power are considered within the stochastic master equation formalism. Even in this scenario the power-based work statistics is in general not able to reproduce qualitative features of the TEMA work statistics.

In search of superluminal quantum communications: recent experiments and possible improvements

NASA Astrophysics Data System (ADS)

Cocciaro, B.; Faetti, S.; Fronzoni, L.

2013-06-01

As shown in the famous EPR paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics is non-local. The Bell theorem and the experiments by Aspect and many others, ruled out the possibility of explaining quantum correlations between entangled particles using local hidden variables models (except for implausible combinations of loopholes). Some authors (Bell, Eberhard, Bohm and Hiley) suggested that quantum correlations could be due to superluminal communications (tachyons) that propagate isotropically with velocity vt > c in a preferred reference frame. For finite values of vt, Quantum Mechanics and superluminal models lead to different predictions. Some years ago a Geneva group and our group did experiments on entangled photons to evidence possible discrepancies between experimental results and quantum predictions. Since no discrepancy was found, these experiments established only lower bounds for the possible tachyon velocities vt. Here we propose an improved experiment that should lead us to explore a much larger range of possible tachyon velocities Vt for any possible direction of velocity vec V of the tachyons preferred frame.

Adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2018-01-01

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.

A channel-based framework for steering, non-locality and beyond

NASA Astrophysics Data System (ADS)

Hoban, Matty J.; Belén Sainz, Ana

2018-05-01

Non-locality and steering are both non-classical phenomena witnessed in nature as a result of quantum entanglement. It is now well-established that one can study non-locality independently of the formalism of quantum mechanics, in the so-called device-independent framework. With regards to steering, although one cannot study it completely independently of the quantum formalism, ‘post-quantum steering’ has been described, which is steering that cannot be reproduced by measurements on entangled states but does not lead to superluminal signalling. In this work we present a framework based on the study of quantum channels in which one can study steering (and non-locality) in quantum theory and beyond. In this framework, we show that kinds of steering, whether quantum or post-quantum, are directly related to particular families of quantum channels that have been previously introduced by Beckman et al (2001 Phys. Rev. A 64 052309). Utilizing this connection we also demonstrate new analytical examples of post-quantum steering, give a quantum channel interpretation of almost quantum non-locality and steering, easily recover and generalize the celebrated Gisin–Hughston–Jozsa–Wootters theorem, and initiate the study of post-quantum Buscemi non-locality and non-classical teleportation. In this way, we see post-quantum non-locality and steering as just two aspects of a more general phenomenon.

Amplitudes for multiphoton quantum processes in linear optics

NASA Astrophysics Data System (ADS)

Urías, Jesús

2011-07-01

The prominent role that linear optical networks have acquired in the engineering of photon states calls for physically intuitive and automatic methods to compute the probability amplitudes for the multiphoton quantum processes occurring in linear optics. A version of Wick's theorem for the expectation value, on any vector state, of products of linear operators, in general, is proved. We use it to extract the combinatorics of any multiphoton quantum processes in linear optics. The result is presented as a concise rule to write down directly explicit formulae for the probability amplitude of any multiphoton process in linear optics. The rule achieves a considerable simplification and provides an intuitive physical insight about quantum multiphoton processes. The methodology is applied to the generation of high-photon-number entangled states by interferometrically mixing coherent light with spontaneously down-converted light.

Topics in black holes and quantum cosmology

NASA Astrophysics Data System (ADS)

Campiglia, Miguel

2012-06-01

Black holes and the big bang beginning of the universe are among the most spectacular predictions of general relativity, having a broad impact that ranges from observational astronomy to quantum gravity. In this thesis we will focus on classical and quantum aspects of these subjects: In the first part we present a coordinate-free way of describing the approach to equilibrium of black holes within the framework of dynamical and isolated horizons. In the second part we focus on loop quantum cosmology. We present a uniqueness theorem of its kinematics, and explore the possible ways to implement its dynamics via path integrals.¹ ¹The topics presented here form part of the research done during my PhD studies. See the Vita at the end of the Thesis for a complete list of my work during this period.

Operational formulation of time reversal in quantum theory

NASA Astrophysics Data System (ADS)

Oreshkov, Ognyan; Cerf, Nicolas J.

2015-10-01

The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born’s rule do not apply backward in time. Here, we resolve this problem within a rigorous operational probabilistic framework. We argue that reconciling time reversal with the probabilistic rules of the theory requires a notion of operation that permits realizations through both pre- and post-selection. We develop the generalized formulation of quantum theory that stems from this approach and give a precise definition of time-reversal symmetry, emphasizing a previously overlooked distinction between states and effects. We prove an analogue of Wigner’s theorem, which characterizes all allowed symmetry transformations in this operationally time-symmetric quantum theory. Remarkably, we find larger classes of symmetry transformations than previously assumed, suggesting a possible direction in the search for extensions of known physics.

Quantum Max-flow/Min-cut

NASA Astrophysics Data System (ADS)

Cui, Shawn X.; Freedman, Michael H.; Sattath, Or; Stong, Richard; Minton, Greg

2016-06-01

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.

Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy

NASA Astrophysics Data System (ADS)

Hasebe, Kazuki

2017-07-01

We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.

Axioms for quantum mechanics: relativistic causality, retrocausality, and the existence of a classical limit

NASA Astrophysics Data System (ADS)

Rohrlich, Daniel

Y. Aharonov and A. Shimony both conjectured that two axioms - relativistic causality (``no superluminal signalling'') and nonlocality - so nearly contradict each other that only quantum mechanics reconciles them. Can we indeed derive quantum mechanics, at least in part, from these two axioms? No: ``PR-box'' correlations show that quantum correlations are not the most nonlocal correlations consistent with relativistic causality. Here we replace ``nonlocality'' with ``retrocausality'' and supplement the axioms of relativistic causality and retrocausality with a natural and minimal third axiom: the existence of a classical limit, in which macroscopic observables commute. That is, just as quantum mechanics has a classical limit, so must any generalization of quantum mechanics. In this limit, PR-box correlations violaterelativistic causality. Generalized to all stronger-than-quantum bipartite correlations, this result is a derivation of Tsirelson's bound (a theorem of quantum mechanics) from the three axioms of relativistic causality, retrocausality and the existence of a classical limit. Although the derivation does not assume quantum mechanics, it points to the Hilbert space structure that underlies quantum correlations. I thank the John Templeton Foundation (Project ID 43297) and the Israel Science Foundation (Grant No. 1190/13) for support.

Computational quantum-classical boundary of noisy commuting quantum circuits

PubMed Central

Fujii, Keisuke; Tamate, Shuhei

2016-01-01

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039

Computational quantum-classical boundary of noisy commuting quantum circuits.

PubMed

Fujii, Keisuke; Tamate, Shuhei

2016-05-18

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

Computational quantum-classical boundary of noisy commuting quantum circuits

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Tamate, Shuhei

2016-05-01

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

Symmetry algebra of a generalized anisotropic harmonic oscillator

NASA Technical Reports Server (NTRS)

Castanos, O.; Lopez-Pena, R.

1993-01-01

It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

A Proposal for Testing Local Realism Without Using Assumptions Related to Hidden Variable States

NASA Technical Reports Server (NTRS)

Ryff, Luiz Carlos

1996-01-01

A feasible experiment is discussed which allows us to prove a Bell's theorem for two particles without using an inequality. The experiment could be used to test local realism against quantum mechanics without the introduction of additional assumptions related to hidden variables states. Only assumptions based on direct experimental observation are needed.

Gaussification and entanglement distillation of continuous-variable systems: a unifying picture.

PubMed

Campbell, Earl T; Eisert, Jens

2012-01-13

Distillation of entanglement using only Gaussian operations is an important primitive in quantum communication, quantum repeater architectures, and distributed quantum computing. Existing distillation protocols for continuous degrees of freedom are only known to converge to a Gaussian state when measurements yield precisely the vacuum outcome. In sharp contrast, non-Gaussian states can be deterministically converted into Gaussian states while preserving their second moments, albeit by usually reducing their degree of entanglement. In this work-based on a novel instance of a noncommutative central limit theorem-we introduce a picture general enough to encompass the known protocols leading to Gaussian states, and new classes of protocols including multipartite distillation. This gives the experimental option of balancing the merits of success probability against entanglement produced.

Composable security proof for continuous-variable quantum key distribution with coherent States.

PubMed

Leverrier, Anthony

2015-02-20

We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, which does not rely on any assumption about the quantum state being measured, will find applications elsewhere, for instance, for the reliable quantification of continuous-variable entanglement in finite-size settings.

Deterministic and efficient quantum cryptography based on Bell's theorem

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

Chen Zengbing; Pan Jianwei; Physikalisches Institut, Universitaet Heidelberg, Philosophenweg 12, 69120 Heidelberg

2006-05-15

We propose a double-entanglement-based quantum cryptography protocol that is both efficient and deterministic. The proposal uses photon pairs with entanglement both in polarization and in time degrees of freedom; each measurement in which both of the two communicating parties register a photon can establish one and only one perfect correlation, and thus deterministically create a key bit. Eavesdropping can be detected by violation of local realism. A variation of the protocol shows a higher security, similar to the six-state protocol, under individual attacks. Our scheme allows a robust implementation under the current technology.

Remote detection of single emitters via optical waveguides

NASA Astrophysics Data System (ADS)

Then, Patrick; Razinskas, Gary; Feichtner, Thorsten; Haas, Philippe; Wild, Andreas; Bellini, Nicola; Osellame, Roberto; Cerullo, Giulio; Hecht, Bert

2014-05-01

The integration of lab-on-a-chip technologies with single-molecule detection techniques may enable new applications in analytical chemistry, biotechnology, and medicine. We describe a method based on the reciprocity theorem of electromagnetic theory to determine and optimize the detection efficiency of photons emitted by single quantum emitters through truncated dielectric waveguides of arbitrary shape positioned in their proximity. We demonstrate experimentally that detection of single quantum emitters via such waveguides is possible, confirming the predicted behavior of the detection efficiency. Our findings blaze the trail towards efficient lensless single-emitter detection compatible with large-scale optofluidic integration.

Bell's "Theorem": loopholes vs. conceptual flaws

NASA Astrophysics Data System (ADS)

Kracklauer, A. F.

2017-12-01

An historical overview and detailed explication of a critical analysis of what has become known as Bell's Theorem to the effect that, it should be impossible to extend Quantum Theory with the addition of local, real variables so as to obtain a version free of the ambiguous and preternatural features of the currently accepted interpretations is presented. The central point on which this critical analysis, due originally to Edwin Jaynes, is that Bell incorrectly applied probabilistic formulas involving conditional probabilities. In addition, mathematical technicalities that have complicated the understanding of the logical or mathematical setting in which current theory and experimentation are embedded, are discussed. Finally, some historical speculations on the sociological environment, in particular misleading aspects, in which recent generations of physicists lived and worked are mentioned.

Validity of black hole complementarity in the BTZ black hole

NASA Astrophysics Data System (ADS)

Gim, Yongwan; Kim, Wontae

2018-01-01

Based on the gedanken experiment for black hole complementarity in the Schwarzschild black hole, we calculate the energy required to duplicate information in the BTZ black hole under the assumption of absorbing boundary condition and its dual solution of the black string, respectively, in order to justify the validity of the no-cloning theorem in quantum mechanics. For the BTZ black hole, the required energy for the duplication of information can be made fairly small, whereas for the black string it exceeds the total mass of the black string, although they are related to each other under the dual transformation. So, the duplication of information might be possible in the BTZ black hole in contrast to the case of the black string, so that the no-cloning theorem could be violated for the former case. To save the duplication of information for the BTZ black hole, we perform an improved gedanken experiment by using the local thermodynamic quantities near the horizon rather than those defined at infinity, and show that the no-cloning theorem could be made valid even in the BTZ black hole. We also discuss how this local treatment for the no-cloning theorem can be applied to the black string as well as the Schwarzschild black hole innocuously.

Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement

PubMed

Pan; Bouwmeester; Daniell; Weinfurter; Zeilinger

2000-02-03

Bell's theorem states that certain statistical correlations predicted by quantum physics for measurements on two-particle systems cannot be understood within a realistic picture based on local properties of each individual particle-even if the two particles are separated by large distances. Einstein, Podolsky and Rosen first recognized the fundamental significance of these quantum correlations (termed 'entanglement' by Schrodinger) and the two-particle quantum predictions have found ever-increasing experimental support. A more striking conflict between quantum mechanical and local realistic predictions (for perfect correlations) has been discovered; but experimental verification has been difficult, as it requires entanglement between at least three particles. Here we report experimental confirmation of this conflict, using our recently developed method to observe three-photon entanglement, or 'Greenberger-Horne-Zeilinger' (GHZ) states. The results of three specific experiments, involving measurements of polarization correlations between three photons, lead to predictions for a fourth experiment; quantum physical predictions are mutually contradictory with expectations based on local realism. We find the results of the fourth experiment to be in agreement with the quantum prediction and in striking conflict with local realism.

Quantum mechanics over sets

NASA Astrophysics Data System (ADS)

Ellerman, David

2014-03-01

In models of QM over finite fields (e.g., Schumacher's ``modal quantum theory'' MQT), one finite field stands out, Z2, since Z2 vectors represent sets. QM (finite-dimensional) mathematics can be transported to sets resulting in quantum mechanics over sets or QM/sets. This gives a full probability calculus (unlike MQT with only zero-one modalities) that leads to a fulsome theory of QM/sets including ``logical'' models of the double-slit experiment, Bell's Theorem, QIT, and QC. In QC over Z2 (where gates are non-singular matrices as in MQT), a simple quantum algorithm (one gate plus one function evaluation) solves the Parity SAT problem (finding the parity of the sum of all values of an n-ary Boolean function). Classically, the Parity SAT problem requires 2n function evaluations in contrast to the one function evaluation required in the quantum algorithm. This is quantum speedup but with all the calculations over Z2 just like classical computing. This shows definitively that the source of quantum speedup is not in the greater power of computing over the complex numbers, and confirms the idea that the source is in superposition.

Capacities of quantum amplifier channels

NASA Astrophysics Data System (ADS)

Qi, Haoyu; Wilde, Mark M.

