Entropy Transfer of Quantum Gravity Information Processing
NASA Astrophysics Data System (ADS)
Gyongyosi, Laszlo; Imre, Sandor
2015-05-01
We introduce the term smooth entanglement entropy transfer, a phenomenon that is a consequence of the causality-cancellation property of the quantum gravity environment. The causality-cancellation of the quantum gravity space removes the causal dependencies of the local systems. We study the physical effects of the causality-cancellation and show that it stimulates entropy transfer between the quantum gravity environment and the independent local systems of the quantum gravity space. The entropy transfer reduces the entropies of the contributing local systems and increases the entropy of the quantum gravity environment. We discuss the space-time geometry structure of the quantum gravity environment and the local quantum systems. We propose the space-time geometry model of the smooth entropy transfer. We reveal on a smooth Cauchy slice that the space-time geometry of the quantum gravity environment dynamically adapts to the vanishing causality. We prove that the Cauchy area expansion, along with the dilation of the Rindler horizon area of the quantum gravity environment, is a corollary of the causality-cancellation of the quantum gravity environment. This work was partially supported by the GOP-1.1.1-11-2012-0092 (Secure quantum key distribution between two units on optical fiber network) project sponsored by the EU and European Structural Fund, and by the COST Action MP1006.
Information conservation and entropy change in quantum measurements
Luo Shunlong
2010-11-15
The information transfer in the system-apparatus-environment trio is of fundamental importance for both the theory and practice of quantum information. Based on a canonical joint purification which encodes the system, apparatus, and environment as well as their interplay, we establish several basic relations involving various entropies arising from the most general quantum measurements. Some celebrated results concerning entropy change and information-disturbance tradeoff are recaptured as particular cases in a unified framework of information conservation.
Information-theoretical meaning of quantum-dynamical entropy
Alicki, Robert
2002-11-01
The theories of noncommutative dynamical entropy and quantum symbolic dynamics for quantum-dynamical systems are analyzed from the point of view of quantum information theory. Using a general quantum-dynamical system as a communication channel, one can define different classical capacities depending on the character of resources applied for encoding and decoding procedures and on the type of information sources. It is shown that for Bernoulli sources, the entanglement-assisted classical capacity, which is the largest one, is bounded from above by the quantum-dynamical entropy defined in terms of operational partitions of unity. Stronger results are proved for the particular class of quantum-dynamical systems--quantum Bernoulli shifts. Different classical capacities are exactly computed and the entanglement-assisted one is equal to the dynamical entropy in this case.
Quantum information entropy for one-dimensional system undergoing quantum phase transition
NASA Astrophysics Data System (ADS)
Xu-Dong, Song; Shi-Hai, Dong; Yu, Zhang
2016-05-01
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic “Landau” potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy Sx and the momentum entropy Sp at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition. Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.
The information-theoretical entropy of some quantum oscillators
Popov, D. Pop, N.; Popov, M.
2014-11-24
The Wehrl entropy or the 'classical' entropy associated with a quantum system is the entropy of the probability distribution in phase space, corresponding to the Husimi Q-function in terms of coherent states. In the present paper, we shall focus our attention on the examination of the Wehrl entropy for both the pure and the mixed (thermal) states of the pseudoharmonic oscillator (PHO). The choice of the PHO is interesting because this oscillator is an intermediate between the ideal one-dimensional harmonic oscillator (HO-1D) and the more practical anharmonicone.
Quantum information entropy and multi-qubit entanglement
NASA Astrophysics Data System (ADS)
Abdel-Aty, Mahmoud
The exciting new features of entanglement are burgeoning with revolutionary new advances in the areas of quantum communication, quantum information processing and quantum computing. We review recent theoretical studies and applications of pure and mixed states entanglement of trapped ions interacting with a laser field. After an introduction to the basic concepts of traditional entanglement measures and methodology, the main phenomena and observations of two-, three- and four-level systems are summarized. In particular, we explore the influence of the various parameters of these systems on the entanglement. The particular advantages of using atomic Wehrl entropy and Shannon entropy are highlighted. A general expression of the mixed state entanglement is obtained with the physical significance and without the diagonal approximation. Based on this result, we provide a general expression for the entanglement in a multi-level system. We show that the mixed-state and specific eigenstates of the two or three-level system posses remarkable entanglement properties that can reveal new insight into quantum correlations present in the multi-level models. Furthermore, we propose an intuitive picture of the behavior of mixed-state entanglement in the presence of the decoherence. After a short presentation of the entanglement measures of two qubits, each defined as an effective two-level system (negativity, Bures metric and concurrence) we discuss the general behaviors of the concurrence as a measure of entanglement. We identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. Most interestingly, it is shown that features of the entanglement are influenced significantly when the multi-photon process is involved.
Measuring Gaussian Quantum Information and Correlations Using the Rényi Entropy of Order 2
NASA Astrophysics Data System (ADS)
Adesso, Gerardo; Girolami, Davide; Serafini, Alessio
2012-11-01
We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.
Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.
Adesso, Gerardo; Girolami, Davide; Serafini, Alessio
2012-11-01
We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy. PMID:23215368
NASA Astrophysics Data System (ADS)
Hansen, Frank
2016-06-01
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We present a truly elementary proof of this fact in the context of the broader family of matrix entropies introduced by Chen and Tropp.
Note on entropies for quantum dynamical systems.
Watanabe, Noboru
2016-05-28
Quantum entropy and channel are fundamental concepts for quantum information theory progressed recently in various directions. We will review the fundamental aspects of mean entropy and mean mutual entropy and calculate them for open system dynamics. PMID:27091165
Quantum information: Jaynes and Shannon entropies in a two-electron entangled artificial atom
Amovilli, Claudio; March, Norman H.
2004-05-01
In the context of quantum information, both Shannon entropy and the different Jaynes entropy for a two-electron 'entangled artificial' atom proposed by Moshinsky are studied here. The Jaynes entropy in this model is shown to be intimately related to the correlation kinetic energy. A generalization of the customary Shannon entropy based on the electron density is then proposed in terms of the electron pair correlation function. Both definitions behave in a similar way to the Jaynes entropy when considered as a function of the strength of the model electron-electron interaction.
Fisher information, Rényi entropy power and quantum phase transition in the Dicke model
NASA Astrophysics Data System (ADS)
Nagy, Á.; Romera, E.
2012-07-01
Fisher information, Rényi entropy power and Fisher-Rényi information product are presented for the Dicke model. There is a quantum phase transition in this quantum optical model. It is pointed out that there is an abrupt change in the Fisher information, Rényi entropy power, the Fisher, Shannon and Rényi lengths at the transition point. It is found that these quantities diverge as the characteristic length: | around the critical value of the coupling strength λc for any value of the parameter β.
State Ensembles and Quantum Entropy
NASA Astrophysics Data System (ADS)
Kak, Subhash
2016-06-01
This paper considers quantum communication involving an ensemble of states. Apart from the von Neumann entropy, it considers other measures one of which may be useful in obtaining information about an unknown pure state and another that may be useful in quantum games. It is shown that under certain conditions in a two-party quantum game, the receiver of the states can increase the entropy by adding another pure state.
Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics
Caticha, Ariel; Bartolomeo, Daniel; Reginatto, Marcel
2015-01-13
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the 'quantum potential' that leads to the Schrödinger equation follows naturally from information geometry.
Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics
NASA Astrophysics Data System (ADS)
Caticha, Ariel; Bartolomeo, Daniel; Reginatto, Marcel
2015-01-01
Entropic Dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. There is no underlying action principle. Instead, the dynamics is driven by entropy subject to the appropriate constraints. In this paper we show how a Hamiltonian dynamics arises as a type of non-dissipative entropic dynamics. We also show that the particular form of the "quantum potential" that leads to the Schrödinger equation follows naturally from information geometry.
NASA Astrophysics Data System (ADS)
Santos, A. P.; Silva, R.; Alcaniz, J. S.; Anselmo, D. H. A. L.
2011-08-01
A deduction of generalized quantum entropies within the Tsallis and Kaniadakis frameworks is derived using a generalization of the ordinary multinomial coefficient. This generalization is based on the respective deformed multiplication and division. We show that the two above entropies are consistent with ones arbitrarily assumed at other contexts.
Quantum Computation and Quantum Information
NASA Astrophysics Data System (ADS)
Nielsen, Michael A.; Chuang, Isaac L.
2010-12-01
Part I. Fundamental Concepts: 1. Introduction and overview; 2. Introduction to quantum mechanics; 3. Introduction to computer science; Part II. Quantum Computation: 4. Quantum circuits; 5. The quantum Fourier transform and its application; 6. Quantum search algorithms; 7. Quantum computers: physical realization; Part III. Quantum Information: 8. Quantum noise and quantum operations; 9. Distance measures for quantum information; 10. Quantum error-correction; 11. Entropy and information; 12. Quantum information theory; Appendices; References; Index.
Quantum chaos: An entropy approach
NASA Astrophysics Data System (ADS)
Sl/omczyński, Wojciech; Życzkowski, Karol
1994-11-01
A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov-Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS-entropy of the corresponding classical map. ``Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.'' John Milton, Paradise Lost, Book II
ERIC Educational Resources Information Center
Ben-Naim, Arieh
2011-01-01
Changes in entropy can "sometimes" be interpreted in terms of changes in disorder. On the other hand, changes in entropy can "always" be interpreted in terms of changes in Shannon's measure of information. Mixing and demixing processes are used to highlight the pitfalls in the association of entropy with disorder. (Contains 3 figures.)
Dehesa, J.S.; Martinez-Finkelshtein, A.; Sorokin, V.N.
2002-12-01
The asymptotics of the Boltzmann-Shannon information entropy as well as the Renyi entropy for the quantum probability density of a single-particle system with a confining (i.e., bounded below) power-type potential V(x)=x{sup 2k} with k is a member of N and x is a member of R, is investigated in the position and momentum spaces within the semiclassical (WKB) approximation. It is found that for highly excited states both physical entropies, as well as their sum, have a logarithmic dependence on its quantum number not only when k=1 (harmonic oscillator), but also for any fixed k. As a by-product, the extremal case k{yields}{infinity} (the infinite well potential) is also rigorously analyzed. It is shown that not only the position-space entropy has the same constant value for all quantum states, which is a known result, but also that the momentum-space entropy is constant for highly excited states.
Monotonicity of the unified quantum ( r, s)-entropy and ( r, s)-mutual information
NASA Astrophysics Data System (ADS)
Fan, Ya-Jing; Cao, Huai-Xin
2015-12-01
Monotonicity of the unified quantum ( r, s)-entropy Ers(ρ ) and the unified quantum ( r, s)-mutual information Irs(ρ ) is discussed in this paper. Some basic properties of them are explored, and the following conclusions are established. (1) For any 0
On variational definition of quantum entropy
Belavkin, Roman V.
2015-01-13
Entropy of distribution P can be defined in at least three different ways: 1) as the expectation of the Kullback-Leibler (KL) divergence of P from elementary δ-measures (in this case, it is interpreted as expected surprise); 2) as a negative KL-divergence of some reference measure ν from the probability measure P; 3) as the supremum of Shannon’s mutual information taken over all channels such that P is the output probability, in which case it is dual of some transportation problem. In classical (i.e. commutative) probability, all three definitions lead to the same quantity, providing only different interpretations of entropy. In non-commutative (i.e. quantum) probability, however, these definitions are not equivalent. In particular, the third definition, where the supremum is taken over all entanglements of two quantum systems with P being the output state, leads to the quantity that can be twice the von Neumann entropy. It was proposed originally by V. Belavkin and Ohya [1] and called the proper quantum entropy, because it allows one to define quantum conditional entropy that is always non-negative. Here we extend these ideas to define also quantum counterpart of proper cross-entropy and cross-information. We also show inequality for the values of classical and quantum information.
Entropies and correlations in classical and quantum systems
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.; Man'ko, Vladimir I.; Marmo, Giuseppe
2016-09-01
We present a review of entropy properties for classical and quantum systems including Shannon entropy, von Neumann entropy, Rényi entropy, and Tsallis entropy. We discuss known and new entropic and information inequalities for classical and quantum systems, both composite and noncomposite. We demonstrate matrix inequalities associated with the entropic subadditivity and strong subadditivity conditions and give a new inequality for matrix elements of unitary matrices.
Quantum information entropies for position-dependent mass Schrödinger problem
Yañez-Navarro, G.; Sun, Guo-Hua; Dytrych, T.; Launey, K.D.; Dong, Shi-Hai; Draayer, J.P.