2017-01-01

Quantum amplifier channels are at the core of several physical processes. Not only do they model the optical process of spontaneous parametric down-conversion, but the transformation corresponding to an amplifier channel also describes the physics of the dynamical Casimir effect in superconducting circuits, the Unruh effect, and Hawking radiation. Here we study the communication capabilities of quantum amplifier channels. Invoking a recently established minimum output-entropy theorem for single-mode phase-insensitive Gaussian channels, we determine capacities of quantum-limited amplifier channels in three different scenarios. First, we establish the capacities of quantum-limited amplifier channels for one of the most general communication tasks, characterized by the trade-off between classical communication, quantum communication, and entanglement generation or consumption. Second, we establish capacities of quantum-limited amplifier channels for the trade-off between public classical communication, private classical communication, and secret key generation. Third, we determine the capacity region for a broadcast channel induced by the quantum-limited amplifier channel, and we also show that a fully quantum strategy outperforms those achieved by classical coherent-detection strategies. In all three scenarios, we find that the capacities significantly outperform communication rates achieved with a naive time-sharing strategy.

Time-reversal symmetry in nonstationary Markov processes with application to some fluctuation theorems

NASA Astrophysics Data System (ADS)

Van Vliet, Carolyne M.

2012-11-01

Nonequilibrium processes require that the density operator of an interacting system with Hamiltonian H(t)=H0(t)+λV converges and produces entropy. Employing projection operators in the state space, the density operator is developed to all orders of perturbation and then resummed. In contrast to earlier treatments by Van Hove [Physica0031-891410.1016/S0031-8914(54)92646-4 21, 517 (1955)] and others [U. Fano, Rev. Mod. Phys.0034-686110.1103/RevModPhys.29.74 29, 74 (1959); U. Fano, in Lectures on the Many-Body Problem, Vol 2, edited by E. R. Caniello (Academic Press, New York, 1964); R. Zwanzig, in Lectures in Theoretical Physics, Vol. III, edited by W. E. Britten, B. W. Downs, and J. Downs (Wiley Interscience, New York, 1961), pp. 116-141; K. M. Van Vliet, J. Math. Phys.0022-248810.1063/1.523833 19, 1345 (1978); K. M. Van Vliet, Can. J. Phys. 56, 1206 (1978)], closed expressions are obtained. From these we establish the time-reversal symmetry property P(γ,t|γ',t')=P˜(γ',t'|γ,t), where the tilde refers to the time-reversed protocol; also a nonstationary Markovian master equation is derived. Time-reversal symmetry is then applied to thermostatted systems yielding the Crooks-Tasaki fluctuation theorem (FT) and the quantum Jarzynski work-energy theorem, as well as the general entropy FT. The quantum mechanical concepts of work and entropy are discussed in detail. Finally, we present a nonequilibrium extension of Mazo's lemma of linear response theory, obtaining some applications via this alternate route.

Coupled-oscillator theory of dispersion and Casimir-Polder interactions

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

Berman, P. R.; Ford, G. W.; Milonni, P. W.

2014-10-28

We address the question of the applicability of the argument theorem (of complex variable theory) to the calculation of two distinct energies: (i) the first-order dispersion interaction energy of two separated oscillators, when one of the oscillators is excited initially and (ii) the Casimir-Polder interaction of a ground-state quantum oscillator near a perfectly conducting plane. We show that the argument theorem can be used to obtain the generally accepted equation for the first-order dispersion interaction energy, which is oscillatory and varies as the inverse power of the separation r of the oscillators for separations much greater than an optical wavelength.more » However, for such separations, the interaction energy cannot be transformed into an integral over the positive imaginary axis. If the argument theorem is used incorrectly to relate the interaction energy to an integral over the positive imaginary axis, the interaction energy is non-oscillatory and varies as r{sup −4}, a result found by several authors. Rather remarkably, this incorrect expression for the dispersion energy actually corresponds to the nonperturbative Casimir-Polder energy for a ground-state quantum oscillator near a perfectly conducting wall, as we show using the so-called “remarkable formula” for the free energy of an oscillator coupled to a heat bath [G. W. Ford, J. T. Lewis, and R. F. O’Connell, Phys. Rev. Lett. 55, 2273 (1985)]. A derivation of that formula from basic results of statistical mechanics and the independent oscillator model of a heat bath is presented.« less

Geometrical and quantum mechanical aspects in observers' mathematics

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2013-10-01

When we create mathematical models for Quantum Mechanics we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We prove that Euclidean Geometry works in sufficiently small neighborhood of the given line, but when we enlarge the neighborhood, non-euclidean Geometry takes over. We prove that the physical speed is a random variable, cannot exceed some constant, and this constant does not depend on an inertial coordinate system. We proved the following theorems: Theorem A (Lagrangian). Let L be a Lagrange function of free material point with mass m and speed v. Then the probability P of L = m 2 v2 is less than 1: P(L = m 2 v2) < 1. Theorem B (Nadezhda effect). On the plane (x, y) on every line y = kx there is a point (x0, y0) with no existing Euclidean distance between origin (0, 0) and this point. Conjecture (Black Hole). Our space-time nature is a black hole: light cannot go out infinitely far from origin.

Lower bound on the time complexity of local adiabatic evolution

NASA Astrophysics Data System (ADS)

Chen, Zhenghao; Koh, Pang Wei; Zhao, Yan

2006-11-01

The adiabatic theorem of quantum physics has been, in recent times, utilized in the design of local search quantum algorithms, and has been proven to be equivalent to standard quantum computation, that is, the use of unitary operators [D. Aharonov in Proceedings of the 45th Annual Symposium on the Foundations of Computer Science, 2004, Rome, Italy (IEEE Computer Society Press, New York, 2004), pp. 42-51]. Hence, the study of the time complexity of adiabatic evolution algorithms gives insight into the computational power of quantum algorithms. In this paper, we present two different approaches of evaluating the time complexity for local adiabatic evolution using time-independent parameters, thus providing effective tests (not requiring the evaluation of the entire time-dependent gap function) for the time complexity of newly developed algorithms. We further illustrate our tests by displaying results from the numerical simulation of some problems, viz. specially modified instances of the Hamming weight problem.

Quantum spaces, central extensions of Lie groups and related quantum field theories

NASA Astrophysics Data System (ADS)

Poulain, Timothé; Wallet, Jean-Christophe

2018-02-01

Quantum spaces with su(2) noncommutativity can be modelled by using a family of SO(3)-equivariant differential *-representations. The quantization maps are determined from the combination of the Wigner theorem for SU(2) with the polar decomposition of the quantized plane waves. A tracial star-product, equivalent to the Kontsevich product for the Poisson manifold dual to su(2) is obtained from a subfamily of differential *-representations. Noncommutative (scalar) field theories free from UV/IR mixing and whose commutative limit coincides with the usual ϕ 4 theory on ℛ3 are presented. A generalization of the construction to semi-simple possibly non simply connected Lie groups based on their central extensions by suitable abelian Lie groups is discussed. Based on a talk presented by Poulain T at the XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25), Prague, June 6-10 2017.

Quantum Information: an invitation for mathematicians

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

Perez-Garcia, David

2009-05-06

Quantum Information is the science that aims to use the unusual behavior of the microscopic world, governed by the laws of Quantum Mechanics, in order to improve the way in which we compute or communicate information. Though the first ideas in this direction come from the early 80's, it is in the last decade when Quantum Information has suffered an spectacular development. It is impossible to resume in a paper like this one the importance and complexity of the field. Therefore, I will limit to briefly explain some of the initial ideas (considered classical by now), and to briefly suggestmore » some of the modern lines of research. By the nature of this exposition, I have decided to avoid rigor and to concentrate more in ideas and intuitions. Anyhow, I have tried to provide with enough references, in such a way that an interested reader could find there proper theorems and proofs.« less

What can we learn from noise? — Mesoscopic nonequilibrium statistical physics —

PubMed Central

KOBAYASHI, Kensuke

2016-01-01

Mesoscopic systems — small electric circuits working in quantum regime — offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics. PMID:27477456

What can we learn from noise? - Mesoscopic nonequilibrium statistical physics.

PubMed

Kobayashi, Kensuke

2016-01-01

Mesoscopic systems - small electric circuits working in quantum regime - offer us a unique experimental stage to explorer quantum transport in a tunable and precise way. The purpose of this Review is to show how they can contribute to statistical physics. We introduce the significance of fluctuation, or equivalently noise, as noise measurement enables us to address the fundamental aspects of a physical system. The significance of the fluctuation theorem (FT) in statistical physics is noted. We explain what information can be deduced from the current noise measurement in mesoscopic systems. As an important application of the noise measurement to statistical physics, we describe our experimental work on the current and current noise in an electron interferometer, which is the first experimental test of FT in quantum regime. Our attempt will shed new light in the research field of mesoscopic quantum statistical physics.

Entropic Barriers for Two-Dimensional Quantum Memories

NASA Astrophysics Data System (ADS)

Brown, Benjamin J.; Al-Shimary, Abbas; Pachos, Jiannis K.

2014-03-01

Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.

Experimental Eavesdropping Based on Optimal Quantum Cloning

NASA Astrophysics Data System (ADS)

Bartkiewicz, Karol; Lemr, Karel; Černoch, Antonín; Soubusta, Jan; Miranowicz, Adam

2013-04-01

The security of quantum cryptography is guaranteed by the no-cloning theorem, which implies that an eavesdropper copying transmitted qubits in unknown states causes their disturbance. Nevertheless, in real cryptographic systems some level of disturbance has to be allowed to cover, e.g., transmission losses. An eavesdropper can attack such systems by replacing a noisy channel by a better one and by performing approximate cloning of transmitted qubits which disturb them but below the noise level assumed by legitimate users. We experimentally demonstrate such symmetric individual eavesdropping on the quantum key distribution protocols of Bennett and Brassard (BB84) and the trine-state spherical code of Renes (R04) with two-level probes prepared using a recently developed photonic multifunctional quantum cloner [Lemr et al., Phys. Rev. A 85, 050307(R) (2012)PLRAAN1050-2947]. We demonstrated that our optimal cloning device with high-success rate makes the eavesdropping possible by hiding it in usual transmission losses. We believe that this experiment can stimulate the quest for other operational applications of quantum cloning.

Is a time symmetric interpretation of quantum theory possible without retrocausality?

NASA Astrophysics Data System (ADS)

Leifer, Matthew S.; Pusey, Matthew F.

2017-06-01

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ-mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.

Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states

PubMed Central

Bonet-Luz, Esther

2016-01-01

The dynamics of quantum expectation values is considered in a geometric setting. First, expectation values of the canonical observables are shown to be equivariant momentum maps for the action of the Heisenberg group on quantum states. Then, the Hamiltonian structure of Ehrenfest’s theorem is shown to be Lie–Poisson for a semidirect-product Lie group, named the Ehrenfest group. The underlying Poisson structure produces classical and quantum mechanics as special limit cases. In addition, quantum dynamics is expressed in the frame of the expectation values, in which the latter undergo canonical Hamiltonian motion. In the case of Gaussian states, expectation values dynamics couples to second-order moments, which also enjoy a momentum map structure. Eventually, Gaussian states are shown to possess a Lie–Poisson structure associated with another semidirect-product group, which is called the Jacobi group. This structure produces the energy-conserving variant of a class of Gaussian moment models that have previously appeared in the chemical physics literature. PMID:27279764

Localization in quantum field theory

NASA Astrophysics Data System (ADS)

Balachandran, A. P.

In non-relativistic quantum mechanics, Born’s principle of localization is as follows: For a single particle, if a wave function ψK vanishes outside a spatial region K, it is said to be localized in K. In particular, if a spatial region K‧ is disjoint from K, a wave function ψK‧ localized in K‧ is orthogonal to ψK. Such a principle of localization does not exist compatibly with relativity and causality in quantum field theory (QFT) (Newton and Wigner) or interacting point particles (Currie, Jordan and Sudarshan). It is replaced by symplectic localization of observables as shown by Brunetti, Guido and Longo, Schroer and others. This localization gives a simple derivation of the spin-statistics theorem and the Unruh effect, and shows how to construct quantum fields for anyons and for massless particles with “continuous” spin. This review outlines the basic principles underlying symplectic localization and shows or mentions its deep implications. In particular, it has the potential to affect relativistic quantum information theory and black hole physics.

Symmetry aspects in emergent quantum mechanics

NASA Astrophysics Data System (ADS)

Elze, Hans-Thomas

2009-06-01

We discuss an explicit realization of the dissipative dynamics anticipated in the proof of 't Hooft's existence theorem, which states that 'For any quantum system there exists at least one deterministic model that reproduces all its dynamics after prequantization'. - There is an energy-parity symmetry hidden in the Liouville equation, which mimics the Kaplan-Sundrum protective symmetry for the cosmological constant. This symmetry may be broken by the coarse-graining inherent in physics at scales much larger than the Planck length. We correspondingly modify classical ensemble theory by incorporating dissipative fluctuations (information loss) - which are caused by discrete spacetime continually 'measuring' matter. In this way, aspects of quantum mechanics, such as the von Neumann equation, including a Lindblad term, arise dynamically and expectations of observables agree with the Born rule. However, the resulting quantum coherence is accompanied by an intrinsic decoherence and continuous localization mechanism. Our proposal leads towards a theory that is linear and local at the quantum mechanical level, but the relation to the underlying classical degrees of freedom is nonlocal.

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

Mouchet, Amaury, E-mail: mouchet@phys.univ-tours.fr

The Noether theorem connecting symmetries and conservation laws can be applied directly in a Hamiltonian framework without using any intermediate Lagrangian formulation. This requires a careful discussion about the invariance of the boundary conditions under a canonical transformation and this paper proposes to address this issue. Then, the unified treatment of Hamiltonian systems offered by Noether’s approach is illustrated on several examples, including classical field theory and quantum dynamics.

Multifield Galileons and higher codimension branes

DOE PAGES

Hinterbichler, Kurt; Trodden, Mark; Wesley, Daniel

2010-12-07

We studied a multi-field generalizations of the galileon - a popular idea of how to modify gravity to account for the acceleration of the universe. We derived an extremely restrictive theory of multiple galileon fields, and explored some properties of this theory, including proving a general non-renormalization theorem: multi-field galileons are not renormalized quantum mechanically to any loop in perturbation theory.

Physical scales in the Wigner-Boltzmann equation

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

Nedjalkov, M., E-mail: mixi@iue.tuwien.ac.at; Selberherr, S.; Ferry, D.K.

2013-01-15

The Wigner-Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner-Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. Itmore » is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner-Boltzmann evolution is demonstrated. - Highlights: Black-Right-Pointing-Pointer Dimensionless parameters determine the ratio of quantum or classical WB evolution. Black-Right-Pointing-Pointer The scaling theorem evaluates the decoherence effect due to scattering. Black-Right-Pointing-Pointer Evolution processes are grouped into classes of equivalence.« less

Generalized energy measurements and modified transient quantum fluctuation theorems

NASA Astrophysics Data System (ADS)

Watanabe, Gentaro; Venkatesh, B. Prasanna; Talkner, Peter

2014-05-01

Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

NASA Astrophysics Data System (ADS)

Andreoli, Francesco; Carvacho, Gonzalo; Santodonato, Luca; Chaves, Rafael; Sciarrino, Fabio

2017-11-01

Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n-locality scenario consisting of n two-qubit quantum states distributed among n+1 nodes of a star-shaped network.

Noncommutative Geometry of the Moyal Plane: Translation Isometries, Connes' Distance on Coherent States, Pythagoras Equality

NASA Astrophysics Data System (ADS)

Martinetti, Pierre; Tomassini, Luca

2013-10-01

We study the metric aspect of the Moyal plane from Connes' noncommutative geometry point of view. First, we compute Connes' spectral distance associated with the natural isometric action of on the algebra of the Moyal plane . We show that the distance between any state of and any of its translated states is precisely the amplitude of the translation. As a consequence, we obtain the spectral distance between coherent states of the quantum harmonic oscillator as the Euclidean distance on the plane. We investigate the classical limit, showing that the set of coherent states equipped with Connes' spectral distance tends towards the Euclidean plane as the parameter of deformation goes to zero. The extension of these results to the action of the symplectic group is also discussed, with particular emphasis on the orbits of coherent states under rotations. Second, we compute the spectral distance in the double Moyal plane, intended as the product of (the minimal unitization of) by . We show that on the set of states obtained by translation of an arbitrary state of , this distance is given by the Pythagoras theorem. On the way, we prove some Pythagoras inequalities for the product of arbitrary unital and non-degenerate spectral triples. Applied to the Doplicher- Fredenhagen-Roberts model of quantum spacetime [DFR], these two theorems show that Connes' spectral distance and the DFR quantum length coincide on the set of states of optimal localization.

Quantum mechanics problems in observer's mathematics

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

Khots, Boris; Khots, Dmitriy; iMath Consulting LLC, Omaha, Nebraska

2012-11-06

This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, andmore » {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.« less

Environment-induced decoherence II. Effect of decoherence on Bell's inequality for an EPR pair

NASA Astrophysics Data System (ADS)

Venugopalan, A.; Kumar, Deepak; Ghosh, R.

1995-02-01

According to Bell's theorem, the degree of correlation between spatially separated measurements on a quantum system is limited by certain inequalities if one assumes the condition of locality. Quantum mechanics predicts that this limit can be exceeded, making it nonlocal. We analyse the effect of an environment modelled by a fluctuating magnetic field on the quantum correlations in an EPR singlet as seen in the Bell inequality. We show that in an EPR setup, the system goes from the usual ‘violation’ of Bell's inequality to a ‘non-violation’ for times larger than a characteristic time scale which is related to the parameters of the fluctuating field. We also look at these inequalities as a function of the spatial separation between the EPR pair.

Implications of causality for quantum biology - I: topology change

NASA Astrophysics Data System (ADS)

Scofield, D. F.; Collins, T. C.

2018-06-01

A framework for describing the causal, topology changing, evolution of interacting biomolecules is developed. The quantum dynamical manifold equations (QDMEs) derived from this framework can be related to the causality restrictions implied by a finite speed of light and to Planck's constant to set a transition frequency scale. The QDMEs imply conserved stress-energy, angular-momentum and Noether currents. The functional whose extremisation leads to this result provides a causal, time-dependent, non-equilibrium generalisation of the Hohenberg-Kohn theorem. The system of dynamical equations derived from this functional and the currents J derived from the QDMEs are shown to be causal and consistent with the first and second laws of thermodynamics. This has the potential of allowing living systems to be quantum mechanically distinguished from non-living ones.

Quantum Max-flow/Min-cut

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

Cui, Shawn X., E-mail: xingshan@math.ucsb.edu; Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052; Freedman, Michael H., E-mail: michaelf@microsoft.com

2016-06-15

The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts ofmore » the tensor network. We show that unlike the classical case, the quantum max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.« less

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

Bradler, Kamil; Hayden, Patrick; Touchette, Dave

Coding theorems in quantum Shannon theory express the ultimate rates at which a sender can transmit information over a noisy quantum channel. More often than not, the known formulas expressing these transmission rates are intractable, requiring an optimization over an infinite number of uses of the channel. Researchers have rarely found quantum channels with a tractable classical or quantum capacity, but when such a finding occurs, it demonstrates a complete understanding of that channel's capabilities for transmitting classical or quantum information. Here we show that the three-dimensional capacity region for entanglement-assisted transmission of classical and quantum information is tractable formore » the Hadamard class of channels. Examples of Hadamard channels include generalized dephasing channels, cloning channels, and the Unruh channel. The generalized dephasing channels and the cloning channels are natural processes that occur in quantum systems through the loss of quantum coherence or stimulated emission, respectively. The Unruh channel is a noisy process that occurs in relativistic quantum information theory as a result of the Unruh effect and bears a strong relationship to the cloning channels. We give exact formulas for the entanglement-assisted classical and quantum communication capacity regions of these channels. The coding strategy for each of these examples is superior to a naieve time-sharing strategy, and we introduce a measure to determine this improvement.« less

Localized magnetoplasmons in quantum dots: Magneto-optical absorption, Raman scattering, and inelastic electron scattering

NASA Astrophysics Data System (ADS)

Kushwaha, M. S.

We investigate a one-component, quasi-zero dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de-Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron-energy-loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron-energy-loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in such diverse fields as quantum computing and medical imaging.

Glueball spectrum and hadronic processes in low-energy QCD

NASA Astrophysics Data System (ADS)

Frasca, Marco

2010-10-01

Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the σ and η-η mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant Λ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.

Remnants, fuzzballs or wormholes?

NASA Astrophysics Data System (ADS)

Mathur, Samir D.

2014-11-01

The black hole information paradox has caused enormous confusion over four decades. But in recent years, the theorem of quantum strong-subadditivity has sorted out the possible resolutions into three sharp categories: (i) No new physics at r ≫ lp; this necessarily implies remnants/information loss. A realization of remnants is given by a baby universe attached near r 0. (ii) Violation of the "no-hair" theorem by nontrivial effects at the horizon r M. This possibility is realized by fuzzballs in string theory, and gives unitary evaporation. (iii) Having the vacuum at the horizon, but requiring that Hawking quanta at r M3 be somehow identified with degrees of freedom inside the black hole. A model for this "extreme nonlocality" is realized by conjecturing that wormholes connect the radiation quanta to the hole.

Bound states for magic state distillation in fault-tolerant quantum computation.

PubMed

Campbell, Earl T; Browne, Dan E

2010-01-22

Magic state distillation is an important primitive in fault-tolerant quantum computation. The magic states are pure nonstabilizer states which can be distilled from certain mixed nonstabilizer states via Clifford group operations alone. Because of the Gottesman-Knill theorem, mixtures of Pauli eigenstates are not expected to be magic state distillable, but it has been an open question whether all mixed states outside this set may be distilled. In this Letter we show that, when resources are finitely limited, nondistillable states exist outside the stabilizer octahedron. In analogy with the bound entangled states, which arise in entanglement theory, we call such states bound states for magic state distillation.

Thermodynamics of energy, charge, and spin currents in a thermoelectric quantum-dot spin valve

NASA Astrophysics Data System (ADS)

Tang, Gaomin; Thingna, Juzar; Wang, Jian

2018-04-01

We provide a thermodynamically consistent description of energy, charge, and spin transfers in a thermoelectric quantum-dot spin valve in the collinear configuration based on nonequilibrium Green's function and full counting statistics. We use the fluctuation theorem symmetry and the concept of entropy production to characterize the efficiency with which thermal gradients can transduce charges or spins against their chemical potentials, arbitrary far from equilibrium. Close to equilibrium, we recover the Onsager reciprocal relations and the connection to linear response notions of performance such as the figure of merit. We also identify regimes where work extraction is more efficient far then close from equilibrium.

Superradiant Decay of Cyclotron Resonance of Two-Dimensional Electron Gases

NASA Astrophysics Data System (ADS)

Zhang, Qi; Arikawa, Takashi; Kato, Eiji; Reno, John L.; Pan, Wei; Watson, John D.; Manfra, Michael J.; Zudov, Michael A.; Tokman, Mikhail; Erukhimova, Maria; Belyanin, Alexey; Kono, Junichiro

2014-07-01

We report on the observation of collective radiative decay, or superradiance, of cyclotron resonance (CR) in high-mobility two-dimensional electron gases in GaAs quantum wells using time-domain terahertz magnetospectroscopy. The decay rate of coherent CR oscillations increases linearly with the electron density in a wide range, which is a hallmark of superradiant damping. Our fully quantum mechanical theory provides a universal formula for the decay rate, which reproduces our experimental data without any adjustable parameter. These results firmly establish the many-body nature of CR decoherence in this system, despite the fact that the CR frequency is immune to electron-electron interactions due to Kohn's theorem.

Thermodynamics and statistical mechanics. [thermodynamic properties of gases

NASA Technical Reports Server (NTRS)

1976-01-01

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

A quantum diffusion law

NASA Astrophysics Data System (ADS)

Satpathi, Urbashi; Sinha, Supurna; Sorkin, Rafael D.

2017-12-01

We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t) . The resulting diffusion-law exhibits several distinct regimes of time and temperature, each with its own characteristic rate of spreading. As with earlier analyses, we find logarithmic spreading in the quantum regime, indicating that this behavior is robust. A consistent R(t) must satisfy the key physical requirements of Wightman positivity and passivity, and we prove that ours does so. We also prove in general that these two conditions are equivalent when the FDT holds. Given current technology, our diffusion law can be tested in a laboratory with ultra cold atoms.

Fluctuation-dissipation theorem in an isolated system of quantum dipolar bosons after a quench.

PubMed

Khatami, Ehsan; Pupillo, Guido; Srednicki, Mark; Rigol, Marcos

2013-08-02

We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find indications that fluctuation-dissipation relations hold if the system is nonintegrable after the quench, as well as if it is integrable after the quench if the initial state is an equilibrium state of a nonintegrable Hamiltonian. On the other hand, we find indications that they fail if the system is integrable both before and after quenching.

Quantum Locality?

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

Stapp, Henry

Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ (CQT) that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues, on the basis of his examination of certain arguments that claim to demonstrate the existence of such nonlocal influences, that such influences do not exist. However, his examination was restricted mainly to hidden-variable-based arguments that include in their premises some essentially classical-physics-type assumptions that are fundamentally incompatible with the precepts of quantum physics. One cannot logically prove properties ofmore » a system by attributing to the system properties alien to that system. Hence Griffiths’ rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive framework. This necessary existence, within the ‘consistent’ framework, of long range essentially instantaneous influences refutes the claim made by Griffiths that his ‘consistent’ framework is superior to the orthodox quantum theory of von Neumann because it does not entail instantaneous influences. An added section responds to Griffiths’ reply, which cites a litany of ambiguities that seem to restrict, devastatingly, the scope of his CQT formalism, apparently to buttress his claim that my use of that formalism to validate the nonlocality theorem is flawed. But the vagaries that he cites do not upset the proof in question. It is show here in detail why the precise statement of this theorem justifies the specified application of CQT. It is also shown, in response to his challenge, why a putative proof of locality that he has proposed is not valid.« less

Deriving robust noncontextuality inequalities from algebraic proofs of the Kochen-Specker theorem: the Peres-Mermin square

NASA Astrophysics Data System (ADS)

Krishna, Anirudh; Spekkens, Robert W.; Wolfe, Elie

2017-12-01

When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that satisfy a particular assumption of context-independence: that sharp measurements are assigned outcomes both deterministically and independently of their context. This notion of noncontextuality is not suited to a direct experimental test because realistic measurements always have some degree of unsharpness due to noise. However, a generalized notion of noncontextuality has been proposed that is applicable to any experimental procedure, including unsharp measurements, but also preparations as well, and for which a quantum no-go result still holds. According to this notion, the model need only specify a probability distribution over the outcomes of a measurement in a context-independent way, rather than specifying a particular outcome. It also implies novel constraints of context-independence for the representation of preparations. In this article, we describe a general technique for translating proofs of the Kochen-Specker theorem into inequality constraints on realistic experimental statistics, the violation of which witnesses the impossibility of a noncontextual model. We focus on algebraic state-independent proofs, using the Peres-Mermin square as our illustrative example. Our technique yields the necessary and sufficient conditions for a particular set of correlations (between the preparations and the measurements) to admit a noncontextual model. The inequalities thus derived are demonstrably robust to noise. We specify how experimental data must be processed in order to achieve a test of these inequalities. We also provide a criticism of prior proposals for experimental tests of noncontextuality based on the Peres-Mermin square.

On the conservation laws of Derrida-Lebowitz-Speer-Spohn equation

NASA Astrophysics Data System (ADS)

San, Sait; Yaşar, Emrullah

2015-05-01

In this study, the nonlocal conservation theorem and multiplier approach are performed on the 1 + 1 dimensional Derrida-Lebowitz-Speer-Spohn (DLSS) equation which arises in quantum semi conductor theory. We obtain local conservation laws by using the both methods. Furthermore by utilizing the relationship between conservation laws and Lie point symmetries, the DLSS equation is reduced to third order ordinary differential equation.

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

Cabello, Adan

We introduce two two-player quantum pseudotelepathy games based on two recently proposed all-versus-nothing (AVN) proofs of Bell's theorem [A. Cabello, Phys. Rev. Lett. 95, 210401 (2005); Phys. Rev. A 72, 050101(R) (2005)]. These games prove that Broadbent and Methot's claim that these AVN proofs do not rule out local-hidden-variable theories in which it is possible to exchange unlimited information inside the same light cone (quant-ph/0511047) is incorrect.

Locality and simultaneous elements of reality

NASA Astrophysics Data System (ADS)

Nisticò, G.; Sestito, A.

2012-12-01

We show that the extension of quantum correlations stemming from a "strict" interpretation of the criterion of reality raises the failure of Hardy's non-locality theorem. Then, by suggesting an ideal experiment, we prove that such an extension, though strictly smaller than the one derived by Einstein, Podolsky and Rosen and usually adopted, allows for the assignment of simultaneous objective values of two non-commuting observables.