2014-09-15
The Shannon entropy for the position-dependent Schrödinger equation for a particle with a nonuniform solitonic mass density is evaluated in the case of a trivial null potential. The position S{sub x} and momentum S{sub p} information entropies for the three lowest-lying states are calculated. In particular, for these states, we are able to derive analytical solutions for the S{sub x} entropy as well as for the Fourier transformed wave functions, while the S{sub p} quantity is calculated numerically. We notice the behavior of the S{sub x} entropy, namely, it decreases as the mass barrier width narrows and becomes negative beyond a particular width. The negative Shannon entropy exists for the probability densities that are highly localized. The mass barrier determines the stability of the system. The dependence of S{sub p} on the width is contrary to the one for S{sub x}. Some interesting features of the information entropy densities ρ{sub s}(x) and ρ{sub s}(p) are demonstrated. In addition, the Bialynicki-Birula–Mycielski (BBM) inequality is tested for a number of states and found to hold for all the cases.
Quantum entanglement and entropy in particle creation
Lin, S.-Y.; Chou, C.-H.; Hu, B. L.
2010-04-15
We investigate the basic theoretical issues in the quantum entanglement of particle pairs created from the vacuum in a time-dependent background field or spacetime. Similar to entropy generation from these processes which depends on the choice of physical variables and how certain information is coarse grained, entanglement dynamics hinges on the choice of measurable quantities and how the two parties are selected as well as the background dynamics of the field or spacetime. We discuss the conditions of separability of quantum states in particle creation processes and point out the differences in how the von Neumann entropy is used as a measure of entropy generation versus for entanglement dynamics. We show by an explicit construction that adoption of a different set of physical variables yields a different entanglement entropy. As an application of these theoretical considerations we show how the particle number and the quantum phase enter the entanglement dynamics in cosmological particle production.
Applications of quantum entropy to statistics
Silver, R.N.; Martz, H.F.
1994-07-01
This paper develops two generalizations of the maximum entropy (ME) principle. First, Shannon classical entropy is replaced by von Neumann quantum entropy to yield a broader class of information divergences (or penalty functions) for statistics applications. Negative relative quantum entropy enforces convexity, positivity, non-local extensivity and prior correlations such as smoothness. This enables the extension of ME methods from their traditional domain of ill-posed in-verse problems to new applications such as non-parametric density estimation. Second, given a choice of information divergence, a combination of ME and Bayes rule is used to assign both prior and posterior probabilities. Hyperparameters are interpreted as Lagrange multipliers enforcing constraints. Conservation principles are proposed to act statistical regularization and other hyperparameters, such as conservation of information and smoothness. ME provides an alternative to heirarchical Bayes methods.
Quantum jumps and entropy production
Breuer, Heinz-Peter
2003-09-01
The irreversible motion of an open quantum system can be represented through an ensemble of state vectors following a stochastic dynamics with piecewise deterministic paths. It is shown that this representation leads to a natural definition of the rate of quantum entropy production. The entropy production rate is expressed in terms of the von Neumann entropy and of the numbers of quantum jumps corresponding to the various decay channels of the open system. The proof of the positivity and of the convexity of the entropy production rate is given. Monte Carlo simulations of the stochastic dynamics of a driven qubit and of a {lambda} configuration involving a dark state are performed in order to illustrate the general theory.
Entropy of quantum states: Ambiguities
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; de Queiroz, A. R.; Vaidya, S.
2013-10-01
The von Neumann entropy of a generic quantum state is not unique unless the state can be uniquely decomposed as a sum of extremal or pure states. As pointed out to us by Sorkin, this happens if the GNS representation (of the algebra of observables in some quantum state) is reducible, and some representations in the decomposition occur with non-trivial degeneracy. This non-unique entropy can occur at zero temperature. We will argue elsewhere in detail that the degeneracies in the GNS representation can be interpreted as an emergent broken gauge symmetry, and play an important role in the analysis of emergent entropy due to non-Abelian anomalies. Finally, we establish the analogue of an H -theorem for this entropy by showing that its evolution is Markovian, determined by a stochastic matrix.
On quantum Rényi entropies: A new generalization and some properties
NASA Astrophysics Data System (ADS)
Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco
2013-12-01
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
On quantum Rényi entropies: A new generalization and some properties
Müller-Lennert, Martin; Dupuis, Frédéric; Szehr, Oleg; Fehr, Serge; Tomamichel, Marco
2013-12-15
The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.
Entropy distance: New quantum phenomena
Weis, Stephan; Knauf, Andreas
2012-10-15
We study a curve of Gibbsian families of complex 3 Multiplication-Sign 3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance, and non-exposed faces of the mean value set. We analyze these problems from various aspects including convex geometry, topology, and information geometry. This research is motivated by a theory of infomax principles, where we contribute by computing first order optimality conditions of the entropy distance.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Quantum Kaniadakis entropy under projective measurement
NASA Astrophysics Data System (ADS)
Ourabah, Kamel; Hamici-Bendimerad, Amel Hiba; Tribeche, Mouloud
2015-09-01
It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property.
Quantum Kaniadakis entropy under projective measurement.
Ourabah, Kamel; Hamici-Bendimerad, Amel Hiba; Tribeche, Mouloud
2015-09-01
It is well known that the von Neumann entropy of a quantum state does not decrease with a projective measurement. This property holds for Tsallis and Rényi entropies as well. We show that the recently introduced quantum version of the Kaniadakis entropy preserves this property. PMID:26465433
Quantum algorithm for SAT problem andquantum mutual entropy
NASA Astrophysics Data System (ADS)
Ohya, Masanori
2005-02-01
It is von Neumann who opened the window for today's information epoch. He definedquantum entropy including Shannon's information more than 20 years ahead of Shannon, and he explained what computation means mathematically. In this paper I discuss two problems studied recently by me and my coworkers. One of them concerns a quantum algorithm in a generalized sense solving the SAT problem (one of NP complete problems) and another concerns quantum mutual entropy properly describing quantum communication processes.
NASA Astrophysics Data System (ADS)
Caticha, Ariel
2007-11-01
What is information? Is it physical? We argue that in a Bayesian theory the notion of information must be defined in terms of its effects on the beliefs of rational agents. Information is whatever constrains rational beliefs and therefore it is the force that induces us to change our minds. This problem of updating from a prior to a posterior probability distribution is tackled through an eliminative induction process that singles out the logarithmic relative entropy as the unique tool for inference. The resulting method of Maximum relative Entropy (ME), which is designed for updating from arbitrary priors given information in the form of arbitrary constraints, includes as special cases both MaxEnt (which allows arbitrary constraints) and Bayes' rule (which allows arbitrary priors). Thus, ME unifies the two themes of these workshops—the Maximum Entropy and the Bayesian methods—into a single general inference scheme that allows us to handle problems that lie beyond the reach of either of the two methods separately. I conclude with a couple of simple illustrative examples.
Quantum collapse rules from the maximum relative entropy principle
NASA Astrophysics Data System (ADS)
Hellmann, Frank; Kamiński, Wojciech; Paweł Kostecki, Ryszard
2016-01-01
We show that the von Neumann-Lüders collapse rules in quantum mechanics always select the unique state that maximises the quantum relative entropy with respect to the premeasurement state, subject to the constraint that the postmeasurement state has to be compatible with the knowledge gained in the measurement. This way we provide an information theoretic characterisation of quantum collapse rules by means of the maximum relative entropy principle.
Information entropy of multi-qubit Rabi system
NASA Astrophysics Data System (ADS)
Abo-Kahla, D. A. M.; Abdel-Aty, M.
2015-09-01
We consider quantum information entropy phenomenon for multi-qubit Rabi system. By introducing different measurements schemes, we establish the relation between information entropy approach and Von Neumann entropy. It is shown that the information entropy is more sensitive to the time development than the Von Neumann entropy. Furthermore, the suggested protocol exhibits excellent scaling of relevant characteristics, with respect to population dynamics, such that more accurate dynamical results may be obtained using information entropy due to variation of the frequency detuning and the coupling constant.
NASA Astrophysics Data System (ADS)
Zhou, Tianci; Chen, Xiao; Fradkin, Eduardo
We investigate the entanglement entropy(EE) of circular entangling surfaces in the 2+1d quantum Lifshitz model, where the spatially conformal invariant ground state is a Rokhsar-Kivelson state with Gibbs weight of 2d free Boson. We use cut-off independent mutual information regulator to define and calculate the subleading correction in the EE. The subtlety due to the Boson compactification in the replica trick is carefully taken care of. Our results show that for circular entangling surface, the subleading term is a constant on both the sphere of arbitrary radius and infinite plane. For the latter case, it parallels the constancy of disk EE in 2+1d conformal field theory, despite the lack of full space time conformal invariance. In the end, we present the mutual information of two disjoint disks and compare its scaling function in the small parameter regime (radii much smaller than their separation) with Cardy's general CFT results. This work was supported in part by the National Science Foundation Grants NSF-DMR-13-06011(TZ) and DMR-1408713 (XC, EF).
Black hole entropy in canonical quantum gravity and superstring theory
Susskind, L.; Uglum, J. )
1994-08-15
In this paper the entropy of an eternal Schwarzschild black hole is studied in the limit of an infinite black hole mass. The problem is addressed from the point of view of both canonical quantum gravity and superstring theory. The entropy per unit area of a free scalar field propagating in a fixed black hole background is shown to be quadratically divergent near the horizon. It is shown that such quantum corrections to the entropy per unit area are equivalent to the quantum corrections to the gravitational coupling. Unlike field theory, superstring theory provides a set of identifiable configurations which give rise to the classical contribution to the entropy per unit area. These configurations can be understood as open superstrings with both ends attached to the horizon. The entropy per unit area is shown to be finite to all orders in superstring perturbation theory. The importance of these conclusions to the resolution of the problem of black hole information loss is reiterated.
Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Rispoli, Matthew; Preiss, Philipp; Tai, Eric; Lukin, Alex; Schittko, Robert; Kaufman, Adam; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2016-05-01
The presence of large-scale entanglement is a defining characteristic of exotic quantum phases of matter. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. However, measuring entanglement remains a challenge. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. We demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. This protocol enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. In general, these experiments exemplify a method enabling the measurement and characterization of quantum phase transitions and in particular would be apt for studying systems such as magnetic ordering within the quantum Ising model.
Entropy flow in quantum heat engines
NASA Astrophysics Data System (ADS)
Ansari, Mohammad; Nazarov, Yuli
2015-03-01
We evaluate Shannon and Renyi entropy flows from generic quantum heat engines (QHE) to a weakly-coupled probe environment kept in thermal equilibrium. We show the flows are determined by two quantities: heat flow and fictitious dissipation that manifest the quantum coherence in the engine. Our theory leads to novel physics in quantum heat engines.
Finiteness of entanglement entropy in a quantum black hole
NASA Astrophysics Data System (ADS)
Wen, Wen-Yu
2016-03-01
A logarithmic but divergent term usually appears in the computation of entanglement entropy circumferencing a black hole, while the leading quantum correction to the Bekenstein-Hawking entropy also takes the logarithmic form. A quench model of CFT within finite Euclidean time was proposed by Kuwakino and Wen (JHEP, 05 (2015) 099) to regard this logarithmic term as entanglement between radiation and the black hole, and this proposal was justified by the alternative sign for n-partite quantum information. However, this preliminary form suffers from the notorious divergence at its low-temperature limit. In this letter, we propose a modified form for black-hole entanglement entropy such that the divergence sickness can be cured. We discuss the final stage of a black hole due to this modification and its relation to the Rényi entropy, higher-loop quantum correction and higher-spin black holes.
Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces
Benatti, Fabio; Oskouei, Samad Khabbazi Deh Abad, Ahmad Shafiei
2014-08-15
We extend the notion of Gacs quantum algorithmic entropy, originally formulated for finitely many qubits, to infinite dimensional quantum spin chains and investigate the relation of this extension with two quantum dynamical entropies that have been proposed in recent years.
Quantum statistical entropy of Schwarzchild-de Sitter spacetime
NASA Astrophysics Data System (ADS)
Zhao, Ren; Zhang, Li-Chun; Zhao, Hui-Hua
2012-10-01
Using the quantum statistical method, we calculate quantum statistical entropy between the black hole horizon and the cosmological horizon in Schwarzchild spacetime and derive the expression of quantum statistical entropy in de Sitter spacetime. Under the Unruh-Verlinde temperature of Schwarzchild-de Sitter spacetime in the entropic force views, we obtain the expression of quantum statistical entropy in de Sitter spacetime. It is shown that in de Sitter spacetime quantum statistical entropy is the sum of thermodynamic entropy corresponding black hole horizon and the one corresponding cosmological horizon. And the correction term of de Sitter spacetime entropy is obtained. Therefore, it is confirmed that the black hole entropy is the entropy of quantum field outside the black hole horizon. The entropy of de Sitter spacetime is the entropy of quantum field between the black hole horizon and the cosmological horizon.
Entropy production of doubly stochastic quantum channels
NASA Astrophysics Data System (ADS)
Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.
2016-02-01
We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
Quantum Rényi relative entropies affirm universality of thermodynamics.
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A K
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory. PMID:26565222
Quantum Rényi relative entropies affirm universality of thermodynamics
NASA Astrophysics Data System (ADS)
Misra, Avijit; Singh, Uttam; Bera, Manabendra Nath; Rajagopal, A. K.
2015-10-01
We formulate a complete theory of quantum thermodynamics in the Rényi entropic formalism exploiting the Rényi relative entropies, starting from the maximum entropy principle. In establishing the first and second laws of quantum thermodynamics, we have correctly identified accessible work and heat exchange in both equilibrium and nonequilibrium cases. The free energy (internal energy minus temperature times entropy) remains unaltered, when all the entities entering this relation are suitably defined. Exploiting Rényi relative entropies we have shown that this "form invariance" holds even beyond equilibrium and has profound operational significance in isothermal process. These results reduce to the Gibbs-von Neumann results when the Rényi entropic parameter α approaches 1. Moreover, it is shown that the universality of the Carnot statement of the second law is the consequence of the form invariance of the free energy, which is in turn the consequence of maximum entropy principle. Further, the Clausius inequality, which is the precursor to the Carnot statement, is also shown to hold based on the data processing inequalities for the traditional and sandwiched Rényi relative entropies. Thus, we find that the thermodynamics of nonequilibrium state and its deviation from equilibrium together determine the thermodynamic laws. This is another important manifestation of the concepts of information theory in thermodynamics when they are extended to the quantum realm. Our work is a substantial step towards formulating a complete theory of quantum thermodynamics and corresponding resource theory.
NASA Astrophysics Data System (ADS)
Winter, Andreas
2016-03-01
We present a bouquet of continuity bounds for quantum entropies, falling broadly into two classes: first, a tight analysis of the Alicki-Fannes continuity bounds for the conditional von Neumann entropy, reaching almost the best possible form that depends only on the system dimension and the trace distance of the states. Almost the same proof can be used to derive similar continuity bounds for the relative entropy distance from a convex set of states or positive operators. As applications, we give new proofs, with tighter bounds, of the asymptotic continuity of the relative entropy of entanglement, E R , and its regularization {E_R^{∞}} , as well as of the entanglement of formation, E F . Using a novel "quantum coupling" of density operators, which may be of independent interest, we extend the latter to an asymptotic continuity bound for the regularized entanglement of formation, aka entanglement cost, {E_C=E_F^{∞}} . Second, we derive analogous continuity bounds for the von Neumann entropy and conditional entropy in infinite dimensional systems under an energy constraint, most importantly systems of multiple quantum harmonic oscillators. While without an energy bound the entropy is discontinuous, it is well-known to be continuous on states of bounded energy. However, a quantitative statement to that effect seems not to have been known. Here, under some regularity assumptions on the Hamiltonian, we find that, quite intuitively, the Gibbs entropy at the given energy roughly takes the role of the Hilbert space dimension in the finite-dimensional Fannes inequality.
Entropy for quantum pure states and quantum H theorem.
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)]. 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. PMID:26172660
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.
Coherent Informational Energy and Entropy.
ERIC Educational Resources Information Center
Avramescu, Aurel
1980-01-01
Seeks to provide a common theoretical foundation for all known bibliometric laws by assimilating a systemic view of the information transfer process with a thermodynamic process, i.e., the conduction of heat in solids. The resulting diffusion model establishes new definitions for informational energy and entropy consistent with corresponding…
Quantum-state reconstruction by maximizing likelihood and entropy.
Teo, Yong Siah; Zhu, Huangjun; Englert, Berthold-Georg; Řeháček, Jaroslav; Hradil, Zdeněk
2011-07-01
Quantum-state reconstruction on a finite number of copies of a quantum system with informationally incomplete measurements, as a rule, does not yield a unique result. We derive a reconstruction scheme where both the likelihood and the von Neumann entropy functionals are maximized in order to systematically select the most-likely estimator with the largest entropy, that is, the least-bias estimator, consistent with a given set of measurement data. This is equivalent to the joint consideration of our partial knowledge and ignorance about the ensemble to reconstruct its identity. An interesting structure of such estimators will also be explored. PMID:21797584
Information entropies of many-electron systems
Yanez, R.J.; Angulo, J.C.; Dehesa, J.S.
1995-12-05
The Boltzmann-Shannon (BS) information entropy S{sub {rho}} = - {integral} {rho}(r)log {rho}(r) dr measures the spread or extent of the one-electron density {rho}(r), which is the basic variable of the density function theory of the many electron systems. This quantity cannot be analytically computed, not even for simple quantum mechanical systems such as, e.g., the harmonic oscillator (HO) and the hydrogen atom (HA) in arbitrary excited states. Here, we first review (i) the present knowledge and open problems in the analytical determination of the BS entropies for the HO and HA systems in both position and momentum spaces and (ii) the known rigorous lower and upper bounds to the position and momentum BS entropies of many-electron systems in terms of the radial expectation values in the corresponding space. Then, we find general inequalities which relate the BS entropies and various density functionals. Particular cases of these results are rigorous relationships of the BS entropies and some relevant density functionals (e.g., the Thomas-Fermi kinetic energy, the Dirac-Slater exchange energy, the average electron density) for finite many-electron systems. 28 refs.
Dissipation and entropy production in open quantum systems
NASA Astrophysics Data System (ADS)
Majima, H.; Suzuki, A.
2010-11-01
A microscopic description of an open system is generally expressed by the Hamiltonian of the form: Htot = Hsys + Henviron + Hsys-environ. We developed a microscopic theory of entropy and derived a general formula, so-called "entropy-Hamiltonian relation" (EHR), that connects the entropy of the system to the interaction Hamiltonian represented by Hsys-environ for a nonequilibrium open quantum system. To derive the EHR formula, we mapped the open quantum system to the representation space of the Liouville-space formulation or thermo field dynamics (TFD), and thus worked on the representation space Script L := Script H otimes , where Script H denotes the ordinary Hilbert space while the tilde Hilbert space conjugates to Script H. We show that the natural transformation (mapping) of nonequilibrium open quantum systems is accomplished within the theoretical structure of TFD. By using the obtained EHR formula, we also derived the equation of motion for the distribution function of the system. We demonstrated that by knowing the microscopic description of the interaction, namely, the specific form of Hsys-environ on the representation space Script L, the EHR formulas enable us to evaluate the entropy of the system and to gain some information about entropy for nonequilibrium open quantum systems.
Measuring entanglement entropy in a quantum many-body system
NASA Astrophysics Data System (ADS)
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M.; Eric Tai, M.; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems. PMID:26632587
Joint entropy of quantum damped harmonic oscillators
NASA Astrophysics Data System (ADS)
Aguiar, V.; Guedes, I.
2014-05-01
We use the dynamical invariant method and a unitary transformation to obtain the exact Schrödinger wave function, ψn(x,t), and calculate for n=0 the time-dependent joint entropy (Leipnik’s entropy) for two classes of quantum damped harmonic oscillators. We observe that the joint entropy does not vary in time for the Caldirola-Kanai oscillator, while it decreases and tends to a constant value (ln({e}/{2})) for asymptotic times for the Lane-Emden ones. This is due to the fact that for the latter, the damping factor decreases as time increases. The results show that the time dependence of the joint entropy is quite complex and does not obey a general trend of monotonously increase with time.
Horizon Entropy from Quantum Gravity Condensates
NASA Astrophysics Data System (ADS)
Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo
2016-05-01
We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one.
Horizon Entropy from Quantum Gravity Condensates.
Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo
2016-05-27
We construct condensate states encoding the continuum spherically symmetric quantum geometry of a horizon in full quantum gravity, i.e., without any classical symmetry reduction, in the group field theory formalism. Tracing over the bulk degrees of freedom, we show how the resulting reduced density matrix manifestly exhibits a holographic behavior. We derive a complete orthonormal basis of eigenstates for the reduced density matrix of the horizon and use it to compute the horizon entanglement entropy. By imposing consistency with the horizon boundary conditions and semiclassical thermodynamical properties, we recover the Bekenstein-Hawking entropy formula for any value of the Immirzi parameter. Our analysis supports the equivalence between the von Neumann (entanglement) entropy interpretation and the Boltzmann (statistical) one. PMID:27284642
Computing Entanglement Entropy in Quantum Monte Carlo
NASA Astrophysics Data System (ADS)
Melko, Roger
2012-02-01
The scaling of entanglement entropy in quantum many-body wavefunctions is expected to be a fruitful resource for studying quantum phases and phase transitions in condensed matter. However, until the recent development of estimators for Renyi entropy in quantum Monte Carlo (QMC), we have been in the dark about the behaviour of entanglement in all but the simplest two-dimensional models. In this talk, I will outline the measurement techniques that allow access to the Renyi entropies in several different QMC methodologies. I will then discuss recent simulation results demonstrating the richness of entanglement scaling in 2D, including: the prevalence of the ``area law''; topological entanglement entropy in a gapped spin liquid; anomalous subleading logarithmic terms due to Goldstone modes; universal scaling at critical points; and examples of emergent conformal-like scaling in several gapless wavefunctions. Finally, I will explore the idea that ``long range entanglement'' may complement the notion of ``long range order'' for quantum phases and phase transitions which lack a conventional order parameter description.
Black holes, entropies, and semiclassical spacetime in quantum gravity
NASA Astrophysics Data System (ADS)
Nomura, Yasunori; Weinberg, Sean J.
2014-10-01
We present a coherent picture of the quantum mechanics of black holes. The picture does not require the introduction of any drastically new physical effect beyond what is already known; it arises mostly from synthesizing and (re)interpreting existing results in appropriate manners. We identify the Bekenstein-Hawking entropy as the entropy associated with coarse-graining performed to obtain semiclassical field theory from a fundamental microscopic theory of quantum gravity. This clarifies the issues around the unitary evolution, the existence of the interior spacetime, and the thermodynamic nature in black hole physics — any result in semiclassical field theory is a statement about the maximally mixed ensemble of microscopic quantum states consistent with the specified background, within the precision allowed by quantum mechanics. We present a detailed analysis of information transfer in Hawking emission and black hole mining processes, clarifying what aspects of the underlying dynamics are (not) visible in semiclassical field theory. We also discuss relations between the black hole entropy and the entanglement entropy across the horizon. We then extend our discussions to more general contexts in quantum gravity. The subjects include extensions to de Sitter and Minkowski spaces and implications for complementarity and cosmology, especially the eternally inflating multiverse.
NASA Astrophysics Data System (ADS)
Zhang, Lin
2016-04-01
We derive a strengthened monotonicity inequality for quantum relative entropy by employing properties of {α}-Rényi relative entropy. We develop a unifying treatment toward the improvement of some quantum entropy inequalities. In particular, an emphasis is put on a lower bound of quantum conditional mutual information (QCMI) as it gives a Pinsker-like lower bound for the QCMI. We also give some improved entropy inequalities based on Rényi relative entropy. The inequalities obtained, thus, extend some well-known ones. We also obtain a condition under which a tripartite operator becomes a Markov state. As a by-product we provide some trace inequalities of operators, which are of independent interest.
Entropy and information causality in general probabilistic theories
NASA Astrophysics Data System (ADS)
Barnum, Howard; Barrett, Jonathan; Orloff Clark, Lisa; Leifer, Matthew; Spekkens, Robert; Stepanik, Nicholas; Wilce, Alex; Wilke, Robin
2010-03-01
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality (IC) recently proposed by Pawlowski et al (2009 arXiv:0905.2292). We consider two entropic quantities, which we term measurement and mixing entropy. In the context of classical and quantum theory, these coincide, being given by the Shannon and von Neumann entropies, respectively; in general, however, they are very different. In particular, while measurement entropy is easily seen to be concave, mixing entropy need not be. In fact, as we show, mixing entropy is not concave whenever the state space is a non-simplicial polytope. Thus, the condition that measurement and mixing entropies coincide is a strong constraint on possible theories. We call theories with this property monoentropic. Measurement entropy is subadditive, but not in general strongly subadditive. Equivalently, if we define the mutual information between two systems A and B by the usual formula I(A: B)=H(A)+H(B)-H(AB), where H denotes the measurement entropy and AB is a non-signaling composite of A and B, then it can happen that I(A:BC)entropy is strongly subadditive, and also satisfies a version of the Holevo bound, is informationally causal, and on the other hand we observe that Popescu-Rohrlich boxes, which violate IC, also violate strong subadditivity. We also explore the interplay between measurement and mixing entropy and various natural conditions on theories that arise in quantum axiomatics.