Hybrid Techniques for Quantum Circuit Simulation

DTIC Science & Technology

2014-02-01

Detailed theorems and proofs describing these results are included in our published manuscript [10]. Embedding of stabilizer geometry in the Hilbert ...space. We also describe how the discrete embedding of stabilizer geometry in Hilbert space complicates several natural geometric tasks. As described...the Hilbert space in which they are embedded, and that they are arranged in a fairly uniform pattern. These factors suggest that, if one seeks a

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

Zero Thermal Noise in Resistors at Zero Temperature

NASA Astrophysics Data System (ADS)

Kish, Laszlo B.; Niklasson, Gunnar A.; Granqvist, Claes-Göran

2016-06-01

The bandwidth of transistors in logic devices approaches the quantum limit, where Johnson noise and associated error rates are supposed to be strongly enhanced. However, the related theory — asserting a temperature-independent quantum zero-point (ZP) contribution to Johnson noise, which dominates the quantum regime — is controversial and resolution of the controversy is essential to determine the real error rate and fundamental energy dissipation limits of logic gates in the quantum limit. The Callen-Welton formula (fluctuation-dissipation theorem) of voltage and current noise for a resistance is the sum of Nyquist’s classical Johnson noise equation and a quantum ZP term with a power density spectrum proportional to frequency and independent of temperature. The classical Johnson-Nyquist formula vanishes at the approach of zero temperature, but the quantum ZP term still predicts non-zero noise voltage and current. Here, we show that this noise cannot be reconciled with the Fermi-Dirac distribution, which defines the thermodynamics of electrons according to quantum-statistical physics. Consequently, Johnson noise must be nil at zero temperature, and non-zero noise found for certain experimental arrangements may be a measurement artifact, such as the one mentioned in Kleen’s uncertainty relation argument.

Discrete symmetries and the propagator approach to coupled fermions in Quantum Field Theory. Generalities: The case of a single fermion-antifermion pair

NASA Astrophysics Data System (ADS)

Duret, Q.; Machet, B.

2010-10-01

Starting from Wigner's symmetry representation theorem, we give a general account of discrete symmetries (parity P, charge conjugation C, time-reversal T), focusing on fermions in Quantum Field Theory. We provide the rules of transformation of Weyl spinors, both at the classical level (grassmanian wave functions) and quantum level (operators). Making use of Wightman's definition of invariance, we outline ambiguities linked to the notion of classical fermionic Lagrangian. We then present the general constraints cast by these transformations and their products on the propagator of the simplest among coupled fermionic system, the one made with one fermion and its antifermion. Last, we put in correspondence the propagation of C eigenstates (Majorana fermions) and the criteria cast on their propagator by C and CP invariance.

Colloquium: The Einstein-Podolsky-Rosen paradox: From concepts to applications

NASA Astrophysics Data System (ADS)

Reid, M. D.; Drummond, P. D.; Bowen, W. P.; Cavalcanti, E. G.; Lam, P. K.; Bachor, H. A.; Andersen, U. L.; Leuchs, G.

2009-10-01

This Colloquium examines the field of the Einstein, Podolsky, and Rosen (EPR) gedanken experiment, from the original paper of Einstein, Podolsky, and Rosen, through to modern theoretical proposals of how to realize both the continuous-variable and discrete versions of the EPR paradox. The relationship with entanglement and Bell’s theorem are analyzed, and the progress to date towards experimental confirmation of the EPR paradox is summarized, with a detailed treatment of the continuous-variable paradox in laser-based experiments. Practical techniques covered include continuous-wave parametric amplifier and optical fiber quantum soliton experiments. Current proposals for extending EPR experiments to massive-particle systems are discussed, including spin squeezing, atomic position entanglement, and quadrature entanglement in ultracold atoms. Finally, applications of this technology to quantum key distribution, quantum teleportation, and entanglement swapping are examined.

Locality, reflection, and wave-particle duality

NASA Astrophysics Data System (ADS)

Mugur-Schächter, Mioara

1987-08-01

Bell's theorem is believed to establish that the quantum mechanical predictions do not generally admit a causal representation compatible with Einsten's principle of separability, thereby proving incompatibility between quantum mechanics and relativity. This interpretation is contested via two convergent approaches which lead to a sharp distinction between quantum nonseparability and violation of Einstein's theory of relativity. In a first approach we explicate from the quantum mechanical formalism a concept of “reflected dependence.” Founded on this concept, we produce a causal representation of the quantum mechanical probability measure involved in Bell's proof, which is clearly separable in Einstein's sense, i.e., it does not involve supraluminal velocities, and nevertheless is “nonlocal” in Bell's sense. So Bell locality and Einstein separability are distinct qualifications, and Bell nonlocality (or Bell nonseparability) and Einstein separability are not incompatible. It is then proved explicitly that with respect to the mentioned representation Bell's derivation does not hold. So Bell's derivation does not establish that any Einstein-separable representation is incompatible with quantum mechanics. This first—negative—conclusion is a syntactic fact. The characteristics of the representation and of the reasoning involved in the mentioned counterexample to the usual interpretation of Bell's theorem suggest that the representation used—notwithstanding its ability to bring forth the specified syntactic fact—is not factually true. Factual truth and syntactic properties also have to be radically distinguished in their turn. So, in a second approach, starting from de Broglie's initial relativistic model of a microsystem, a deeper, factually acceptable representation is constructed. The analyses leading to this second representation show that quantum mechanics does indeed involve basically a certain sort of nonseparability, called here de Broglie-Bohr quantum nonseparability. But the de Broglie-Bohr quantum nonseparability is shown to stem directly from the relativistic character of the considerations which led Louis de Broglie to the fundamental relation p = h/λ, thereby being essentially consistent with relativity. As to Einstein separability, it appears to be a still insufficiently specified concept of which a future, improved specification, will probably be explicitly harmonizable with the de Broglie-Bohr quantum nonseparability. The ensemble of the conclusions obtained here brings forth a new concept of causality, a concept of folded, zigzag, reflexive causality, with respect to which the type of causality conceived of up to now appears as a particular case of outstretched, one-way causality. The reflexive causality is found compatible with the results of Aspect's experiment, and it suggests new experiments. Considered globally, the conclusions obtained in the present work might convert the conceptual situation created by Bell's proof into a process of unification of quantum mechanics and relativity.

Quantum Hamiltonian daemons: Unitary analogs of combustion engines

NASA Astrophysics Data System (ADS)

Thesing, Eike P.; Gilz, Lukas; Anglin, James R.

2017-07-01

Hamiltonian daemons have recently been defined classically as small, closed Hamiltonian systems which can exhibit secular energy transfer from high-frequency to low-frequency degrees of freedom (steady downconversion), analogous to the steady transfer of energy in a combustion engine from the high terahertz frequencies of molecular excitations to the low kilohertz frequencies of piston motion [L. Gilz, E. P. Thesing, and J. R. Anglin, Phys. Rev. E 94, 042127 (2016), 10.1103/PhysRevE.94.042127]. Classical daemons achieve downconversion within a small, closed system by exploiting nonlinear resonances; the adiabatic theorem permits their operation but imposes nontrivial limitations on their efficiency. Here we investigate a simple example of a quantum mechanical daemon. In the correspondence regime it obeys similar efficiency limits to its classical counterparts, but in the strongly quantum mechanical regime the daemon operates in an entirely different manner. It maintains an engine-like behavior in a distinctly quantum mechanical form: a weight is lifted at a steady average speed through a long sequence of quantum jumps in momentum, at each of which a quantum of fuel is consumed. The quantum daemon can cease downconversion at any time through nonadiabatic Landau-Zener transitions, and continuing operation of the quantum daemon is associated with steadily growing entanglement between fast and slow degrees of freedom.

On the quantum Landau collision operator and electron collisions in dense plasmas

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

Daligault, Jérôme, E-mail: daligaul@lanl.gov

2016-03-15

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck formmore » of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.« less

On the quantum Landau collision operator and electron collisions in dense plasmas

NASA Astrophysics Data System (ADS)

Daligault, Jérôme

2016-03-01

The quantum Landau collision operator, which extends the widely used Landau/Fokker-Planck collision operator to include quantum statistical effects, is discussed. The quantum extension can serve as a reference model for including electron collisions in non-equilibrium dense plasmas, in which the quantum nature of electrons cannot be neglected. In this paper, the properties of the Landau collision operator that have been useful in traditional plasma kinetic theory and plasma transport theory are extended to the quantum case. We outline basic properties in connection with the conservation laws, the H-theorem, and the global and local equilibrium distributions. We discuss the Fokker-Planck form of the operator in terms of three potentials that extend the usual two Rosenbluth potentials. We establish practical closed-form expressions for these potentials under local thermal equilibrium conditions in terms of Fermi-Dirac and Bose-Einstein integrals. We study the properties of linearized quantum Landau operator, and extend two popular approximations used in plasma physics to include collisions in kinetic simulations. We apply the quantum Landau operator to the classic test-particle problem to illustrate the physical effects embodied in the quantum extension. We present useful closed-form expressions for the electron-ion momentum and energy transfer rates. Throughout the paper, similarities and differences between the quantum and classical Landau collision operators are emphasized.

Light for the quantum. Entangled photons and their applications: a very personal perspective

NASA Astrophysics Data System (ADS)

Zeilinger, Anton

2017-07-01

The quantum physics of light is a most fascinating field. Here I present a very personal viewpoint, focusing on my own path to quantum entanglement and then on to applications. I have been fascinated by quantum physics ever since I heard about it for the first time in school. The theory struck me immediately for two reasons: (1) its immense mathematical beauty, and (2) the unparalleled precision to which its predictions have been verified again and again. Particularly fascinating for me were the predictions of quantum mechanics for individual particles, individual quantum systems. Surprisingly, the experimental realization of many of these fundamental phenomena has led to novel ideas for applications. Starting from my early experiments with neutrons, I later became interested in quantum entanglement, initially focusing on multi-particle entanglement like GHZ states. This work opened the experimental possibility to do quantum teleportation and quantum hyper-dense coding. The latter became the first entanglement-based quantum experiment breaking a classical limitation. One of the most fascinating phenomena is entanglement swapping, the teleportation of an entangled state. This phenomenon is fundamentally interesting because it can entangle two pairs of particles which do not share any common past. Surprisingly, it also became an important ingredient in a number of applications, including quantum repeaters which will connect future quantum computers with each other. Another application is entanglement-based quantum cryptography where I present some recent long-distance experiments. Entanglement swapping has also been applied in very recent so-called loophole-free tests of Bell’s theorem. Within the physics community such loophole-free experiments are perceived as providing nearly definitive proof that local realism is untenable. While, out of principle, local realism can never be excluded entirely, the 2015 achievements narrow down the remaining possibilities for local realistic explanations of the quantum phenomenon of entanglement in a significant way. These experiments may go down in the history books of science. Future experiments will address particularly the freedom-of-choice loophole using cosmic sources of randomness. Such experiments confirm that unconditionally secure quantum cryptography is possible, since quantum cryptography based on Bell’s theorem can provide unconditional security. The fact that the experiments were loophole-free proves that an eavesdropper cannot avoid detection in an experiment that correctly follows the protocol. I finally discuss some recent experiments with single- and entangled-photon states in higher dimensions. Such experiments realized quantum entanglement between two photons, each with quantum numbers beyond 10 000 and also simultaneous entanglement of two photons where each carries more than 100 dimensions. Thus they offer the possibility of quantum communication with more than one bit or qubit per photon. The paper concludes discussing Einstein’s contributions and viewpoints of quantum mechanics. Even if some of his positions are not supported by recent experiments, he has to be given credit for the fact that his analysis of fundamental issues gave rise to developments which led to a new information technology. Finally, I reflect on some of the lessons learned by the fact that nature cannot be local, that objective randomness exists and about the emergence of a classical world. It is suggestive that information plays a fundamental role also in the foundations of quantum physics.

The World According to de Finetti: On de Finetti's Theory of Probability and Its Application to Quantum Mechanics

NASA Astrophysics Data System (ADS)

Berkovitz, Joseph

Bruno de Finetti is one of the founding fathers of the subjectivist school of probability, where probabilities are interpreted as rational degrees of belief. His work on the relation between the theorems of probability and rationality is among the corner stones of modern subjective probability theory. De Finetti maintained that rationality requires that degrees of belief be coherent, and he argued that the whole of probability theory could be derived from these coherence conditions. De Finetti's interpretation of probability has been highly influential in science. This paper focuses on the application of this interpretation to quantum mechanics. We argue that de Finetti held that the coherence conditions of degrees of belief in events depend on their verifiability. Accordingly, the standard coherence conditions of degrees of belief that are familiar from the literature on subjective probability only apply to degrees of belief in events which could (in principle) be jointly verified; and the coherence conditions of degrees of belief in events that cannot be jointly verified are weaker. While the most obvious explanation of de Finetti's verificationism is the influence of positivism, we argue that it could be motivated by the radical subjectivist and instrumental nature of probability in his interpretation; for as it turns out, in this interpretation it is difficult to make sense of the idea of coherent degrees of belief in, and accordingly probabilities of unverifiable events. We then consider the application of this interpretation to quantum mechanics, concentrating on the Einstein-Podolsky-Rosen experiment and Bell's theorem.

Is a time symmetric interpretation of quantum theory possible without retrocausality?

PubMed Central

Pusey, Matthew F.

2017-01-01

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ-mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology. PMID:28690401

Noise resistance of the violation of local causality for pure three-qutrit entangled states

NASA Astrophysics Data System (ADS)

Laskowski, Wiesław; Ryu, Junghee; Żukowski, Marek

2014-10-01

Bell's theorem started with two qubits (spins 1/2). It is a ‘no-go’ statement on classical (local causal) models of quantum correlations. After 25 years, it turned out that for three qubits the situation is even more astonishing. General statements concerning higher dimensional systems, qutrits, etc, started to appear even later, once the picture with spin (higher than 1/2) was replaced by a broader one, allowing all possible observables. This work is a continuation of the Gdansk effort to take advantage of the fact that Bell's theorem can be put in the form of a linear programming problem, which in turn can be translated into a computer code. Our results are numerical and classify the strength of the violation of local causality by various families of three-qutrit states, as measured by the resistance to noise. This is previously uncharted territory. The results may be helpful in suggesting which three-qutrit states will be handy for applications in quantum information protocols. One of the surprises is that the W state turns out to reveal a stronger violation of local causality than the GHZ (Greenberger-Horne-Zeilinger) state. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell's theorem’.