Quantum Statistical Entropy of Five-Dimensional Black Hole
NASA Astrophysics Data System (ADS)
Zhao, Ren; Wu, Yue-Qin; Zhang, Sheng-Li
2006-05-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
Covariant entropy bound and loop quantum cosmology
Ashtekar, Abhay; Wilson-Ewing, Edward
2008-09-15
We examine Bousso's covariant entropy bound conjecture in the context of radiation filled, spatially flat, Friedmann-Robertson-Walker models. The bound is violated near the big bang. However, the hope has been that quantum gravity effects would intervene and protect it. Loop quantum cosmology provides a near ideal setting for investigating this issue. For, on the one hand, quantum geometry effects resolve the singularity and, on the other hand, the wave function is sharply peaked at a quantum corrected but smooth geometry, which can supply the structure needed to test the bound. We find that the bound is respected. We suggest that the bound need not be an essential ingredient for a quantum gravity theory but may emerge from it under suitable circumstances.
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.
Quantum Information and Computing
NASA Astrophysics Data System (ADS)
Accardi, L.; Ohya, Masanori; Watanabe, N.
2006-03-01
Preface -- Coherent quantum control of [symbol]-atoms through the stochastic limit / L. Accardi, S. V. Kozyrev and A. N. Pechen -- Recent advances in quantum white noise calculus / L. Accardi and A. Boukas -- Control of quantum states by decoherence / L. Accardi and K. Imafuku -- Logical operations realized on the Ising chain of N qubits / M. Asano, N. Tateda and C. Ishii -- Joint extension of states of fermion subsystems / H. Araki -- Quantum filtering and optimal feedback control of a Gaussian quantum free particle / S. C. Edwards and V. P. Belavkin -- On existence of quantum zeno dynamics / P. Exner and T. Ichinose -- Invariant subspaces and control of decoherence / P. Facchi, V. L. Lepore and S. Pascazio -- Clauser-Horner inequality for electron counting statistics in multiterminal mesoscopic conductors / L. Faoro, F. Taddei and R. Fazio -- Fidelity of quantum teleportation model using beam splittings / K.-H. Fichtner, T. Miyadera and M. Ohya -- Quantum logical gates realized by beam splittings / W. Freudenberg ... [et al.] -- Information divergence for quantum channels / S. J. Hammersley and V. P. Belavkin -- On the uniqueness theorem in quantum information geometry / H. Hasegawa -- Noncanonical representations of a multi-dimensional Brownian motion / Y. Hibino -- Some of future directions of white noise theory / T. Hida -- Information, innovation and elemental random field / T. Hida -- Generalized quantum turing machine and its application to the SAT chaos algorithm / S. Iriyama, M. Ohya and I. Volovich -- A Stroboscopic approach to quantum tomography / A. Jamiolkowski -- Positive maps and separable states in matrix algebras / A. Kossakowski -- Simulating open quantum systems with trapped ions / S. Maniscalco -- A purification scheme and entanglement distillations / H. Nakazato, M. Unoki and K. Yuasa -- Generalized sectors and adjunctions to control micro-macro transitions / I. Ojima -- Saturation of an entropy bound and quantum Markov states / D. Petz -- An
A family of generalized quantum entropies: definition and properties
NASA Astrophysics Data System (ADS)
Bosyk, G. M.; Zozor, S.; Holik, F.; Portesi, M.; Lamberti, P. W.
2016-08-01
We present a quantum version of the generalized (h,φ )-entropies, introduced by Salicrú et al. for the study of classical probability distributions. We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum (h,φ )-entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.
A family of generalized quantum entropies: definition and properties
NASA Astrophysics Data System (ADS)
Bosyk, G. M.; Zozor, S.; Holik, F.; Portesi, M.; Lamberti, P. W.
2016-05-01
We present a quantum version of the generalized (h,φ ) -entropies, introduced by Salicrú et al. for the study of classical probability distributions. We establish their basic properties and show that already known quantum entropies such as von Neumann, and quantum versions of Rényi, Tsallis, and unified entropies, constitute particular classes of the present general quantum Salicrú form. We exhibit that majorization plays a key role in explaining most of their common features. We give a characterization of the quantum (h,φ ) -entropies under the action of quantum operations and study their properties for composite systems. We apply these generalized entropies to the problem of detection of quantum entanglement and introduce a discussion on possible generalized conditional entropies as well.
Consistency of the Shannon entropy in quantum experiments
Luca Mana, Piero G.
2004-06-01
The consistency of the Shannon entropy, when applied to outcomes of quantum experiments, is analyzed. It is shown that the Shannon entropy is fully consistent and its properties are never violated in quantum settings, but attention must be paid to logical and experimental contexts. This last remark is shown to apply regardless of the quantum or classical nature of the experiments.
Misra, Avijit; Biswas, Anindya; Pati, Arun K; Sen De, Aditi; Sen, Ujjwal
2015-05-01
Quantum discord is a measure of quantum correlations beyond the entanglement-separability paradigm. It is conceptualized by using the von Neumann entropy as a measure of disorder. We introduce a class of quantum correlation measures as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies. We compare our results with those obtained by using the traditional relative entropies. We find that the measures satisfy all the plausible axioms for quantum correlations. We evaluate the measures for shared pure as well as paradigmatic classes of mixed states. We show that the measures can faithfully detect the quantum critical point in the transverse quantum Ising model and find that they can be used to remove an unquieting feature of nearest-neighbor quantum discord in this respect. Furthermore, the measures provide better finite-size scaling exponents of the quantum critical point than the ones for other known order parameters, including entanglement and information-theoretic measures of quantum correlations. PMID:26066137
Rényi entropy flows from quantum heat engines
NASA Astrophysics Data System (ADS)
Ansari, Mohammad H.; Nazarov, Yuli V.
2015-03-01
We evaluate Rényi entropy flows from generic quantum heat engines (QHE) to a weakly coupled probe environment kept in thermal equilibrium. We show that the flows are determined not only by heat flow but also by a quantum coherent flow that can be separately measured in experiment apart from the heat flow measurement. The same pertains to Shannon entropy flow. This appeals for a revision of the concept of entropy flows in quantum nonequlibrium thermodynamics.
Towards information inequalities for generalized graph entropies.
Sivakumar, Lavanya; Dehmer, Matthias
2012-01-01
In this article, we discuss the problem of establishing relations between information measures for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the Rényi entropy have been considered for this study. Our main results involve establishing formal relationships, by means of inequalities, between these two kinds of measures. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and partition-independent entropy measures. In addition, several explicit inequalities are derived for special classes of graphs. PMID:22715375
Time Dependence of Joint Entropy of Oscillating Quantum Systems
NASA Astrophysics Data System (ADS)
Özcan, Özgür; Aktürk, Ethem; Sever, Ramazan
2008-12-01
The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.
Entropy and Information: A Multidisciplinary Overview.
ERIC Educational Resources Information Center
Shaw, Debora; Davis, Charles H.
1983-01-01
Cites representative extensions of concept of entropy (measure of the amount of energy unavailable for useful work; from the second law of thermodynamics) noting basic relationships between entropy, order, information, and meaning in such disciplines as biology, economics, information science, the arts, and religion. Seventy-eight references are…
Average diagonal entropy in nonequilibrium isolated quantum systems.
Giraud, Olivier; García-Mata, Ignacio
2016-07-01
The diagonal entropy was introduced as a good entropy candidate especially for isolated quantum systems out of equilibrium. Here we present an analytical calculation of the average diagonal entropy for systems undergoing unitary evolution and an external perturbation in the form of a cyclic quench. We compare our analytical findings with numerical simulations of various quantum systems. Our calculations elucidate various heuristic relations proposed recently in the literature. PMID:27575092
Quantum Fokker-Planck-Kramers equation and entropy production
NASA Astrophysics Data System (ADS)
de Oliveira, Mário J.
2016-07-01
We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance.
Entanglement entropy in dynamic quantum-coherent conductors
NASA Astrophysics Data System (ADS)
Thomas, Konrad H.; Flindt, Christian
2015-03-01
We investigate the entanglement and the Rényi entropies of two electronic leads connected by a quantum point contact. For noninteracting electrons, the entropies can be related to the cumulants of the full counting statistics of transferred charge which in principle are measurable. We consider the entanglement entropy generated by operating the quantum point contact as a quantum switch which is opened and closed in a periodic manner. Using a numerically exact approach we analyze the conditions under which a logarithmic growth of the entanglement entropy predicted by conformal field theory should be observable in an electronic conductor. In addition, we consider clean single-particle excitations on top of the Fermi sea (levitons) generated by applying designed pulses to the leads. We identify a Hong-Ou-Mandel-like suppression of the entanglement entropy by interfering two levitons on a quantum point contact tuned to half transmission.
Replacing energy by von Neumann entropy in quantum phase transitions
Kopp, Angela; Jia Xun; Chakravarty, Sudip . E-mail: sudip@physics.ucla.edu
2007-06-15
We propose that quantum phase transitions are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a quantum phase transition.
Impact of Information Entropy on Teaching Effectiveness
ERIC Educational Resources Information Center
Wang, Zhi-guo
2007-01-01
Information entropy refers to the process in which information is sent out from the information source, transmitted through information channel and acquired by information sink, while the teaching process is the one of transmitting teaching information from teachers and teaching material to students. How to improve teaching effectiveness is…
Block entropy and quantum phase transition in the anisotropic Kondo necklace model
Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.
2010-06-15
We study the von Neumann block entropy in the Kondo necklace model for different anisotropies {eta} in the XY interaction between conduction spins using the density matrix renormalization group method. It was found that the block entropy presents a maximum for each {eta} considered, and, comparing it with the results of the quantum criticality of the model based on the behavior of the energy gap, we observe that the maximum block entropy occurs at the quantum critical point between an antiferromagnetic and a Kondo singlet state, so this measure of entanglement is useful for giving information about where a quantum phase transition occurs in this model. We observe that the block entropy also presents a maximum at the quantum critical points that are obtained when an anisotropy {Delta} is included in the Kondo exchange between localized and conduction spins; when {Delta} diminishes for a fixed value of {eta}, the critical point increases, favoring the antiferromagnetic phase.
Nonrelativistic Shannon information entropy for Kratzer potential
NASA Astrophysics Data System (ADS)
S, A. Najafizade; H, Hassanabadi; S, Zarrinkamar
2016-04-01
The Shannon information entropy is investigated within the nonrelativistic framework. The Kratzer potential is considered as the interaction and the problem is solved in a quasi-exact analytical manner to discuss the ground and first excited states. Some interesting features of the information entropy densities as well as the probability densities are demonstrated. The Bialynicki–Birula–Mycielski inequality is also tested and found to hold for these cases.
Continuity of the entropy of macroscopic quantum systems.
Swendsen, Robert H
2015-11-01
The proper definition of entropy is fundamental to the relationship between statistical mechanics and thermodynamics. It also plays a major role in the recent debate about the validity of the concept of negative temperature. In this paper, I analyze and calculate the thermodynamic entropy for large but finite quantum mechanical systems. A special feature of this analysis is that the thermodynamic energy of a quantum system is shown to be a continuous variable, rather than being associated with discrete energy eigenvalues. Calculations of the entropy as a function of energy can be carried out with a Legendre transform of thermodynamic potentials obtained from a canonical ensemble. The resultant expressions for the entropy are able to describe equilibrium between quantum systems having incommensurate energy-level spacings. This definition of entropy preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics. It demonstrates the consistency of the concept of negative temperature with the principles of thermodynamics. PMID:26651650
The conditional entropy power inequality for Gaussian quantum states
Koenig, Robert
2015-02-15
We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.
Symmetric polynomials in information theory: Entropy and subentropy
Jozsa, Richard; Mitchison, Graeme
2015-06-15
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.
Classical data compression with quantum side information
Devetak, I.; Winter, A.
2003-10-01
The problem of classical data compression when the decoder has quantum side information at his disposal is considered. This is a quantum generalization of the classical Slepian-Wolf theorem. The optimal compression rate is found to be reduced from the Shannon entropy of the source by the Holevo information between the source and side information.
Remainder terms for some quantum entropy inequalities
Carlen, Eric A.; Lieb, Elliott H.
2014-04-15
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from equality, including an improved version of Pinsker's inequality.
Entropy and predictability of information carriers.
Ebeling, W; Frömmel, C
1998-04-01
The structure of linear strings carrying information is investigated by means of entropy concepts. First conditional entropy and transinformation are introduced and several generalizations are discussed. The capability to describe the structure of information carriers as DNA, proteins, texts and musical strings is investigated. The relation between order and the predictability of informational strings is discussed. As examples we study the mutual information function of virus DNA and several long proteins. Further we show some (rather formal) analogies to the structure of texts, and strings generated by musical melodies. It is shown that several information carriers show long-range correlations. PMID:9648674
A note on quantum entropy inequalities and channel capacities
NASA Astrophysics Data System (ADS)
Fan, Heng
2003-12-01
Quantum entropy inequalities are studied. Some quantum entropy inequalities are obtained by several methods. For an entanglement breaking channel, we show that the entanglement-assisted classical capacity is upper bounded by log d. A relationship between entanglement-assisted and one-shot unassisted capacities is obtained. This relationship shows the entanglement-assisted channel capacity is upper bounded by the sum of log d and the one-shot unassisted classical capacity.
Asymptotics of information entropies of some Toda-like potentials
NASA Astrophysics Data System (ADS)
Dehesa, J. S.; Martínez-Finkelshtein, A.; Sorokin, V. N.
2003-01-01
The spreading of the quantum probability density for the highly-excited states of a single-particle system with an exponential-type potential on the positive semiaxis is quantitatively determined in both position and momentum spaces by means of the Boltzmann-Shannon information entropy. This problem boils down to the calculation of the asymptotics of the entropy-like integrals of the modified Bessel function of the second kind (also called the Mcdonald function or Basset function). The dependence of the two physical entropies on the large quantum number n is given in detail. It is shown that the semiclassical (WKB) position-space entropy grows slower than the corresponding quantity of not only the harmonic oscillator but also the single-particle systems with any power-type potential of the form V(x)=x2k, x∈R and k∈N. The momentum-space entropy, calculated with a method based on the properties of the Mcdonald function, is rigorously found to have a behavior of the form -ln ln n, in strong contrast with the corresponding quantity of other one-dimensional systems known up to now (power-type potentials, infinite well).
On determining absolute entropy without quantum theory or the third law of thermodynamics
NASA Astrophysics Data System (ADS)
Steane, Andrew M.
2016-04-01
We employ classical thermodynamics to gain information about absolute entropy, without recourse to statistical methods, quantum mechanics or the third law of thermodynamics. The Gibbs–Duhem equation yields various simple methods to determine the absolute entropy of a fluid. We also study the entropy of an ideal gas and the ionization of a plasma in thermal equilibrium. A single measurement of the degree of ionization can be used to determine an unknown constant in the entropy equation, and thus determine the absolute entropy of a gas. It follows from all these examples that the value of entropy at absolute zero temperature does not need to be assigned by postulate, but can be deduced empirically.
Quantum state tomography with incomplete data: Maximum entropy and variational quantum tomography
NASA Astrophysics Data System (ADS)
Gonçalves, D. S.; Lavor, C.; Gomes-Ruggiero, M. A.; Cesário, A. T.; Vianna, R. O.; Maciel, T. O.
2013-05-01
Whenever we do not have an informationally complete set of measurements, the estimate of a quantum state cannot be uniquely determined. In this case, among the density matrices compatible with the available data, the one commonly preferred is the one which is the most uncommitted to the missing information. This is the purpose of the maximum entropy estimation (MaxEnt) and the variational quantum tomography (VQT). Here, we propose a variant of VQT and show its relationship with MaxEnt methods in quantum tomographies with an incomplete set of measurements. We prove their equivalence in the case of eigenbasis measurements, and through numerical simulations we stress their similar behavior. Hence, in the modified VQT formulation we have an estimate of a quantum state as unbiased as in MaxEnt and with the benefit that VQT can be more efficiently solved by means of linear semidefinite programs.
Universal Entanglement Entropy in 2D Conformal Quantum Critical Points
Hsu, Benjamin; Mulligan, Michael; Fradkin, Eduardo; Kim, Eun-Ah
2008-12-05
We study the scaling behavior of the entanglement entropy of two dimensional conformal quantum critical systems, i.e. systems with scale invariant wave functions. They include two-dimensional generalized quantum dimer models on bipartite lattices and quantum loop models, as well as the quantum Lifshitz model and related gauge theories. We show that, under quite general conditions, the entanglement entropy of a large and simply connected sub-system of an infinite system with a smooth boundary has a universal finite contribution, as well as scale-invariant terms for special geometries. The universal finite contribution to the entanglement entropy is computable in terms of the properties of the conformal structure of the wave function of these quantum critical systems. The calculation of the universal term reduces to a problem in boundary conformal field theory.
Investigate the entanglement of a quintuple quantum dot molecule via entropy
NASA Astrophysics Data System (ADS)
Arzhang, B.; Mehmannavaz, M. R.; Rezaei, M.
2015-12-01
The time evaluation of quantum entropy in the quintuple-coupled quantum dots based on a GaAs/AlGaAs heterostructure is theoretically investigated. The quantum entanglement of quantum dot molecules (QDMs) and their spontaneous emission fields is then discussed via quantum entropy. The effects of the tunneling effect, i.e. T , an incoherent pumping field and voltage controllable detuning on entanglement between QDMs and their spontaneous emission fields is then discussed. We found that in the presence of the tunneling effect and an incoherent pumping field the entanglement between the QDMs and their spontaneous emission fields is increased, while in the presence of voltage controllable detuning the entanglement reduced. Finally, we investigated the switching time from a disentangled state to an entangled state. The results may provide some new possibilities for technological applications in optoelectronics, solid-state quantum information science, quantum computing, teleportation, encryption, and compression codec.
Comparison of quantum discord and relative entropy in some bipartite quantum systems
NASA Astrophysics Data System (ADS)
Mahdian, M.; Arjmandi, M. B.
2016-04-01
The study of quantum correlations in high-dimensional bipartite systems is crucial for the development of quantum computing. We propose relative entropy as a distance measure of correlations may be measured by means of the distance from the quantum state to the closest classical-classical state. In particular, we establish relations between relative entropy and quantum discord quantifiers obtained by means of orthogonal projection measurements. We show that for symmetrical X-states density matrices the quantum discord is equal to relative entropy. At the end of paper, various examples of X-states such as two-qubit and qubit-qutrit have been demonstrated.
Quantum Fokker-Planck-Kramers equation and entropy production.
de Oliveira, Mário J
2016-07-01
We use a canonical quantization procedure to set up a quantum Fokker-Planck-Kramers equation that accounts for quantum dissipation in a thermal environment. The dissipation term is chosen to ensure that the thermodynamic equilibrium is described by the Gibbs state. An expression for the quantum entropy production that properly describes quantum systems in a nonequilibrium stationary state is also provided. The time-dependent solution is given for a quantum harmonic oscillator in contact with a heat bath. We also obtain the stationary solution for a system of two coupled harmonic oscillators in contact with reservoirs at distinct temperatures, from which we obtain the entropy production and the quantum thermal conductance. PMID:27575097
Reply to "Comment on `Quantum Kaniadakis entropy under projective measurement' "
NASA Astrophysics Data System (ADS)
Ourabah, Kamel; Tribeche, Mouloud
2016-08-01
We rely on our proof of the nondecreasing character of quantum Kaniadakis entropy under projective measurement [Phys. Rev. E 92, 032114 (2015), 10.1103/PhysRevE.92.032114], and we put it into perspective with the results of Bosyk et al. [Quantum Inf Process 15, 3393 (2016), 10.1007/s11128-016-1329-5]. Our method, adopted for the proof that Kaniadakis entropy does not decrease under a projective measurement, is based on Jensen's inequalities, while the method proposed by the authors of the Comment represents another alternative and clearly correct method to prove the same thing. Furthermore, we clarify that our interest in Kaniadakis entropy is due to the fact that this entropy has a transparent physical significance, emerging within the special relativity.
Reply to "Comment on 'Quantum Kaniadakis entropy under projective measurement' ".
Ourabah, Kamel; Tribeche, Mouloud
2016-08-01
We rely on our proof of the nondecreasing character of quantum Kaniadakis entropy under projective measurement [Phys. Rev. E 92, 032114 (2015)PLEEE81539-375510.1103/PhysRevE.92.032114], and we put it into perspective with the results of Bosyk et al. [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5]. Our method, adopted for the proof that Kaniadakis entropy does not decrease under a projective measurement, is based on Jensen's inequalities, while the method proposed by the authors of the Comment represents another alternative and clearly correct method to prove the same thing. Furthermore, we clarify that our interest in Kaniadakis entropy is due to the fact that this entropy has a transparent physical significance, emerging within the special relativity. PMID:27627426
Nonequilibrium entropy in classical and quantum field theory
NASA Astrophysics Data System (ADS)
Kandrup, Henry E.
1987-06-01
This paper proposes a definition of nonequilibrium entropy appropriate for a bosonic classical or quantum field, viewed as a collection of oscillators with equations of motion which satisfy a Liouville theorem (as is guaranteed for a Hamiltonian system). This entropy S is constructed explicitly to provide a measure of correlations and, as such, is conserved absolutely in the absence of couplings between degrees of freedom. This means, e.g., that there can be no entropy generation for a source-free linear field in flat space, but that S need no longer be conserved in the presence of couplings induced by nonlinearities, material sources, or a nontrivial dynamical background space-time. Moreover, through the introduction of a ``subdynamics,'' it is proved that, in the presence of such couplings, the entropy will satisfy an H-theorem inequality, at least in one particular limit. Specifically, if at some initial time t0 the field is free of any correlations, it then follows rigorously that, at time t0+Δt, the entropy will be increasing: dS/dt>0. Similar arguments demonstrate that this S is the only measure of ``entropy'' consistent mathematically with the subdynamics. It is argued that this entropy possesses an intrinsic physical meaning, this meaning being especially clear in the context of a quantum theory, where a direct connection exists between entropy generation and particle creation. Reasonable conjectures regarding the more general time dependence of the entropy, which parallel closely the conventional wisdom of particle mechanics, lead to an interpretation of S which corroborates one's naive intuition as to the behavior of an ``entropy.''
Information, entropy and fidelity in visual communication
NASA Technical Reports Server (NTRS)
Huck, Friedrich O.; Fales, Carl L.; Alter-Gartenberg, Rachel; Rahman, Zia-Ur
1992-01-01
This paper presents an assessment of visual communication that integrates the critical limiting factors of image gathering and display with the digital processing that is used to code and restore images. The approach focuses on two mathematical criteria, information and fidelity, and on their relationships to the entropy of the encoded data and to the visual quality of the restored image.
Work, heat and entropy production in bipartite quantum systems
NASA Astrophysics Data System (ADS)
Hossein-Nejad, Hoda; O'Reilly, Edward J.; Olaya-Castro, Alexandra
2015-07-01
In bipartite quantum systems commutation relations between the Hamiltonian of each subsystem and the interaction impose fundamental constraints on the dynamics of each partition. Here we investigate work, heat and entropy production in bipartite systems characterized by particular commutators between their local Hamiltonians and the interaction operator. We consider the formalism of (Weimer et al 2008 Europhys. Lett. 83 30008), in which heat (work) is identified with energy changes that (do not) alter the local von Neumann entropy, as observed in an effective local measurement basis. We demonstrate the consequences of the commutation relations on the work and heat fluxes into each partition, and extend the formalism to open quantum systems where one, or both, partitions are subject to a Markovian thermal bath. We also discuss the relation between heat and entropy in bipartite quantum systems out of thermal equilibrium, and reconcile the aforementioned approach with the second law of thermodynamics.
Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime
NASA Astrophysics Data System (ADS)
Engelhardt, Netta; Wall, Aron C.
2015-01-01
We propose that holographic entanglement entropy can be calculated at arbitrary orders in the bulk Planck constant using the concept of a "quantum extremal surface": a surface which extremizes the generalized entropy, i.e. the sum of area and bulk entanglement entropy. At leading order in bulk quantum corrections, our proposal agrees with the formula of Faulkner, Lewkowycz, and Maldacena, which was derived only at this order; beyond leading order corrections, the two conjectures diverge. Quantum extremal surfaces lie outside the causal domain of influence of the boundary region as well as its complement, and in some spacetimes there are barriers preventing them from entering certain regions. We comment on the implications for bulk reconstruction.
Study of quantum correlation swapping with relative entropy methods
NASA Astrophysics Data System (ADS)
Xie, Chuanmei; Liu, Yimin; Chen, Jianlan; Zhang, Zhanjun
2016-02-01
To generate long-distance shared quantum correlations (QCs) for information processing in future quantum networks, recently we proposed the concept of QC repeater and its kernel technique named QC swapping. Besides, we extensively studied the QC swapping between two simple QC resources (i.e., a pair of Werner states) with four different methods to quantify QCs (Xie et al. in Quantum Inf Process 14:653-679, 2015). In this paper, we continue to treat the same issue by employing other three different methods associated with relative entropies, i.e., the MPSVW method (Modi et al. in Phys Rev Lett 104:080501, 2010), the Zhang method (arXiv:1011.4333 [quant-ph]) and the RS method (Rulli and Sarandy in Phys Rev A 84:042109, 2011). We first derive analytic expressions of all QCs which occur during the swapping process and then reveal their properties about monotonicity and threshold. Importantly, we find that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed. In addition, we simply compare our present results with our previous ones.