A nodal domain theorem for integrable billiards in two dimensions

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

Samajdar, Rhine; Jain, Sudhir R., E-mail: srjain@barc.gov.in

Eigenfunctions of integrable planar billiards are studied — in particular, the number of nodal domains, ν of the eigenfunctions with Dirichlet boundary conditions are considered. The billiards for which the time-independent Schrödinger equation (Helmholtz equation) is separable admit trivial expressions for the number of domains. Here, we discover that for all separable and non-separable integrable billiards, ν satisfies certain difference equations. This has been possible because the eigenfunctions can be classified in families labelled by the same value of mmodkn, given a particular k, for a set of quantum numbers, m,n. Further, we observe that the patterns in a familymore » are similar and the algebraic representation of the geometrical nodal patterns is found. Instances of this representation are explained in detail to understand the beauty of the patterns. This paper therefore presents a mathematical connection between integrable systems and difference equations. - Highlights: • We find that the number of nodal domains of eigenfunctions of integrable, planar billiards satisfy a class of difference equations. • The eigenfunctions labelled by quantum numbers (m,n) can be classified in terms of mmodkn. • A theorem is presented, realising algebraic representations of geometrical patterns exhibited by the domains. • This work presents a connection between integrable systems and difference equations.« less

Zeno Meets Modern Science

NASA Astrophysics Data System (ADS)

Silagadze, Z. K.

2005-10-01

``No one has ever touched Zeno without refuting him''. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his famous paradoxes of motion. Reflections on continuity of space and time lead us to Banach and Tarski and to their celebrated paradox, which is in fact not a paradox at all but a strict mathematical theorem, although very counterintuitive. Quantum mechanics brings another flavour in Zeno paradoxes. Quantum Zeno and anti-Zeno effects are really paradoxical but now experimental facts. Then we discuss supertasks and bifurcated supertasks. The concept of localisation leads us to Newton and Wigner and to interesting phenomenon of quantum revivals. At last we note that the paradoxical idea of timeless universe, defended by Zeno and Parmenides at ancient times, is still alive in quantum gravity. The list of references that follows is necessarily incomplete but we hope it will assist interested reader to fill in details.

Distinguishability of generic quantum states

NASA Astrophysics Data System (ADS)

Puchała, Zbigniew; Pawela, Łukasz; Życzkowski, Karol

2016-06-01

Properties of random mixed states of dimension N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N , due to the concentration of measure, the trace distance between two random states tends to a fixed number D ˜=1 /4 +1 /π , which yields the Helstrom bound on their distinguishability. To arrive at this result, we apply free random calculus and derive the symmetrized Marchenko-Pastur distribution, which is shown to describe numerical data for the model of coupled quantum kicked tops. Asymptotic value for the root fidelity between two random states, √{F }=3/4 , can serve as a universal reference value for further theoretical and experimental studies. Analogous results for quantum relative entropy and Chernoff quantity provide other bounds on the distinguishablity of both states in a multiple measurement setup due to the quantum Sanov theorem. We study also mean entropy of coherence of random pure and mixed states and entanglement of a generic mixed state of a bipartite system.

Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices

NASA Astrophysics Data System (ADS)

Tabia, Gelo Noel M.

2012-12-01

It is crucial for various quantum information processing tasks that the state of a quantum system can be determined reliably and efficiently from general quantum measurements. One important class of measurements for this purpose is symmetric informationally complete positive operator-valued measurements (SIC-POVMs). SIC-POVMs have the advantage of providing an unbiased estimator for the quantum state with the minimal number of outcomes needed for full tomography. By virtue of Naimark's dilation theorem, any POVM can always be realized with a suitable coupling between the system and an auxiliary system and by performing a projective measurement on the joint system. In practice, finding the appropriate coupling is rather nontrivial. Here we propose an experimental design for directly implementing SIC-POVMs using multiport devices and path-encoded qubits and qutrits, the utility of which has recently been demonstrated by several experimental groups around the world. Furthermore, we describe how these multiports can be attained in practice with an integrated photonic system composed of nested linear optical elements.

Generalized Entanglement Entropies of Quantum Designs.

PubMed

Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao; Zhu, Huangjun

2018-03-30

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.

Positive Wigner functions render classical simulation of quantum computation efficient.

PubMed

Mari, A; Eisert, J

2012-12-07

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

Generalized Entanglement Entropies of Quantum Designs

NASA Astrophysics Data System (ADS)

Liu, Zi-Wen; Lloyd, Seth; Zhu, Elton Yechao; Zhu, Huangjun

2018-03-01

The entanglement properties of random quantum states or dynamics are important to the study of a broad spectrum of disciplines of physics, ranging from quantum information to high energy and many-body physics. This Letter investigates the interplay between the degrees of entanglement and randomness in pure states and unitary channels. We reveal strong connections between designs (distributions of states or unitaries that match certain moments of the uniform Haar measure) and generalized entropies (entropic functions that depend on certain powers of the density operator), by showing that Rényi entanglement entropies averaged over designs of the same order are almost maximal. This strengthens the celebrated Page's theorem. Moreover, we find that designs of an order that is logarithmic in the dimension maximize all Rényi entanglement entropies and so are completely random in terms of the entanglement spectrum. Our results relate the behaviors of Rényi entanglement entropies to the complexity of scrambling and quantum chaos in terms of the degree of randomness, and suggest a generalization of the fast scrambling conjecture.

Black hole firewalls require huge energy of measurement

NASA Astrophysics Data System (ADS)

Hotta, Masahiro; Matsumoto, Jiro; Funo, Ken

2014-06-01

The unitary moving mirror model is one of the best quantum systems for checking the reasoning of the original firewall paradox of Almheiri et al. [J. High Energy Phys. 02 (2013) 062] in quantum black holes. Though the late-time part of radiations emitted from the mirror is fully entangled with the early part, no firewall exists with a deadly, huge average energy flux in this model. This is because the high-energy entanglement structure of the discretized systems in almost maximally entangled states is modified so as to yield the correct description of low-energy effective field theory. Furthermore, the strong subadditivity paradox of firewalls is resolved using nonlocality of general one-particle states and zero-point fluctuation entanglement. Due to the Reeh-Schlieder theorem in quantum field theory, another firewall paradox is inevitably raised with quantum remote measurements in the model. We resolve this paradox from the viewpoint of the energy cost of measurements. No firewall appears, as long as the energy for the measurement is much smaller than the ultraviolet cutoff scale.

Statistical quasi-particle theory for open quantum systems

NASA Astrophysics Data System (ADS)

Zhang, Hou-Dao; Xu, Rui-Xue; Zheng, Xiao; Yan, YiJing

2018-04-01

This paper presents a comprehensive account on the recently developed dissipaton-equation-of-motion (DEOM) theory. This is a statistical quasi-particle theory for quantum dissipative dynamics. It accurately describes the influence of bulk environments, with a few number of quasi-particles, the dissipatons. The novel dissipaton algebra is then followed, which readily bridges the Schrödinger equation to the DEOM theory. As a fundamental theory of quantum mechanics in open systems, DEOM characterizes both the stationary and dynamic properties of system-and-bath interferences. It treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that could be experimentally measurable. Examples are the linear or nonlinear Fano interferences and the Herzberg-Teller vibronic couplings in optical spectroscopies. This review covers the DEOM construction, the underlying dissipaton algebra and theorems, the physical meanings of dynamical variables, the possible identifications of dissipatons, and some recent advancements in efficient DEOM evaluations on various problems. The relations of the present theory to other nonperturbative methods are also critically presented.

On Schrödinger's bridge problem

NASA Astrophysics Data System (ADS)

Friedland, S.

2017-11-01

In the first part of this paper we generalize Georgiou-Pavon's result that a positive square matrix can be scaled uniquely to a column stochastic matrix which maps a given positive probability vector to another given positive probability vector. In the second part we prove that a positive quantum channel can be scaled to another positive quantum channel which maps a given positive definite density matrix to another given positive definite density matrix using Brouwer's fixed point theorem. This result proves the Georgiou-Pavon conjecture for two positive definite density matrices, made in their recent paper. We show that the fixed points are unique for certain pairs of positive definite density matrices. Bibliography: 15 titles.

Statistics of work performed on a forced quantum oscillator.

PubMed

Talkner, Peter; Burada, P Sekhar; Hänggi, Peter

2008-07-01

Various aspects of the statistics of work performed by an external classical force on a quantum mechanical system are elucidated for a driven harmonic oscillator. In this special case two parameters are introduced that are sufficient to completely characterize the force protocol. Explicit results for the characteristic function of work and the corresponding probability distribution are provided and discussed for three different types of initial states of the oscillator: microcanonical, canonical, and coherent states. Depending on the choice of the initial state the probability distributions of the performed work may greatly differ. This result in particular also holds true for identical force protocols. General fluctuation and work theorems holding for microcanonical and canonical initial states are confirmed.

A new quantum sealed-bid auction protocol with secret order in post-confirmation

NASA Astrophysics Data System (ADS)

Wang, Jing-Tao; Chen, Xiu-Bo; Xu, Gang; Meng, Xiang-Hua; Yang, Yi-Xian

2015-10-01

A new security protocol for quantum sealed-bid auction is proposed to resist the collusion attack from some malicious bidders. The most significant feature of this protocol is that bidders prepare their particles with secret order in post-confirmation for encoding bids. In addition, a new theorem and its proof are given based on the theory of combinatorial mathematics, which can be used as evaluation criteria for the collusion attack. It is shown that the new protocol is immune to the collusion attack and meets the demand for a secure auction. Compared with those previous protocols, the security, efficiency and availability of the proposed protocol are largely improved.

Millicharged dark matter in quantum gravity and string theory.

PubMed

Shiu, Gary; Soler, Pablo; Ye, Fang

2013-06-14

We examine the millicharged dark matter scenario from a string theory perspective. In this scenario, kinetic and mass mixings of the photon with extra U(1) bosons are claimed to give rise to small electric charges, carried by dark matter particles, whose values are determined by continuous parameters of the theory. This seems to contradict folk theorems of quantum gravity that forbid the existence of irrational charges in theories with a single massless gauge field. By considering the underlying structure of the U(1) mass matrix that appears in type II string compactifications, we show that millicharges arise exclusively through kinetic mixing, and require the existence of at least two exactly massless gauge bosons.

Possible violation of the optical theorem in LHC experiments

NASA Astrophysics Data System (ADS)

Kupczynski, M.

2014-12-01

The optical theorem (OT), allowing the determination of the total cross section for a hadron-hadron scattering from the imaginary part of the forward elastic scattering amplitude, is believed to be an unavoidable consequence of the conservation of probability and of the unitary S matrix. This is a fundamental theorem which contains an imaginary part of the forward elastic scattering amplitude that is not directly measurable. The impossibility of scattering phenomena without the elastic channel is considered to be a part of the quantum magic. However, if one takes seriously the idea that the hadrons are extended particles, one may define a unitary S matrix such that one cannot prove the OT. Moreover, data violating the OT do exist, but they are not conclusive due to the uncertainties related to the extrapolation of the differential elastic cross-section to the forward direction. These results were published several years ago, but they were forgotten. In this paper we will recall these results in an understandable way, and we will give the additional arguments why the OT can be violated in high energy strong interaction scattering and why it should be tested and not simply used as a tool in LHC experiments.

The capacity to transmit classical information via black holes

NASA Astrophysics Data System (ADS)

Adami, Christoph; Ver Steeg, Greg

2013-03-01

One of the most vexing problems in theoretical physics is the relationship between quantum mechanics and gravity. According to an argument originally by Hawking, a black hole must destroy any information that is incident on it because the only radiation that a black hole releases during its evaporation (the Hawking radiation) is precisely thermal. Surprisingly, this claim has never been investigated within a quantum information-theoretic framework, where the black hole is treated as a quantum channel to transmit classical information. We calculate the capacity of the quantum black hole channel to transmit classical information (the Holevo capacity) within curved-space quantum field theory, and show that the information carried by late-time particles sent into a black hole can be recovered with arbitrary accuracy, from the signature left behind by the stimulated emission of radiation that must accompany any absorption event. We also show that this stimulated emission turns the black hole into an almost-optimal quantum cloning machine, where the violation of the no-cloning theorem is ensured by the noise provided by the Hawking radiation. Thus, rather than threatening the consistency of theoretical physics, Hawking radiation manages to save it instead.

Localized magnetoplasmons in quantum dots: Scrutinizing the eligibility of FIR, Raman, and electron energy-loss spectroscopies

NASA Astrophysics Data System (ADS)

Kushwaha, M.

We report on a one-component, quasi-zero dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de-Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron-energy-loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron-energy-loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in such diverse fields as quantum computing and medical imaging1. 1. M.S. Kushwaha, Unpublished.

The series product for gaussian quantum input processes

NASA Astrophysics Data System (ADS)

Gough, John E.; James, Matthew R.

2017-02-01

We present a theory for connecting quantum Markov components into a network with quantum input processes in a Gaussian state (including thermal and squeezed). One would expect on physical grounds that the connection rules should be independent of the state of the input to the network. To compute statistical properties, we use a version of Wicks' theorem involving fictitious vacuum fields (Fock space based representation of the fields) and while this aids computation, and gives a rigorous formulation, the various representations need not be unitarily equivalent. In particular, a naive application of the connection rules would lead to the wrong answer. We establish the correct interconnection rules, and show that while the quantum stochastic differential equations of motion display explicitly the covariances (thermal and squeezing parameters) of the Gaussian input fields we introduce the Wick-Stratonovich form which leads to a way of writing these equations that does not depend on these covariances and so corresponds to the universal equations written in terms of formal quantum input processes. We show that a wholly consistent theory of quantum open systems in series can be developed in this way, and as required physically, is universal and in particular representation-free.

SU(p,q) coherent states and a Gaussian de Finetti theorem

NASA Astrophysics Data System (ADS)

Leverrier, Anthony

2018-04-01

We prove a generalization of the quantum de Finetti theorem when the local space is an infinite-dimensional Fock space. In particular, instead of considering the action of the permutation group on n copies of that space, we consider the action of the unitary group U(n) on the creation operators of the n modes and define a natural generalization of the symmetric subspace as the space of states invariant under unitaries in U(n). Our first result is a complete characterization of this subspace, which turns out to be spanned by a family of generalized coherent states related to the special unitary group SU(p, q) of signature (p, q). More precisely, this construction yields a unitary representation of the noncompact simple real Lie group SU(p, q). We therefore find a dual unitary representation of the pair of groups U(n) and SU(p, q) on an n(p + q)-mode Fock space. The (Gaussian) SU(p, q) coherent states resolve the identity on the symmetric subspace, which implies a Gaussian de Finetti theorem stating that tracing over a few modes of a unitary-invariant state yields a state close to a mixture of Gaussian states. As an application of this de Finetti theorem, we show that the n × n upper-left submatrix of an n × n Haar-invariant unitary matrix is close in total variation distance to a matrix of independent normal variables if n3 = O(m).