Quantum entropy for the fuzzy sphere and its monopoles
NASA Astrophysics Data System (ADS)
Acharyya, Nirmalendu; Chandra, Nitin; Vaidya, Sachindeo
2014-11-01
Using generalized bosons, we construct the fuzzy sphere SF 2 and monopoles on SF 2 in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.
Approximate reversibility in the context of entropy gain, information gain, and complete positivity
NASA Astrophysics Data System (ADS)
Buscemi, Francesco; Das, Siddhartha; Wilde, Mark M.
2016-06-01
There are several inequalities in physics which limit how well we can process physical systems to achieve some intended goal, including the second law of thermodynamics, entropy bounds in quantum information theory, and the uncertainty principle of quantum mechanics. Recent results provide physically meaningful enhancements of these limiting statements, determining how well one can attempt to reverse an irreversible process. In this paper, we apply and extend these results to give strong enhancements to several entropy inequalities, having to do with entropy gain, information gain, entropic disturbance, and complete positivity of open quantum systems dynamics. Our first result is a remainder term for the entropy gain of a quantum channel. This result implies that a small increase in entropy under the action of a subunital channel is a witness to the fact that the channel's adjoint can be used as a recovery map to undo the action of the original channel. We apply this result to pure-loss, quantum-limited amplifier, and phase-insensitive quantum Gaussian channels, showing how a quantum-limited amplifier can serve as a recovery from a pure-loss channel and vice versa. Our second result regards the information gain of a quantum measurement, both without and with quantum side information. We find here that a small information gain implies that it is possible to undo the action of the original measurement if it is efficient. The result also has operational ramifications for the information-theoretic tasks known as measurement compression without and with quantum side information. Our third result shows that the loss of Holevo information caused by the action of a noisy channel on an input ensemble of quantum states is small if and only if the noise can be approximately corrected on average. We finally establish that the reduced dynamics of a system-environment interaction are approximately completely positive and trace preserving if and only if the data processing
Entanglement entropy between real and virtual particles in ϕ4 quantum field theory
NASA Astrophysics Data System (ADS)
Ardenghi, Juan Sebastián
2015-04-01
The aim of this work is to compute the entanglement entropy of real and virtual particles by rewriting the generating functional of ϕ4 theory as a mean value between states and observables defined through the correlation functions. Then the von Neumann definition of entropy can be applied to these quantum states and in particular, for the partial traces taken over the internal or external degrees of freedom. This procedure can be done for each order in the perturbation expansion showing that the entanglement entropy for real and virtual particles behaves as ln (m0). In particular, entanglement entropy is computed at first order for the correlation function of two external points showing that mutual information is identical to the external entropy and that conditional entropies are negative for all the domain of m0. In turn, from the definition of the quantum states, it is possible to obtain general relations between total traces between different quantum states of a ϕr theory. Finally, discussion about the possibility of taking partial traces over external degrees of freedom is considered, which implies the introduction of some observables that measure space-time points where an interaction occurs.
The Tsallis entropy of natural information
NASA Astrophysics Data System (ADS)
Sneddon, Robert
2007-12-01
Estimating the information contained in natural data, such as electroencephalography data, is unusually difficult because the relationship between the physical data and the information that it encodes is unknown. This unknown relationship is often called the encoding problem. The present work provides a solution to this problem by deriving a method to estimate the Tsallis entropy in natural data. The method is based on two findings. The first finding is that the physical instantiation of any information event, that is, the physical occurrence of a symbol of information, must begin and end at a discontinuity or critical point (maximum, minimum, or saddle point) in the data. The second finding is that, in certain data types such as the encephalogram (EEG), the variance within of an EEG waveform event is directly proportional to its probability of occurrence. These two outcomes yield two results. The first is the easy binning of data into separate information events. The second is the ability to estimate probabilities in two ways: frequency counting and computing the variance within of an EEG waveform. These results are used to derive a linear estimator of the Tsallis entropy functional, allowing it to be estimated without deducing the encoding. This method for estimating the Tsallis entropy is first used to estimate the information in simple signals. The amount of information estimated is highly accurate. The method is then applied to two problems in electroencephalography. The first is distinguishing normal aging from very early Alzheimer's disease (mild cognitive impairment), and the second is medication monitoring of Alzheimer's disease treatment. The former is done with an accuracy of 92% and the latter with an accuracy of 91%. This detection accuracy is the highest published accuracy in the literature, which suggests that this method for Tsallis entropy estimation is both accurate and useful.
Entropy, complexity, and spatial information
NASA Astrophysics Data System (ADS)
Batty, Michael; Morphet, Robin; Masucci, Paolo; Stanilov, Kiril
2014-10-01
We pose the central problem of defining a measure of complexity, specifically for spatial systems in general, city systems in particular. The measures we adopt are based on Shannon's (in Bell Syst Tech J 27:379-423, 623-656, 1948) definition of information. We introduce this measure and argue that increasing information is equivalent to increasing complexity, and we show that for spatial distributions, this involves a trade-off between the density of the distribution and the number of events that characterize it; as cities get bigger and are characterized by more events—more places or locations, information increases, all other things being equal. But sometimes the distribution changes at a faster rate than the number of events and thus information can decrease even if a city grows. We develop these ideas using various information measures. We first demonstrate their applicability to various distributions of population in London over the last 100 years, then to a wider region of London which is divided into bands of zones at increasing distances from the core, and finally to the evolution of the street system that characterizes the built-up area of London from 1786 to the present day. We conclude by arguing that we need to relate these measures to other measures of complexity, to choose a wider array of examples, and to extend the analysis to two-dimensional spatial systems.
Entropy, complexity, and spatial information
NASA Astrophysics Data System (ADS)
Batty, Michael; Morphet, Robin; Masucci, Paolo; Stanilov, Kiril
2014-09-01
We pose the central problem of defining a measure of complexity, specifically for spatial systems in general, city systems in particular. The measures we adopt are based on Shannon's (in Bell Syst Tech J 27:379-423, 623-656, 1948) definition of information. We introduce this measure and argue that increasing information is equivalent to increasing complexity, and we show that for spatial distributions, this involves a trade-off between the density of the distribution and the number of events that characterize it; as cities get bigger and are characterized by more events—more places or locations, information increases, all other things being equal. But sometimes the distribution changes at a faster rate than the number of events and thus information can decrease even if a city grows. We develop these ideas using various information measures. We first demonstrate their applicability to various distributions of population in London over the last 100 years, then to a wider region of London which is divided into bands of zones at increasing distances from the core, and finally to the evolution of the street system that characterizes the built-up area of London from 1786 to the present day. We conclude by arguing that we need to relate these measures to other measures of complexity, to choose a wider array of examples, and to extend the analysis to two-dimensional spatial systems.
Chain rules for quantum Rényi entropies
Dupuis, Frédéric
2015-02-15
We present chain rules for a new definition of the quantum Rényi conditional entropy sometimes called the “sandwiched” Rényi conditional entropy. More precisely, we prove analogues of the equation H(AB|C) = H(A|BC) + H(B|C), which holds as an identity for the von Neumann conditional entropy. In the case of the Rényi entropy, this relation no longer holds as an equality but survives as an inequality of the form H{sub α}(AB|C) ⩾ H{sub β}(A|BC) + H{sub γ}(B|C), where the parameters α, β, γ obey the relation (α)/(α−1) =(β)/(β−1) +(γ)/(γ−1) and (α − 1)(β − 1)(γ − 1) > 1; if (α − 1)(β − 1)(γ − 1) < 1, the direction of the inequality is reversed.
Information Flows? A Critique of Transfer Entropies
NASA Astrophysics Data System (ADS)
James, Ryan G.; Barnett, Nix; Crutchfield, James P.
2016-06-01
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be dominated by the transfer entropy. Via straightforward examples, we show that it and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information. At one and the same time they can overestimate flow or underestimate influence. We isolate why this is the case and propose several avenues to alternate measures for information flow. We also address an auxiliary consequence: The proliferation of networks as a now-common theoretical model for large-scale systems, in concert with the use of transferlike entropies, has shoehorned dyadic relationships into our structural interpretation of the organization and behavior of complex systems. This interpretation thus fails to include the effects of polyadic dependencies. The net result is that much of the sophisticated organization of complex systems may go undetected.
Information Flows? A Critique of Transfer Entropies.
James, Ryan G; Barnett, Nix; Crutchfield, James P
2016-06-10
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be dominated by the transfer entropy. Via straightforward examples, we show that it and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information. At one and the same time they can overestimate flow or underestimate influence. We isolate why this is the case and propose several avenues to alternate measures for information flow. We also address an auxiliary consequence: The proliferation of networks as a now-common theoretical model for large-scale systems, in concert with the use of transferlike entropies, has shoehorned dyadic relationships into our structural interpretation of the organization and behavior of complex systems. This interpretation thus fails to include the effects of polyadic dependencies. The net result is that much of the sophisticated organization of complex systems may go undetected. PMID:27341264
Life, Information, Entropy, and Time
Crofts, Antony R.
2008-01-01
Attempts to understand how information content can be included in an accounting of the energy flux of the biosphere have led to the conclusion that, in information transmission, one component, the semantic content, or “the meaning of the message,” adds no thermodynamic burden over and above costs arising from coding, transmission and translation. In biology, semantic content has two major roles. For all life forms, the message of the genotype encoded in DNA specifies the phenotype, and hence the organism that is tested against the real world through the mechanisms of Darwinian evolution. For human beings, communication through language and similar abstractions provides an additional supra-phenotypic vehicle for semantic inheritance, which supports the cultural heritages around which civilizations revolve. The following three postulates provide the basis for discussion of a number of themes that demonstrate some important consequences. (i) Information transmission through either pathway has thermodynamic components associated with data storage and transmission. (ii) The semantic content adds no additional thermodynamic cost. (iii) For all semantic exchange, meaning is accessible only through translation and interpretation, and has a value only in context. (1) For both pathways of semantic inheritance, translational and copying machineries are imperfect. As a consequence both pathways are subject to mutation and to evolutionary pressure by selection. Recognition of semantic content as a common component allows an understanding of the relationship between genes and memes, and a reformulation of Universal Darwinism. (2) The emergent properties of life are dependent on a processing of semantic content. The translational steps allow amplification in complexity through combinatorial possibilities in space and time. Amplification depends on the increased potential for complexity opened by 3D interaction specificity of proteins, and on the selection of useful variants
Entanglement Entropy of d-DIMENSIONAL Black Hole and Quantum Isolated Horizon
NASA Astrophysics Data System (ADS)
Zhao, Hui-Hua; Li, Guang-Liang; Zhao, Ren; Ma, Meng-Sen; Zhang, Li-Chun
2013-09-01
Based on the works of Ghosh et al. who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH), the entropy of d-dimensional black hole is studied. According to the Unruh-Verlinde temperature deduced from the concept of entropic force, the statistical entropy of quantum fields under the background of d-dimensional spacetime is calculated by means of quantum statistics. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states and display the effects of dimensions on the correction terms of the entanglement entropy.
Quantum entropy and uncertainty for two-mode squeezed, coherent and intelligent spin states
NASA Technical Reports Server (NTRS)
Aragone, C.; Mundarain, D.
1993-01-01
We compute the quantum entropy for monomode and two-mode systems set in squeezed states. Thereafter, the quantum entropy is also calculated for angular momentum algebra when the system is either in a coherent or in an intelligent spin state. These values are compared with the corresponding values of the respective uncertainties. In general, quantum entropies and uncertainties have the same minimum and maximum points. However, for coherent and intelligent spin states, it is found that some minima for the quantum entropy turn out to be uncertainty maxima. We feel that the quantum entropy we use provides the right answer, since it is given in an essentially unique way.
Nonequilibrium work and entropy production by quantum projective measurements.
Yi, Juyeon; Kim, Yong Woon
2013-09-01
We study the thermodynamic notion of quantum projective measurements, using a framework for the fluctuation theorem of nonequilibrium work. The energy change induced by measurements satisfies the Jarzynski equality, leading us to the interpretation that the quantum projective measurements perform nonequilibrium work on the measured system. The work average exhibits intriguing limiting behaviors due to the heat-up effect caused by repeated measurements and the quantum Zeno effect caused by measurements of an infinite frequency. If the measured system relaxes back to its initial equilibrium state, the work is completely dissipated in the form of heat into a reservoir. The corresponding entropy increase in the reservoir is shown to be not less than the von Neumann entropy change generated during the course of the measurements, proving Landauer's principle. PMID:24125212
Relative information entropy in cosmology: The problem of information entanglement
NASA Astrophysics Data System (ADS)
Czinner, Viktor G.; Mena, Filipe C.
2016-07-01
The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the Rényi relative entropy formula.