Reconstructing quantum entropy production to probe irreversibility and correlations

NASA Astrophysics Data System (ADS)

Gherardini, Stefano; Müller, Matthias M.; Trombettoni, Andrea; Ruffo, Stefano; Caruso, Filippo

2018-07-01

One of the major goals of quantum thermodynamics is the characterization of irreversibility and its consequences in quantum processes. Here, we discuss how entropy production provides a quantification of the irreversibility in open quantum systems through the quantum fluctuation theorem. We start by introducing a two-time quantum measurement scheme, in which the dynamical evolution between the measurements is described by a completely positive, trace-preserving (CPTP) quantum map (forward process). By inverting the measurement scheme and applying the time-reversed version of the quantum map, we can study how this backward process differs from the forward one. When the CPTP map is unital, we show that the stochastic quantum entropy production is a function only of the probabilities to get the initial measurement outcomes in correspondence of the forward and backward processes. For bipartite open quantum systems we also prove that the mean value of the stochastic quantum entropy production is sub-additive with respect to the bipartition (except for product states). Hence, we find a method to detect correlations between the subsystems. Our main result is the proposal of an efficient protocol to determine and reconstruct the characteristic functions of the stochastic entropy production for each subsystem. This procedure enables to reconstruct even others thermodynamical quantities, such as the work distribution of the composite system and the corresponding internal energy. Efficiency and possible extensions of the protocol are also discussed. Finally, we show how our findings might be experimentally tested by exploiting the state of-the-art trapped-ion platforms.

Quantum cluster algebras and quantum nilpotent algebras.

PubMed

Goodearl, Kenneth R; Yakimov, Milen T

2014-07-08

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein-Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405-455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337-397] for the case of symmetric Kac-Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1-52] associated with double Bruhat cells coincide with the corresponding cluster algebras.

Quantum error suppression with commuting Hamiltonians: two local is too local.

PubMed

Marvian, Iman; Lidar, Daniel A

2014-12-31

We consider error suppression schemes in which quantum information is encoded into the ground subspace of a Hamiltonian comprising a sum of commuting terms. Since such Hamiltonians are gapped, they are considered natural candidates for protection of quantum information and topological or adiabatic quantum computation. However, we prove that they cannot be used to this end in the two-local case. By making the favorable assumption that the gap is infinite, we show that single-site perturbations can generate a degeneracy splitting in the ground subspace of this type of Hamiltonian which is of the same order as the magnitude of the perturbation, and is independent of the number of interacting sites and their Hilbert space dimensions, just as in the absence of the protecting Hamiltonian. This splitting results in decoherence of the ground subspace, and we demonstrate that for natural noise models the coherence time is proportional to the inverse of the degeneracy splitting. Our proof involves a new version of the no-hiding theorem which shows that quantum information cannot be approximately hidden in the correlations between two quantum systems. The main reason that two-local commuting Hamiltonians cannot be used for quantum error suppression is that their ground subspaces have only short-range (two-body) entanglement.

Philosophical Concepts in Physics

NASA Astrophysics Data System (ADS)

Cushing, James T.

1998-01-01

Preface; Part I. The Scientific Enterprise: 1. Ways of knowing; 2. Aristotle and Francis Bacon; 3. Science and metaphysics; Part II. Ancient and Modern Models of the Universe: 4. Observational astronomy and the Ptolemaic model; 5. The Copernican model and Kepler's laws; 6. Galileo on motion; Part III. The Newtonian Universe: 7. Newton's Principia; 8. Newton's law of universal gravitation; 9. Some old questions revisited; Part IV. A Perspective: 10. Galileo's Letter to the Grand Duchess; 11. An overarching Newtonian framework; 12. A view of the world based on science: determinism; Part V. Mechanical Versus Electrodynamical World Views: 13. Models of the aether; 14. Maxwell's theory; 15. The Kaufmann experiments; Part VI. The Theory of Relativity: 16. The background to and essentials of special relativity; 17. Further logical consequences of Einstein's postulates; 18. General relativity and the expanding universe; Part VII. The Quantum World and the Completeness of Quantum Mechanics: 19. The road to quantum mechanics; 20. 'Copenhage' quantum mechanics; 21. Is quantum mechanics complete?; Part VIII. Some Philosophical Lessons from Quantum Mechanics: 22. The EPR paper and Bell's theorem; 23. An alternative version of quantum mechanics; 24. An essential role for historical contingency?; Part IX. A Retrospective: 25. The goals of science and the status of its knowledge; Notes; General references; Bibliography; Author index; Subject index.

Quantum cluster algebras and quantum nilpotent algebras

PubMed Central

Goodearl, Kenneth R.; Yakimov, Milen T.

2014-01-01

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

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

Lami, L.; Giovannetti, V.

The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a maximally entangled configuration, preserve its entanglement even when applied an arbitrary number of times. In other words, a quantum channel ψ is said to be ES if its powers ψ{sup n} are not entanglement-breaking for all integers n. We also characterize the properties of the Asymptotic Entanglement Saving (AES) maps. These form a proper subset of the ES channels that is constituted by those maps that not onlymore » preserve entanglement for all finite n but which also sustain an explicitly not null level of entanglement in the asymptotic limit n → ∞. Structure theorems are provided for ES and for AES maps which yield an almost complete characterization of the former and a full characterization of the latter.« less

Comment on 'Nonlocality, Counterfactuals and Quantum Mechanics'

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

Stapp, H.P.

A recent proof [H. P. Stapp, Am. J. Phys. 65, 300 (1997)], formulated in the symbolic language of modal logic, claims to show that contemporary quantum theory, viewed as a set of rules that allow us to calculate statistical predictions among certain kinds of observations, cannot be imbedded in any rational framework that conforms to the principles that (1) the experimenters' choices of which experiments they will perform can be considered to be free choices, (2) outcomes of measurements are unique, and (3) the free choices just mentioned have no backward-in-time effects of any kind. This claim is similar tomore » Bell's theorem, but much stronger, because no reality assumption alien to quantum philosophy is used. The paper being commented on [W. Unruh, Phys. Rev. A 59, 126 (1999)] argues that some such reality assumption has been ''smuggled'' in. That argument is examined here and shown, I believe, to be defective.« less

Finite conformal quantum gravity and spacetime singularities

NASA Astrophysics Data System (ADS)

Modesto, Leonardo; Rachwał, Lesław

2017-12-01

We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.

Implementation of quantum and classical discrete fractional Fourier transforms.

PubMed

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

Implementation of quantum and classical discrete fractional Fourier transforms

PubMed Central

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Spectral Automorphisms in Quantum Logics

NASA Astrophysics Data System (ADS)

Ivanov, Alexandru; Caragheorgheopol, Dan

2010-12-01

In quantum mechanics, the Hilbert space formalism might be physically justified in terms of some axioms based on the orthomodular lattice (OML) mathematical structure (Piron in Foundations of Quantum Physics, Benjamin, Reading, 1976). We intend to investigate the extent to which some fundamental physical facts can be described in the more general framework of OMLs, without the support of Hilbert space-specific tools. We consider the study of lattice automorphisms properties as a “substitute” for Hilbert space techniques in investigating the spectral properties of observables. This is why we introduce the notion of spectral automorphism of an OML. Properties of spectral automorphisms and of their spectra are studied. We prove that the presence of nontrivial spectral automorphisms allow us to distinguish between classical and nonclassical theories. We also prove, for finite dimensional OMLs, that for every spectral automorphism there is a basis of invariant atoms. This is an analogue of the spectral theorem for unitary operators having purely point spectrum.

Nonclassicality of Temporal Correlations.

PubMed

Brierley, Stephen; Kosowski, Adrian; Markiewicz, Marcin; Paterek, Tomasz; Przysiężna, Anna

2015-09-18

The results of spacelike separated measurements are independent of distant measurement settings, a property one might call two-way no-signaling. In contrast, timelike separated measurements are only one-way no-signaling since the past is independent of the future but not vice versa. For this reason some temporal correlations that are formally identical to nonclassical spatial correlations can still be modeled classically. We propose a new formulation of Bell's theorem for temporal correlations; namely, we define nonclassical temporal correlations as the ones which cannot be simulated by propagating in time the classical information content of a quantum system given by the Holevo bound. We first show that temporal correlations between results of any projective quantum measurements on a qubit can be simulated classically. Then we present a sequence of general measurements on a single m-level quantum system that cannot be explained by propagating in time an m-level classical system and using classical computers with unlimited memory.

Linear stability analysis of a levitated nanomagnet in a static magnetic field: Quantum spin stabilized magnetic levitation

NASA Astrophysics Data System (ADS)

Rusconi, C. C.; Pöchhacker, V.; Cirac, J. I.; Romero-Isart, O.

2017-10-01

We theoretically study the levitation of a single magnetic domain nanosphere in an external static magnetic field. We show that, apart from the stability provided by the mechanical rotation of the nanomagnet (as in the classical Levitron), the quantum spin origin of its magnetization provides two additional mechanisms to stably levitate the system. Despite the Earnshaw theorem, such stable phases are present even in the absence of mechanical rotation. For large magnetic fields, the Larmor precession of the quantum magnetic moment stabilizes the system in full analogy with magnetic trapping of a neutral atom. For low magnetic fields, the magnetic anisotropy stabilizes the system via the Einstein-de Haas effect. These results are obtained with a linear stability analysis of a single magnetic domain rigid nanosphere with uniaxial anisotropy in a Ioffe-Pritchard magnetic field.

Communication: Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Motta, Mario; Zhang, Shiwei

2018-05-01

We propose an algorithm for accurate, systematic, and scalable computation of interatomic forces within the auxiliary-field quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellmann-Feynman theorem and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.

Center for Quantum Algorithms and Complexity

DTIC Science & Technology

2014-05-12

precisely, it asserts that for any subset L of particles, the entanglement entropy between L and L̄ is bounded by the surface area of L (the area is...ground states of gapped local Hamiltonians. Roughly, it says that the entanglement in such states is very local, and the entanglement entropy scales...the theorem states that the entanglement entropy is bounded by exp(X), where X = log(d/?). Hastingss result implies that ground states of gapped 1D

A Bell-type theorem without hidden variables

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

Stapp, Henry P.

2003-09-12

It is shown that no theory that satisfies certain premises can exclude faster-than-light influences. The premises include neither the existence of hidden variables nor counterfactual definiteness, nor any premise that effectively entails the general existence of outcomes of unperformed local measurements. All the premises are compatible with Copenhagen philosophy and the principles and predictions of relativistic quantum field theory. The present proof is contrasted with an earlier one with the same objective.

Noncommutative Valuation of Options

NASA Astrophysics Data System (ADS)

Herscovich, Estanislao

2016-12-01

The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.

Density functional theory across chemistry, physics and biology.

PubMed

van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre

2014-03-13

The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT.

Violation of local realism with freedom of choice

PubMed Central

Scheidl, Thomas; Ursin, Rupert; Kofler, Johannes; Ramelow, Sven; Ma, Xiao-Song; Herbst, Thomas; Ratschbacher, Lothar; Fedrizzi, Alessandro; Langford, Nathan K.; Jennewein, Thomas; Zeilinger, Anton

2010-01-01

Bell’s theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell’s inequality which can be violated in experiments using entangled quantum states. Bell’s theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, “loopholes” arise which allow observed violations to still be explained by local realistic theories. Violating Bell’s inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell’s inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism. PMID:21041665

Violation of local realism with freedom of choice.

PubMed

Scheidl, Thomas; Ursin, Rupert; Kofler, Johannes; Ramelow, Sven; Ma, Xiao-Song; Herbst, Thomas; Ratschbacher, Lothar; Fedrizzi, Alessandro; Langford, Nathan K; Jennewein, Thomas; Zeilinger, Anton

2010-11-16

Bell's theorem shows that local realistic theories place strong restrictions on observable correlations between different systems, giving rise to Bell's inequality which can be violated in experiments using entangled quantum states. Bell's theorem is based on the assumptions of realism, locality, and the freedom to choose between measurement settings. In experimental tests, "loopholes" arise which allow observed violations to still be explained by local realistic theories. Violating Bell's inequality while simultaneously closing all such loopholes is one of the most significant still open challenges in fundamental physics today. In this paper, we present an experiment that violates Bell's inequality while simultaneously closing the locality loophole and addressing the freedom-of-choice loophole, also closing the latter within a reasonable set of assumptions. We also explain that the locality and freedom-of-choice loopholes can be closed only within nondeterminism, i.e., in the context of stochastic local realism.

Maximum one-shot dissipated work from Rényi divergences

NASA Astrophysics Data System (ADS)

Yunger Halpern, Nicole; Garner, Andrew J. P.; Dahlsten, Oscar C. O.; Vedral, Vlatko

2018-05-01

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

Maximum one-shot dissipated work from Rényi divergences.

PubMed

Yunger Halpern, Nicole; Garner, Andrew J P; Dahlsten, Oscar C O; Vedral, Vlatko

2018-05-01

Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

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.

Quantum State Tomography via Linear Regression Estimation

PubMed Central

Qi, Bo; Hou, Zhibo; Li, Li; Dong, Daoyi; Xiang, Guoyong; Guo, Guangcan

2013-01-01

A simple yet efficient state reconstruction algorithm of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. An asymptotic mean squared error (MSE) upper bound for all possible states to be estimated is given analytically, which depends explicitly upon the involved measurement bases. This analytical MSE upper bound can guide one to choose optimal measurement sets. The computational complexity of LRE is O(d4) where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography. PMID:24336519

Derivation of a generalized Schrödinger equation from the theory of scale relativity

NASA Astrophysics Data System (ADS)

Chavanis, Pierre-Henri

2017-06-01

Using Nottale's theory of scale relativity relying on a fractal space-time, we derive a generalized Schrödinger equation taking into account the interaction of the system with the external environment. This equation describes the irreversible evolution of the system towards a static quantum state. We first interpret the scale-covariant equation of dynamics stemming from Nottale's theory as a hydrodynamic viscous Burgers equation for a potential flow involving a complex velocity field and an imaginary viscosity. We show that the Schrödinger equation can be directly obtained from this equation by performing a Cole-Hopf transformation equivalent to the WKB transformation. We then introduce a friction force proportional and opposite to the complex velocity in the scale-covariant equation of dynamics in a way that preserves the local conservation of the normalization condition. We find that the resulting generalized Schrödinger equation, or the corresponding fluid equations obtained from the Madelung transformation, involve not only a damping term but also an effective thermal term. The friction coefficient and the temperature are related to the real and imaginary parts of the complex friction coefficient in the scale-covariant equation of dynamics. This may be viewed as a form of fluctuation-dissipation theorem. We show that our generalized Schrödinger equation satisfies an H-theorem for the quantum Boltzmann free energy. As a result, the probability distribution relaxes towards an equilibrium state which can be viewed as a Boltzmann distribution including a quantum potential. We propose to apply this generalized Schrödinger equation to dark matter halos in the Universe, possibly made of self-gravitating Bose-Einstein condensates.

Quantum cryptography with finite resources: unconditional security bound for discrete-variable protocols with one-way postprocessing.

PubMed

Scarani, Valerio; Renner, Renato

2008-05-23

We derive a bound for the security of quantum key distribution with finite resources under one-way postprocessing, based on a definition of security that is composable and has an operational meaning. While our proof relies on the assumption of collective attacks, unconditional security follows immediately for standard protocols such as Bennett-Brassard 1984 and six-states protocol. For single-qubit implementations of such protocols, we find that the secret key rate becomes positive when at least N approximately 10(5) signals are exchanged and processed. For any other discrete-variable protocol, unconditional security can be obtained using the exponential de Finetti theorem, but the additional overhead leads to very pessimistic estimates.

Topological Proximity Effect: A Gauge Influence from Distant Fields on Planar Quantum-Coherent Systems

NASA Astrophysics Data System (ADS)

Moulopoulos, K.

2015-06-01

A quantum system that lies nearby a magnetic or time-varying electric field region, and that is under periodic boundary conditions parallel to the interface, is shown to exhibit a "hidden" Aharonov-Bohm effect (magnetic or electric), caused by fluxes that are not enclosed by, but are merely neighboring to our system - its origin being the absence of magnetic monopoles in 3D space (with corresponding spacetime generalizations). Novel possibilities then arise, where a field-free system can be dramatically affected by manipulating fields in an adjacent or even distant land, provided that these nearby fluxes are not quantized (i.e. they are fractional or irrational parts of the flux quantum). Topological effects (such as Quantum Hall types of behaviors) can therefore be induced from outside our system (that is always field-free and can even reside in simply-connected space). Potential novel applications are outlined, and exotic consequences in solid state physics are pointed out (i.e. the possibility of field-free quantum periodic systems that violate Bloch's theorem), while formal analogies with certain high energy physics phenomena and with some rather under-explored areas in mechanics and thermodynamics are noted.

There are no particles, there are only fields

NASA Astrophysics Data System (ADS)

Hobson, Art

2013-03-01

Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply that unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying that it's also true of nonrelativistic systems. Particles are epiphenomena arising from fields. Thus, the Schrödinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the two-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the two-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories.

EPR and Bell's theorem: A critical review

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

Stapp, H.P.

1991-01-01

The argument of Einstein, Podolsky, and Rosen is reviewed with attention to logical structure and character of assumptions. Bohr's reply is discussed. Bell's contribution is formulated without use of hidden variables, and efforts to equate hidden variables to realism are critically examined. An alternative derivation of nonlocality that makes no use of hidden variables, microrealism, counterfactual definiteness, or any other assumption alien to orthodox quantum thinking is described in detail, with particular attention to the quartet or broken-square question.

Quantum Noise of Electron-Phonon Heat Current

NASA Astrophysics Data System (ADS)

Pekola, Jukka P.; Karimi, Bayan

2018-06-01

We analyze heat current fluctuations between electrons and phonons in a metal. In equilibrium we recover the standard result consistent with the fluctuation-dissipation theorem. Here we show that heat current noise at finite frequencies remains non-vanishing down to zero temperature. From the experimental point of view, it is a small effect and up to now elusive. We briefly discuss the impact of electron-phonon heat current fluctuations on calorimetry, particularly in the regime of single microwave-photon detection.

Large gauge transformations and little group for soft photons

NASA Astrophysics Data System (ADS)

Hamada, Yuta; Seo, Min-Seok; Shiu, Gary

2017-11-01

Recently, large gauge transformation (LGT), the residual gauge symmetry after gauge fixing that survives at null infinity, has drawn much attention concerning soft theorems and the memory effect. We point out that LGT charges in quantum electrodynamics are in fact one of noncompact generators of the two dimensional Euclidean group. Moreover, by comparing two equivalent descriptions of gauge transformation, we suggest that LGT is simply another way of describing the gauged little group for massless soft photons.

Static solutions for fourth order gravity

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

Nelson, William

2010-11-15

The Lichnerowicz and Israel theorems are extended to higher order theories of gravity. In particular it is shown that Schwarzschild is the unique spherically symmetric, static, asymptotically flat, black-hole solution, provided the spatial curvature is less than the quantum gravity scale outside the horizon. It is then shown that in the presence of matter (satisfying certain positivity requirements), the only static and asymptotically flat solutions of general relativity that are also solutions of higher order gravity are the vacuum solutions.

Oscillating potential well in the complex plane and the adiabatic theorem

NASA Astrophysics Data System (ADS)

Longhi, Stefano

2017-10-01

A quantum particle in a slowly changing potential well V (x ,t ) =V ( x -x0(ɛ t ) ) , periodically shaken in time at a slow frequency ɛ , provides an important quantum mechanical system where the adiabatic theorem fails to predict the asymptotic dynamics over time scales longer than ˜1 /ɛ . Specifically, we consider a double-well potential V (x ) sustaining two bound states spaced in frequency by ω0 and periodically shaken in a complex plane. Two different spatial displacements x0(t ) are assumed: the real spatial displacement x0(ɛ t ) =A sin(ɛ t ) , corresponding to ordinary Hermitian shaking, and the complex one x0(ɛ t ) =A -A exp(-i ɛ t ) , corresponding to non-Hermitian shaking. When the particle is initially prepared in the ground state of the potential well, breakdown of adiabatic evolution is found for both Hermitian and non-Hermitian shaking whenever the oscillation frequency ɛ is close to an odd resonance of ω0. However, a different physical mechanism underlying nonadiabatic transitions is found in the two cases. For the Hermitian shaking, an avoided crossing of quasienergies is observed at odd resonances and nonadiabatic transitions between the two bound states, resulting in Rabi flopping, can be explained as a multiphoton resonance process. For the complex oscillating potential well, breakdown of adiabaticity arises from the appearance of Floquet exceptional points at exact quasienergy crossing.

Non-commutative methods in quantum mechanics

NASA Astrophysics Data System (ADS)

Millard, Andrew Clive

1997-09-01

Non-commutativity appears in physics almost hand in hand with quantum mechanics. Non-commuting operators corresponding to observables lead to Heisenberg's Uncertainty Principle, which is often used as a prime example of how quantum mechanics transcends 'common sense', while the operators that generate a symmetry group are usually given in terms of their commutation relations. This thesis discusses a number of new developments which go beyond the usual stopping point of non-commuting quantities as matrices with complex elements. Chapter 2 shows how certain generalisations of quantum mechanics, from using complex numbers to using other (often non-commutative) algebras, can still be written as linear systems with symplectic phase flows. Chapter 3 deals with Adler's trace dynamics, a non-linear graded generalisation of Hamiltonian dynamics with supersymmetry applications, where the phase space coordinates are (generally non-commuting) operators, and reports on aspects of a demonstration that the statistical averages of the dynamical variables obey the rules of complex quantum field theory. The last two chapters discuss specific aspects of quaternionic quantum mechanics. Chapter 4 reports a generalised projective representation theory and presents a structure theorem that categorises quaternionic projective representations. Chapter 5 deals with a generalisation of the coherent states formalism and examines how it may be applied to two commonly used groups.

Majorana-Fermions, Their-Own Antiparticles, Following Non-Abelian Anyon/Semion Quantum-Statistics : Solid-State MEETS Particle Physics Neutrinos: Spin-Orbit-Coupled Superconductors and/or Superfluids to Neutrinos; Insulator-Heisenberg-Antiferromagnet MnF2 Majorana-Siegel-Birgenau-Keimer - Effect

NASA Astrophysics Data System (ADS)

Majorana-Fermi-Segre, E.-L.; Antonoff-Overhauser-Salam, Marvin-Albert-Abdus; Siegel, Edward Carl-Ludwig

2013-03-01

Majorana-fermions, being their own antiparticles, following non-Abelian anyon/semion quantum-statistics: in Zhang et.al.-...-Detwiler et.al.-...``Worlds-in-Collision'': solid-state/condensed-matter - physics spin-orbit - coupled topological-excitations in superconductors and/or superfluids -to- particle-physics neutrinos: ``When `Worlds' Collide'', analysis via Siegel[Schrodinger Centenary Symp., Imperial College, London (1987); in The Copenhagen-Interpretation Fifty-Years After the Como-Lecture, Symp. Fdns. Mod.-Phys., Joensu(1987); Symp. on Fractals, MRS Fall-Mtg., Boston(1989)-5-papers!!!] ``complex quantum-statistics in fractal-dimensions'', which explains hidden-dark-matter(HDM) IN Siegel ``Sephirot'' scenario for The Creation, uses Takagi[Prog.Theo.Phys. Suppl.88,1(86)]-Ooguri[PR D33,357(85)] - Picard-Lefschetz-Arnol'd-Vassil'ev[``Principia Read After 300 Years'', Not.AMS(1989); quantum-theory caveats comment-letters(1990); Applied Picard-Lefschetz Theory, AMS(2006)] - theorem quantum-statistics, which via Euler- formula becomes which via de Moivre- -formula further becomes which on unit-circle is only real for only, i.e, for, versus complex with imaginary-damping denominator for, i.e, for, such that Fermi-Dirac quantum-statistics for

Quasi-superradiant soliton state of matter in quantum metamaterials

NASA Astrophysics Data System (ADS)

Asai, Hidehiro; Kawabata, Shiro; Savel'ev, Sergey E.; Zagoskin, Alexandre M.

2018-02-01

Strong interaction of a system of quantum emitters (e.g., two-level atoms) with electromagnetic field induces specific correlations in the system accompanied by a drastic increase of emitted radiation (superradiation or superfluorescence). Despite the fact that since its prediction this phenomenon was subject to a vigorous experimental and theoretical research, there remain open question, in particular, concerning the possibility of a first order phase transition to the superradiant state from the vacuum state. In systems of natural and charge-based artificial atom this transition is prohibited by "no-go" theorems. Here we demonstrate numerically and confirm analytically a similar transition in a one-dimensional quantum metamaterial - a chain of artificial atoms (qubits) strongly interacting with classical electromagnetic fields in a transmission line. The system switches from vacuum state to the quasi-superradiant (QS) phase with one or several magnetic solitons and finite average occupation of qubit excited states along the transmission line. A quantum metamaterial in the QS phase circumvents the "no-go" restrictions by considerably decreasing its total energy relative to the vacuum state by exciting nonlinear electromagnetic solitons.

Pseudothermalization in driven-dissipative non-Markovian open quantum systems

NASA Astrophysics Data System (ADS)

Lebreuilly, José; Chiocchetta, Alessio; Carusotto, Iacopo

2018-03-01

We investigate a pseudothermalization effect, where an open quantum system coupled to a nonequilibrated environment consisting of several non-Markovian reservoirs presents an emergent thermal behavior. This thermal behavior is visible at both static and dynamical levels and the system satisfies the fluctuation-dissipation theorem. Our analysis is focused on the exactly solvable model of a weakly interacting driven-dissipative Bose gas in presence of frequency-dependent particle pumping and losses, and is based on a quantum Langevin theory, which we derive starting from a microscopical quantum optics model. For generic non-Markovian reservoirs, we demonstrate that the emergence of thermal properties occurs in the range of frequencies corresponding to low-energy excitations. For the specific case of non-Markovian baths verifying the Kennard-Stepanov relation, we show that pseudothermalization can instead occur at all energy scales. The possible implications regarding the interpretation of thermal laws in low-temperature exciton-polariton experiments are discussed. We finally show that the presence of either a saturable pumping or a dispersive environment leads to a breakdown of the pseudothermalization effect.

Multiparameter Estimation in Networked Quantum Sensors

NASA Astrophysics Data System (ADS)

Proctor, Timothy J.; Knott, Paul A.; Dunningham, Jacob A.

2018-02-01

We introduce a general model for a network of quantum sensors, and we use this model to consider the following question: When can entanglement between the sensors, and/or global measurements, enhance the precision with which the network can measure a set of unknown parameters? We rigorously answer this question by presenting precise theorems proving that for a broad class of problems there is, at most, a very limited intrinsic advantage to using entangled states or global measurements. Moreover, for many estimation problems separable states and local measurements are optimal, and can achieve the ultimate quantum limit on the estimation uncertainty. This immediately implies that there are broad conditions under which simultaneous estimation of multiple parameters cannot outperform individual, independent estimations. Our results apply to any situation in which spatially localized sensors are unitarily encoded with independent parameters, such as when estimating multiple linear or nonlinear optical phase shifts in quantum imaging, or when mapping out the spatial profile of an unknown magnetic field. We conclude by showing that entangling the sensors can enhance the estimation precision when the parameters of interest are global properties of the entire network.

Quantum gravity in three dimensions, Witten spinors and the quantisation of length

NASA Astrophysics Data System (ADS)

Wieland, Wolfgang

2018-05-01

In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU (2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.

Linear maps preserving maximal deviation and the Jordan structure of quantum systems

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

Hamhalter, Jan

2012-12-15

In the algebraic approach to quantum theory, a quantum observable is given by an element of a Jordan algebra and a state of the system is modelled by a normalized positive functional on the underlying algebra. Maximal deviation of a quantum observable is the largest statistical deviation one can obtain in a particular state of the system. The main result of the paper shows that each linear bijective transformation between JBW algebras preserving maximal deviations is formed by a Jordan isomorphism or a minus Jordan isomorphism perturbed by a linear functional multiple of an identity. It shows that only onemore » numerical statistical characteristic has the power to determine the Jordan algebraic structure completely. As a consequence, we obtain that only very special maps can preserve the diameter of the spectra of elements. Nonlinear maps preserving the pseudometric given by maximal deviation are also described. The results generalize hitherto known theorems on preservers of maximal deviation in the case of self-adjoint parts of von Neumann algebras proved by Molnar.« less

Design of a universal logic block for fault-tolerant realization of any logic operation in trapped-ion quantum circuits

NASA Astrophysics Data System (ADS)

Goudarzi, H.; Dousti, M. J.; Shafaei, A.; Pedram, M.