Holographic entanglement entropy close to quantum phase transitions
NASA Astrophysics Data System (ADS)
Ling, Yi; Liu, Peng; Niu, Chao; Wu, Jian-Pin; Xian, Zhuo-Yu
2016-04-01
We investigate the holographic entanglement entropy (HEE) of a strip geometry in four dimensional Q-lattice backgrounds, which exhibit metal-insulator transitions in the dual field theory. Remarkably, we find that the HEE always displays a peak in the vicinity of the quantum critical points. Our model provides the first direct evidence that the HEE can be used to characterize the quantum phase transition (QPT). We also conjecture that the maximization behavior of HEE at quantum critical points would be universal in general holographic models.
Fuzzy geometry, entropy, and image information
NASA Technical Reports Server (NTRS)
Pal, Sankar K.
1991-01-01
Presented here are various uncertainty measures arising from grayness ambiguity and spatial ambiguity in an image, and their possible applications as image information measures. Definitions are given of an image in the light of fuzzy set theory, and of information measures and tools relevant for processing/analysis e.g., fuzzy geometrical properties, correlation, bound functions and entropy measures. Also given is a formulation of algorithms along with management of uncertainties for segmentation and object extraction, and edge detection. The output obtained here is both fuzzy and nonfuzzy. Ambiguity in evaluation and assessment of membership function are also described.
DeSitter entropy, quantum entanglement and ADS/CFT
NASA Astrophysics Data System (ADS)
Hawking, Stephen; Maldacena, Juan; Strominger, Andrew
2001-05-01
A de Sitter brane-world bounding regions of anti-de Sitter space has a macroscopic entropy given by one-quarter the area of the observer horizon. A proposed variant of the AdS/CFT correspondence gives a dual description of this cosmology as conformal field theory coupled to gravity in de Sitter space. In the case of two-dimensional de Sitter space this provides a microscopic derivation of the entropy, including the one-quarter, as quantum entanglement of the conformal field theory across the horizon.
Quantum-corrected finite entropy of noncommutative acoustic black holes
NASA Astrophysics Data System (ADS)
Anacleto, M. A.; Brito, F. A.; Luna, G. C.; Passos, E.; Spinelly, J.
2015-11-01
In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2 + 1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.
Entropy of the information retrieved from black holes
NASA Astrophysics Data System (ADS)
Mersini-Houghton, Laura
2016-07-01
The retrieval of black hole information was recently presented in two interesting proposals in the ‘Hawking Radiation’ conference: a revised version by Hooft of a proposal he initially suggested 20 years ago and, a new proposal by Hawking. Both proposals address the problem of black hole information loss at the classical level and derive an expression for the scattering matrix. The former uses gravitation back reaction of incoming particles that imprints its information on the outgoing modes. The latter uses supertranslation symmetry of horizons to relate a phase delay of the outgoing wave packet compared to their incoming wave partners. The difficulty in both proposals is that the entropy obtained from them appears to be infinite. By including quantum effects into the Hawking and Hooft’s proposals, I show that a subtlety arising from the inescapable measurement process, the quantum Zeno effect, not only tames divergences but it actually recovers the correct 1/4 of the area Bekenstein–Hawking entropy law of black holes.
Quantum information causality.
Pitalúa-García, Damián
2013-05-24
How much information can a transmitted physical system fundamentally communicate? We introduce the principle of quantum information causality, which states the maximum amount of quantum information that a quantum system can communicate as a function of its dimension, independently of any previously shared quantum physical resources. We present a new quantum information task, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs. PMID:23745844
Electrical and optical control of entanglement entropy in a coupled triple quantum dot system
NASA Astrophysics Data System (ADS)
Mehmannavaz, Mohammad Reza
2015-10-01
We investigated theoretically the entanglement creation through tunneling rate and fields in a four-level triple quantum dot molecule based on InAs/GaAs/AlGaAs heterostructure in both steady state and transient state. We demonstrate that the entanglement entropy among the QDM and its spontaneous emission fields can be controlled by coherent and incoherent pumping field and tunnel-coupled electronics levels. The results may provide some new possibilities for technological applications in solid-state quantum information science, quantum computing, teleportation, encryption, compression codec, and optoelectronics.
Entanglement entropy in quantum spin chains with broken reflection symmetry
Kadar, Zoltan; Zimboras, Zoltan
2010-09-15
We investigate the entanglement entropy of a block of L sites in quasifree translation-invariant spin chains concentrating on the effect of reflection-symmetry breaking. The Majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these, it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large L asymptotics of the entropy are calculated analytically for general gauge-invariant models, which have, until now, been done only for the reflection-symmetric sector. Analytical results are also derived for certain nongauge-invariant models (e.g., for the Ising model with Dzyaloshinskii-Moriya interaction). We also study numerically finite chains of length N with a nonreflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first L spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for noncritical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the saturation entropy as we approach the critical line. The paper also provides a concise but extensive review of the block-entropy asymptotics in translation-invariant quasifree spin chains with an analysis of the nearest-neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.
Entanglement Entropy in Quantum Spin Chains with Finite Range Interaction
NASA Astrophysics Data System (ADS)
Its, A. R.; Mezzadri, F.; Mo, M. Y.
2008-11-01
We study the entropy of entanglement of the ground state in a wide family of one-dimensional quantum spin chains whose interaction is of finite range and translation invariant. Such systems can be thought of as generalizations of the XY model. The chain is divided in two parts: one containing the first consecutive L spins; the second the remaining ones. In this setting the entropy of entanglement is the von Neumann entropy of either part. At the core of our computation is the explicit evaluation of the leading order term as L → ∞ of the determinant of a block-Toeplitz matrix with symbol Φ(z) = left(begin{array}{cc} iλ & g(z) \\ g^{-1}(z) & i λ right), where g( z) is the square root of a rational function and g(1/ z) = g -1( z). The asymptotics of such determinant is computed in terms of multi-dimensional theta-functions associated to a hyperelliptic curve {mathcal{L}} of genus g ≥ 1, which enter into the solution of a Riemann-Hilbert problem. Phase transitions for these systems are characterized by the branch points of {mathcal{L}} approaching the unit circle. In these circumstances the entropy diverges logarithmically. We also recover, as particular cases, the formulae for the entropy discovered by Jin and Korepin [14] for the XX model and Its, Jin and Korepin [12, 13] for the XY model.
Quantum Particles From Quantum Information
NASA Astrophysics Data System (ADS)
Görnitz, T.; Schomäcker, U.
2012-08-01
Many problems in modern physics demonstrate that for a fundamental entity a more general conception than quantum particles or quantum fields are necessary. These concepts cannot explain the phenomena of dark energy or the mind-body-interaction. Instead of any kind of "small elementary building bricks", the Protyposis, an abstract and absolute quantum information, free of special denotation and open for some purport, gives the solution in the search for a fundamental substance. However, as long as at least relativistic particles are not constructed from the Protyposis, such an idea would remain in the range of natural philosophy. Therefore, the construction of relativistic particles without and with rest mass from quantum information is shown.
Entropy and correlation functions of a driven quantum spin chain
Cherng, R. W.; Levitov, L. S.
2006-04-15
We present an exact solution for a quantum spin chain driven through its critical points. Our approach is based on a many-body generalization of the Landau-Zener transition theory, applied to a fermionized spin Hamiltonian. The resulting nonequilibrium state of the system, while being a pure quantum state, has local properties of a mixed state characterized by finite entropy density associated with Kibble-Zurek defects. The entropy and the finite spin correlation length are functions of the rate of sweep through the critical point. We analyze the anisotropic XY spin-1/2 model evolved with a full many-body evolution operator. With the help of Toeplitz determinant calculus, we obtain an exact form of correlation functions. The properties of the evolved system undergo an abrupt change at a certain critical sweep rate, signaling the formation of ordered domains. We link this phenomenon to the behavior of complex singularities of the Toeplitz generating function.
Characterization of quantum phase transition using holographic entanglement entropy
NASA Astrophysics Data System (ADS)
Ling, Yi; Liu, Peng; Wu, Jian-Pin
2016-06-01
The entanglement exhibits extremal or singular behavior near quantum critical points (QCPs) in many condensed matter models. These intriguing phenomena, however, still call for a widely accepted understanding. In this paper we study this issue in holographic framework. We investigate the connection between the holographic entanglement entropy (HEE) and the quantum phase transition (QPT) in a lattice-deformed Einstein-Maxwell-Dilaton theory. Novel backgrounds exhibiting metal-insulator transitions (MIT) have been constructed in which both metallic phase and insulating phase have vanishing entropy density in zero temperature limit. We find that the first order derivative of HEE with respect to lattice parameters exhibits extremal behavior near QCPs. We propose that it would be a universal feature that HEE or its derivatives with respect to system parameters can characterize QPT in a generic holographic system. Our work opens a window for understanding the relation between entanglement and the QPT from a holographic perspective.
Postprocessing for quantum random-number generators: Entropy evaluation and randomness extraction
NASA Astrophysics Data System (ADS)
Ma, Xiongfeng; Xu, Feihu; Xu, He; Tan, Xiaoqing; Qi, Bing; Lo, Hoi-Kwong
2013-06-01
Quantum random-number generators (QRNGs) can offer a means to generate information-theoretically provable random numbers, in principle. In practice, unfortunately, the quantum randomness is inevitably mixed with classical randomness due to classical noises. To distill this quantum randomness, one needs to quantify the randomness of the source and apply a randomness extractor. Here, we propose a generic framework for evaluating quantum randomness of real-life QRNGs by min-entropy, and apply it to two different existing quantum random-number systems in the literature. Moreover, we provide a guideline of QRNG data postprocessing for which we implement two information-theoretically provable randomness extractors: Toeplitz-hashing extractor and Trevisan's extractor.
Quantum information and computation
Bennett, C.H.
1995-10-01
A new quantum theory of communication and computation is emerging, in which the stuff transmitted or processed is not classical information, but arbitrary superpositions of quantum states. {copyright} 1995 {ital American} {ital Institute} {ital of} {ital Physics}.
Information Divergence and Distance Measures for Quantum States
NASA Astrophysics Data System (ADS)
Jiang, Nan; Zhang, Zhaozhi
2015-02-01
Both information divergence and distance are measures of closeness of two quantum states which are widely used in the theory of information processing and quantum cryptography. For example, the quantum relative entropy and trace distance are well known. Here we introduce a number of new quantum information divergence and distance measures into the literature and discuss their relations and properties. We also propose a method to analyze the properties and relations of various distance and pseudo-distance measures.
Trovato, M.; Reggiani, L.
2011-12-15
By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ({h_bar}/2{pi}){sup 2}. In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when ({h_bar}/2{pi}){yields}0.
Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution.
Brandão, Fernando G S L; Harrow, Aram W; Oppenheim, Jonathan; Strelchuk, Sergii
2015-07-31
We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite reductions. Namely, we show that the conditional mutual information is an upper bound on the regularized relative entropy distance between the quantum state and its reconstructed version. It is also an upper bound for the measured relative entropy distance of the state to its reconstructed version. The main ingredient of the proof is the fact that the conditional mutual information is the optimal quantum communication rate in the task of state redistribution. PMID:26274402
Comment on "Quantum Kaniadakis entropy under projective measurement"
NASA Astrophysics Data System (ADS)
Bosyk, G. M.; Zozor, S.; Holik, F.; Portesi, M.; Lamberti, P. W.
2016-08-01
We comment on the main result given by Ourabah et al. [Phys. Rev. E 92, 032114 (2015), 10.1103/PhysRevE.92.032114], noting that it can be derived as a special case of the more general study that we have provided in [Quantum Inf Process 15, 3393 (2016), 10.1007/s11128-016-1329-5]. Our proof of the nondecreasing character under projective measurements of so-called generalized (h ,ϕ ) entropies (that comprise the Kaniadakis family as a particular case) has been based on majorization and Schur-concavity arguments. As a consequence, we have obtained that this property is obviously satisfied by Kaniadakis entropy but at the same time is fulfilled by all entropies preserving majorization. In addition, we have seen that our result holds for any bistochastic map, being a projective measurement a particular case. We argue here that looking at these facts from the point of view given in [Quantum Inf Process 15, 3393 (2016), 10.1007/s11128-016-1329-5] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.
Zaletel, Michael P; Bardarson, Jens H; Moore, Joel E
2011-07-01
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the "Shannon entropy" of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut. PMID:21797582
NASA Astrophysics Data System (ADS)
Kuramochi, Yui; Ueda, Masahito
2015-03-01
We consider the information flow on a system observable X corresponding to a positive-operator-valued measure under a quantum measurement process Y described by a completely positive instrument from the viewpoint of the relative entropy. We establish a sufficient condition for the relative-entropy conservation law which states that the average decrease in the relative entropy of the system observable X equals the relative entropy of the measurement outcome of Y , i.e., the information gain due to measurement. This sufficient condition is interpreted as an assumption of classicality in the sense that there exists a sufficient statistic in a joint successive measurement of Y followed by X such that the probability distribution of the statistic coincides with that of a single measurement of X for the premeasurement state. We show that in the case when X is a discrete projection-valued measure and Y is discrete, the classicality condition is equivalent to the relative-entropy conservation for arbitrary states. The general theory on the relative-entropy conservation is applied to typical quantum measurement models, namely, quantum nondemolition measurement, destructive sharp measurements on two-level systems, a photon counting, a quantum counting, homodyne and heterodyne measurements. These examples except for the nondemolition and photon-counting measurements do not satisfy the known Shannon-entropy conservation law proposed by Ban [M. Ban, J. Phys. A: Math. Gen. 32, 1643 (1999), 10.1088/0305-4470/32/9/012], implying that our approach based on the relative entropy is applicable to a wider class of quantum measurements.