2014-05-01

This paper presents a physical mapping tool for quantum circuits, which generates the optimal universal logic block (ULB) that can, on average, perform any logical fault-tolerant (FT) quantum operations with the minimum latency. The operation scheduling, placement, and qubit routing problems tackled by the quantum physical mapper are highly dependent on one another. More precisely, the scheduling solution affects the quality of the achievable placement solution due to resource pressures that may be created as a result of operation scheduling, whereas the operation placement and qubit routing solutions influence the scheduling solution due to resulting distances between predecessor and current operations, which in turn determines routing latencies. The proposed flow for the quantum physical mapper captures these dependencies by applying (1) a loose scheduling step, which transforms an initial quantum data flow graph into one that explicitly captures the no-cloning theorem of the quantum computing and then performs instruction scheduling based on a modified force-directed scheduling approach to minimize the resource contention and quantum circuit latency, (2) a placement step, which uses timing-driven instruction placement to minimize the approximate routing latencies while making iterative calls to the aforesaid force-directed scheduler to correct scheduling levels of quantum operations as needed, and (3) a routing step that finds dynamic values of routing latencies for the qubits. In addition to the quantum physical mapper, an approach is presented to determine the single best ULB size for a target quantum circuit by examining the latency of different FT quantum operations mapped onto different ULB sizes and using information about the occurrence frequency of operations on critical paths of the target quantum algorithm to weigh these latencies. Experimental results show an average latency reduction of about 40 % compared to previous work.

Solving quantum optimal control problems using Clebsch variables and Lin constraints

NASA Astrophysics Data System (ADS)

Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

2018-01-01

Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

Principles of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Landé, Alfred

2013-10-01

Preface; Introduction: 1. Observation and interpretation; 2. Difficulties of the classical theories; 3. The purpose of quantum theory; Part I. Elementary Theory of Observation (Principle of Complementarity): 4. Refraction in inhomogeneous media (force fields); 5. Scattering of charged rays; 6. Refraction and reflection at a plane; 7. Absolute values of momentum and wave length; 8. Double ray of matter diffracting light waves; 9. Double ray of matter diffracting photons; 10. Microscopic observation of ρ (x) and σ (p); 11. Complementarity; 12. Mathematical relation between ρ (x) and σ (p) for free particles; 13. General relation between ρ (q) and σ (p); 14. Crystals; 15. Transition density and transition probability; 16. Resultant values of physical functions; matrix elements; 17. Pulsating density; 18. General relation between ρ (t) and σ (є); 19. Transition density; matrix elements; Part II. The Principle of Uncertainty: 20. Optical observation of density in matter packets; 21. Distribution of momenta in matter packets; 22. Mathematical relation between ρ and σ; 23. Causality; 24. Uncertainty; 25. Uncertainty due to optical observation; 26. Dissipation of matter packets; rays in Wilson Chamber; 27. Density maximum in time; 28. Uncertainty of energy and time; 29. Compton effect; 30. Bothe-Geiger and Compton-Simon experiments; 31. Doppler effect; Raman effect; 32. Elementary bundles of rays; 33. Jeans' number of degrees of freedom; 34. Uncertainty of electromagnetic field components; Part III. The Principle of Interference and Schrödinger's equation: 35. Physical functions; 36. Interference of probabilities for p and q; 37. General interference of probabilities; 38. Differential equations for Ψp (q) and Xq (p); 39. Differential equation for фβ (q); 40. The general probability amplitude Φβ' (Q); 41. Point transformations; 42. General theorem of interference; 43. Conjugate variables; 44. Schrödinger's equation for conservative systems; 45. Schrödinger's equation for non-conservative systems; 46. Pertubation theory; 47. Orthogonality, normalization and Hermitian conjugacy; 48. General matrix elements; Part IV. The Principle of Correspondence: 49. Contact transformations in classical mechanics; 50. Point transformations; 51. Contact transformations in quantum mechanics; 52. Constants of motion and angular co-ordinates; 53. Periodic orbits; 54. De Broglie and Schrödinger function; correspondence to classical mechanics; 55. Packets of probability; 56. Correspondence to hydrodynamics; 57. Motion and scattering of wave packets; 58. Formal correspondence between classical and quantum mechanics; Part V. Mathematical Appendix: Principle of Invariance: 59. The general theorem of transformation; 60. Operator calculus; 61. Exchange relations; three criteria for conjugacy; 62. First method of canonical transformation; 63. Second method of canonical transformation; 64. Proof of the transformation theorem; 65. Invariance of the matrix elements against unitary transformations; 66. Matrix mechanics; Index of literature; Index of names and subjects.

Estimating Optimal Transformations for Multiple Regression and Correlation.

DTIC Science & Technology

1982-07-01

algorithm; we minimize (2.4) e2 (,,, ...,) = E[e(Y) - 1I (X 2 j=l j 2holding EO =1, E6 = E0, =.-. =Ecp = 0, through a series of single function minimizations...X, x = INU = lIVe . Then (5.16) THEOREM. If 6*, p* is an optimal transformation for regression, then = ue*o Conversely, if e satisfies Xe = U6, Nll1...Stanford University, Tech. Report ORIONOO6. Gasser, T. and Rosenblatt, M. (eds.) (1979). Smoothing Techniques for Curve Estimation, in Lecture Notes in

Quantum cryptography and applications in the optical fiber network

NASA Astrophysics Data System (ADS)

Luo, Yuhui

2005-09-01

Quantum cryptography, as part of quantum information and communications, can provide absolute security for information transmission because it is established on the fundamental laws of quantum theory, such as the principle of uncertainty, No-cloning theorem and quantum entanglement. In this thesis research, a novel scheme to implement quantum key distribution based on multiphoton entanglement with a new protocol is proposed. Its advantages are: a larger information capacity can be obtained with a longer transmission distance and the detection of multiple photons is easier than that of a single photon. The security and attacks pertaining to such a system are also studied. Next, a quantum key distribution over wavelength division multiplexed (WDM) optical fiber networks is realized. Quantum key distribution in networks is a long-standing problem for practical applications. Here we combine quantum cryptography and WDM to solve this problem because WDM technology is universally deployed in the current and next generation fiber networks. The ultimate target is to deploy quantum key distribution over commercial networks. The problems arising from the networks are also studied in this part. Then quantum key distribution in multi-access networks using wavelength routing technology is investigated in this research. For the first time, quantum cryptography for multiple individually targeted users has been successfully implemented in sharp contrast to that using the indiscriminating broadcasting structure. It overcomes the shortcoming that every user in the network can acquire the quantum key signals intended to be exchanged between only two users. Furthermore, a more efficient scheme of quantum key distribution is adopted, hence resulting in a higher key rate. Lastly, a quantum random number generator based on quantum optics has been experimentally demonstrated. This device is a key component for quantum key distribution as it can create truly random numbers, which is an essential requirement to perform quantum key distribution. This new generator is composed of a single optical fiber coupler with fiber pigtails, which can be easily used in optical fiber communications.

Non-commuting two-local Hamiltonians for quantum error suppression

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Rieffel, Eleanor G.

2017-04-01

Physical constraints make it challenging to implement and control many-body interactions. For this reason, designing quantum information processes with Hamiltonians consisting of only one- and two-local terms is a worthwhile challenge. Enabling error suppression with two-local Hamiltonians is particularly challenging. A no-go theorem of Marvian and Lidar (Phys Rev Lett 113(26):260504, 2014) demonstrates that, even allowing particles with high Hilbert space dimension, it is impossible to protect quantum information from single-site errors by encoding in the ground subspace of any Hamiltonian containing only commuting two-local terms. Here, we get around this no-go result by encoding in the ground subspace of a Hamiltonian consisting of non-commuting two-local terms arising from the gauge operators of a subsystem code. Specifically, we show how to protect stored quantum information against single-qubit errors using a Hamiltonian consisting of sums of the gauge generators from Bacon-Shor codes (Bacon in Phys Rev A 73(1):012340, 2006) and generalized-Bacon-Shor code (Bravyi in Phys Rev A 83(1):012320, 2011). Our results imply that non-commuting two-local Hamiltonians have more error-suppressing power than commuting two-local Hamiltonians. While far from providing full fault tolerance, this approach improves the robustness achievable in near-term implementable quantum storage and adiabatic quantum computations, reducing the number of higher-order terms required to encode commonly used adiabatic Hamiltonians such as the Ising Hamiltonians common in adiabatic quantum optimization and quantum annealing.

Quantum Strategies and Local Operations

NASA Astrophysics Data System (ADS)

Gutoski, Gus

2010-02-01

This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game. In Part II we establish several properties of a class of quantum operations that can be implemented locally with shared quantum entanglement or classical randomness. In particular, we establish the existence of a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. The existence of this ball is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. We also provide characterizations of local operations in terms of linear functionals that are positive and "completely" positive on a certain cone of Hermitian operators, under a natural notion of complete positivity appropriate to that cone. We end the thesis with a discussion of the properties of no-signaling quantum operations.

Hidden symmetries of the Kerr metric and Goldstone’s theorem

NASA Astrophysics Data System (ADS)

Penna, Robert F.

2011-12-01

Perturbations of the Kerr metric admit a spectrum of massless excitations, which we interpret as Goldstone modes coming from the metric’s broken spherical symmetry. The zero-frequency mode is related to the conformal Yano-Killing tensor which encodes Carter’s constant and the Killing vectors of the spacetime. The modes are described by a conformal field theory, which becomes two-dimensional Liouville theory in the near-horizon limit. Directly counting the quantum microstates of this theory reproduces the Bekenstein-Hawking area law.

The maximum efficiency of nano heat engines depends on more than temperature

NASA Astrophysics Data System (ADS)

Woods, Mischa; Ng, Nelly; Wehner, Stephanie

Sadi Carnot's theorem regarding the maximum efficiency of heat engines is considered to be of fundamental importance in the theory of heat engines and thermodynamics. Here, we show that at the nano and quantum scale, this law needs to be revised in the sense that more information about the bath other than its temperature is required to decide whether maximum efficiency can be achieved. In particular, we derive new fundamental limitations of the efficiency of heat engines at the nano and quantum scale that show that the Carnot efficiency can only be achieved under special circumstances, and we derive a new maximum efficiency for others. A preprint can be found here arXiv:1506.02322 [quant-ph] Singapore's MOE Tier 3A Grant & STW, Netherlands.

Holography and the Coleman-Mermin-Wagner theorem

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

Anninos, Dionysios; Hartnoll, Sean A.; Iqbal, Nabil

2010-09-15

In 2+1 dimensions at finite temperature, spontaneous symmetry breaking of global symmetries is precluded by large thermal fluctuations of the order parameter. The holographic correspondence implies that analogous effects must also occur in 3+1 dimensional theories with gauged symmetries in certain curved spacetimes with horizon. By performing a one loop computation in the background of a holographic superconductor, we show that bulk quantum fluctuations wash out the classical order parameter at sufficiently large distance scales. The low temperature phase is seen to exhibit algebraic long-range order. Beyond the specific example we study, holography suggests that IR singular quantum fluctuations ofmore » the fields and geometry will play an interesting role for many 3+1 dimensional asymptotically anti-de Sitter spacetimes with planar horizon.« less

Mode Matching for Optical Antennas

NASA Astrophysics Data System (ADS)

Feichtner, Thorsten; Christiansen, Silke; Hecht, Bert

2017-11-01

The emission rate of a point dipole can be strongly increased in the presence of a well-designed optical antenna. Yet, optical antenna design is largely based on radio-frequency rules, ignoring, e.g., Ohmic losses and non-negligible field penetration in metals at optical frequencies. Here, we combine reciprocity and Poynting's theorem to derive a set of optical-frequency antenna design rules for benchmarking and optimizing the performance of optical antennas driven by single quantum emitters. Based on these findings a novel plasmonic cavity antenna design is presented exhibiting a considerably improved performance compared to a reference two-wire antenna. Our work will be useful for the design of high-performance optical antennas and nanoresonators for diverse applications ranging from quantum optics to antenna-enhanced single-emitter spectroscopy and sensing.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

Synthetic Unruh effect in cold atoms

NASA Astrophysics Data System (ADS)

Rodríguez-Laguna, Javier; Tarruell, Leticia; Lewenstein, Maciej; Celi, Alessio

2017-01-01

We propose to simulate a Dirac field near an event horizon using ultracold atoms in an optical lattice. Such a quantum simulator allows for the observation of the celebrated Unruh effect. Our proposal involves three stages: (1) preparation of the ground state of a massless two-dimensional Dirac field in Minkowski space-time; (2) quench of the optical lattice setup to simulate how an accelerated observer would view that state; (3) measurement of the local quantum fluctuation spectra by one-particle excitation spectroscopy in order to simulate a De Witt detector. According to Unruh's prediction, fluctuations measured in such a way must be thermal. Moreover, following Takagi's inversion theorem, they will obey the Bose-Einstein distribution, which will smoothly transform into the Fermi-Dirac as one of the dimensions of the lattice is reduced.

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

Zhou Huanqiang; School of Physical Sciences, University of Queensland, Brisbane, Queensland 4072; Barthel, Thomas

We investigate boundary critical phenomena from a quantum-information perspective. Bipartite entanglement in the ground state of one-dimensional quantum systems is quantified using the Renyi entropy S{sub {alpha}}, which includes the von Neumann entropy ({alpha}{yields}1) and the single-copy entanglement ({alpha}{yields}{infinity}) as special cases. We identify the contribution of the boundaries to the Renyi entropy, and show that there is an entanglement loss along boundary renormalization group (RG) flows. This property, which is intimately related to the Affleck-Ludwig g theorem, is a consequence of majorization relations between the spectra of the reduced density matrix along the boundary RG flows. We also pointmore » out that the bulk contribution to the single-copy entanglement is half of that to the von Neumann entropy, whereas the boundary contribution is the same.« less

The origins of cosmic rays and quantum effects on gravity

NASA Technical Reports Server (NTRS)

Tomozawa, Y.

1985-01-01

The energy spectrum of primary cosmic rays is explained by particles emitted during a thermal expansion of explosive objects inside and near the galaxy, remnants of which may be supernova and/or active talaxies, or even stars or galaxies that disappeared from our sight after the explosion. A power law energy spectrum for cosmic rays, E to the (-alpha -1, is obtained from an expansion rate T is proportional to R to the alpha. Using the solution of the Einstein equation, we obtain a spectrum which agrees very well with experimental data. The implication of an inflationary early universe on the cosmic ray spectrum is also discussed. It is also suggested that the conflict between this model and the singularity theorem in classical general relativity may be eliminated by quantum effects.

Dynamic symmetries and quantum nonadiabatic transitions

DOE PAGES

Li, Fuxiang; Sinitsyn, Nikolai A.

2016-05-30

Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. Here we generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between anmore » arbitrary initial state and its time reversed counterpart is exactly zero. Lastly, we also discuss applications of this result to the multistate Landau–Zener (LZ) theory.« less