Thermodynamic and Information Entropy in Electroconvection
NASA Astrophysics Data System (ADS)
Cressman, John; Daum, Marcus; Patrick, David; Cerbus, Rory; Goldburg, Walter
Transitions in driven systems often produce wild fluctuations that can be both detrimental and beneficial. Our fundamental understanding of these transients is inadequate to permit optimal interactions with systems ranging from biology, to energy generation, to finance. Here we report on experiments performed in electroconvecting liquid crystals where we abruptly change the electrical forcing across the sample from a state below defect turbulence into a state of defect turbulence. We simultaneously measure the electrical power flow through the liquid crystal as well as image the structure in the sample. These measurements enable us to simultaneously track the evolution of the thermodynamic and information entropies. Our experiments demonstrate that there are strong correlations between the fluctuations in these two entropic measures however they are not exact. We will discuss these discrepancies as well as the relevance of large transient fluctuations in non-equilibrium transitions in general.
Markov entropy decomposition: a variational dual for quantum belief propagation.
Poulin, David; Hastings, Matthew B
2011-02-25
We present a lower bound for the free energy of a quantum many-body system at finite temperature. This lower bound is expressed as a convex optimization problem with linear constraints, and is derived using strong subadditivity of von Neumann entropy and a relaxation of the consistency condition of local density operators. The dual to this minimization problem leads to a set of quantum belief propagation equations, thus providing a firm theoretical foundation to that approach. The minimization problem is numerically tractable, and we find good agreement with quantum Monte Carlo calculations for spin-1/2 Heisenberg antiferromagnet in two dimensions. This lower bound complements other variational upper bounds. We discuss applications to Hamiltonian complexity theory and give a generalization of the structure theorem of [P. Hayden et al., Commun. Math. Phys. 246, 359 (2004).] to trees in an appendix. PMID:21405554
Markov Entropy Decomposition: A Variational Dual for Quantum Belief Propagation
NASA Astrophysics Data System (ADS)
Poulin, David; Hastings, Matthew B.
2011-02-01
We present a lower bound for the free energy of a quantum many-body system at finite temperature. This lower bound is expressed as a convex optimization problem with linear constraints, and is derived using strong subadditivity of von Neumann entropy and a relaxation of the consistency condition of local density operators. The dual to this minimization problem leads to a set of quantum belief propagation equations, thus providing a firm theoretical foundation to that approach. The minimization problem is numerically tractable, and we find good agreement with quantum Monte Carlo calculations for spin-(1)/(2) Heisenberg antiferromagnet in two dimensions. This lower bound complements other variational upper bounds. We discuss applications to Hamiltonian complexity theory and give a generalization of the structure theorem of [P. Hayden , Commun. Math. Phys. 246, 359 (2004).CMPHAY0010-361610.1007/s00220-004-1049-z] to trees in an appendix.
Entanglement entropy in quantum gravity and the Plateau problem
Fursaev, Dmitri V.
2008-06-15
In a quantum gravity theory the entropy of entanglement S between the fundamental degrees of freedom spatially divided by a surface is discussed. Classical gravity is considered as an emergent phenomenon and arguments are presented that (1) S is a macroscopical quantity which can be determined without knowing a real microscopical content of the fundamental theory; (2) S is given by the Bekenstein-Hawking formula in terms of the area of a codimension 2 hypesurface B; (3) in static space-times B can be defined as a minimal hypersurface of a least volume separating the system in a constant-time slice. It is shown that properties of S are in agreement with basic properties of the von Neumann entropy. Explicit variational formulae for S in different physical examples are considered.
Quantum Correlations, Chaos and Information
NASA Astrophysics Data System (ADS)
Madhok, Vaibhav
Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The measurement record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on
Information and entropic characteristics of photon and qudit quantum states
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.
2010-09-01
The probability distribution determining the quantum states of photons and qudits are reviewed. Shannon, Rényi and Tsallis entropies associated with the probability distributions are discussed. Shannon information associated with quantum states in the probability representation is considered. Known inequalities for the classical joint probability distributions determining quantum states of multipartite systems are discussed in detail and the relationship to the inequalities known for quantum von Neumann entropy of the states is presented. Properties of subadditivity and strong subadditivity of the von Neumann entropy of two-partite and multipartite qudit states are considered in view of the subadditivity and strong subadditivity properties of Shannon entropies associated with classical joint probability distributions determining the multiqudit quantum states. The new entropic uncertainty relationships for optical tomograms are suggested as a test for accuracy of the homodyne reconstructing the photon state.
Mismatched quantum filtering and entropic information
NASA Astrophysics Data System (ADS)
Tsang, Mankei
2014-03-01
Quantum filtering is a signal processing technique that estimates the posterior state of a quantum system under continuous measurements and has become a standard tool in quantum information processing, with applications in quantum state preparation, quantum metrology, and quantum control. If the filter assumes a wrong model due to assumptions or approximations, however, the estimation accuracy is bound to suffer. In this talk I shall present formulas that relate the error penalty caused by quantum filter mismatch to the relative entropy between the true model and the nominal model, with one formula for Gaussian measurements, such as homodyne detection, and another for Poissonian measurements, such as photon counting. These formulas generalize recent seminal results in classical information theory and provide new operational meanings to relative entropy, mutual information, and channel capacity in the context of quantum experiments. See http://arxiv.org/abs/1310.0291 for details. This work is supported by the Singapore National Research Foundation under NRF Grant No. NRF-NRFF2011-07.
Fisher Information and Shannon Entropy in Confined 1D Harmonic Oscillator
Stevanovic, Ljiljana
2010-01-21
Study of the linear harmonic oscillator confined in the square well with impenetrable walls is of great interest since its application for modeling parabolic quantum well semiconductor heterostructures. Fisher information and Shannon entropy, as a complexity measure for its ground and some excited energy levels are reported here.
Statistics, holography, and black hole entropy in loop quantum gravity
NASA Astrophysics Data System (ADS)
Ghosh, Amit; Noui, Karim; Perez, Alejandro
2014-04-01
In loop quantum gravity the quantum states of a black hole horizon consist of pointlike discrete quantum geometry excitations (or punctures) labeled by spin j. The excitations possibly carry other internal degrees of freedom, and the associated quantum states are eigenstates of the area A operator. The appropriately scaled area operator A/(8πℓ) can also be interpreted as the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance ℓ from the horizon. Thus, the local energy is entirely accounted for by the geometric operator A. Assuming that: Close to the horizon the quantum state has a regular energy momentum tensor and hence the local temperature measured by stationary observers is the Unruh temperature. Degeneracy of matter states is exponential with the area exp(λA/ℓp2), which is supported by the well-established results of QFT in curved spacetimes, which do not determine λ but assert an exponential behavior. The geometric excitations of the horizon (punctures) are indistinguishable. And finally that the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound, viz., λ must be equal to 1/4. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy S =A/(4ℓp2). The number of horizon punctures goes like N∝√A/ℓp2 ; i.e., the number of punctures N remains large in the semiclassical limit. Fluctuations of the horizon area are small ΔA/A ∝(ℓp2/A)1/4, while fluctuations of the area of an individual puncture are large (large spins dominate). A precise notion of local conformal invariance of the thermal state is recovered in the A→∞ limit where the near horizon geometry becomes Rindler. We also show how the present model (constructed from loop quantum gravity) provides a regularization of (and gives a concrete meaning to) the formal
Hybrid quantum information processing
Furusawa, Akira
2014-12-04
I will briefly explain the definition and advantage of hybrid quantum information processing, which is hybridization of qubit and continuous-variable technologies. The final goal would be realization of universal gate sets both for qubit and continuous-variable quantum information processing with the hybrid technologies. For that purpose, qubit teleportation with a continuousvariable teleporter is one of the most important ingredients.
NASA Astrophysics Data System (ADS)
Luitz, David J.; Alet, Fabien; Laflorencie, Nicolas
2014-03-01
Shannon-Renyi entropies are measures of the participation of basis states in a wave function. Previous work for one dimensional systems showed that they exhibit a subleading scaling behavior with system size that contains universal information, such as e.g. the Luttinger Liquid parameter. Here, we introduce quantum Monte Carlo schemes to calculate these quantities and the related participation spectra for unfrustrated quantum many body systems in any dimension and apply them to interacting spin systems. Our results demonstrate the universality of subleading scaling terms for different kinds of phase transitions with a spontaneous breaking of discrete or continuous symmetries and at quantum critical points. Aditionally, we also discuss the signature of quantum phase transitions in the participation spectra of subsystems.
Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum.
Fradkin, Eduardo; Moore, Joel E
2006-08-01
The entanglement entropy of a pure quantum state of a bipartite system A union or logical sumB is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. In one dimension, the entanglement of critical ground states diverges logarithmically in the subsystem size, with a universal coefficient that for conformally invariant critical points is related to the central charge of the conformal field theory. We find that the entanglement entropy of a standard class of z=2 conformal quantum critical points in two spatial dimensions, in addition to a nonuniversal "area law" contribution linear in the size of the AB boundary, generically has a universal logarithmically divergent correction, which is completely determined by the geometry of the partition and by the central charge of the field theory that describes the critical wave function. PMID:17026083
Minimax Quantum Tomography: Estimators and Relative Entropy Bounds
NASA Astrophysics Data System (ADS)
Ferrie, Christopher; Blume-Kohout, Robin
2016-03-01
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O (1 /√{N }) —in contrast to that of classical probability estimation, which is O (1 /N )—where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states.
Minimax Quantum Tomography: Estimators and Relative Entropy Bounds.
Ferrie, Christopher; Blume-Kohout, Robin
2016-03-01
A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of nonadaptive tomography scales as O(1/sqrt[N])-in contrast to that of classical probability estimation, which is O(1/N)-where N is the number of copies of the quantum state used. We trace this deficiency to sampling mismatch: future observations that determine risk may come from a different sample space than the past data that determine the estimate. This makes minimax estimators very biased, and we propose a computationally tractable alternative with similar behavior in the worst case, but superior accuracy on most states. PMID:26991163
NASA Astrophysics Data System (ADS)
Zaletel, Michael P.; Bardarson, Jens H.; Moore, Joel E.
2011-07-01
Universal logarithmic terms in the entanglement entropy appear at quantum critical points (QCPs) in one dimension (1D) and have been predicted in 2D at QCPs described by 2D conformal field theories. The entanglement entropy in a strip geometry at such QCPs can be obtained via the “Shannon entropy” of a 1D spin chain with open boundary conditions. The Shannon entropy of the XXZ chain is found to have a logarithmic term that implies, for the QCP of the square-lattice quantum dimer model, a logarithm with universal coefficient ±0.25. However, the logarithm in the Shannon entropy of the transverse-field Ising model, which corresponds to entanglement in the 2D Ising conformal QCP, is found to have a singular dependence on the replica or Rényi index resulting from flows to different boundary conditions at the entanglement cut.
An analytical description of the atomic information entropy in a multi-level system
NASA Astrophysics Data System (ADS)
Obada, A.-S. F.; Abdel-Aty, Mahmoud
2008-05-01
We construct a complete representation of the atomic information entropy of an arbitrary multi-level system. Our approach is applicable to all scenarios in which the quantum state shared by a single particle and fields is known. As illustrations we apply our findings to a single four-level atom strongly coupled to a cavity field and driven by a coherent laser field. In this framework, we discuss connections with entanglement frustration and entropic forms. We conclude by showing how the atomic information entropy can be extended to examine entanglement in multi-level atomic systems.
Quantum Gravity corrections and entropy at the Planck time
Basilakos, Spyros; Vagenas, Elias C.; Das, Saurya E-mail: saurya.das@uleth.ca
2010-09-01
We investigate the effects of Quantum Gravity on the Planck era of the universe. In particular, using different versions of the Generalized Uncertainty Principle and under specific conditions we find that the main Planck quantities such as the Planck time, length, mass and energy become larger by a factor of order 10−10{sup 4} compared to those quantities which result from the Heisenberg Uncertainty Principle. However, we prove that the dimensionless entropy enclosed in the cosmological horizon at the Planck time remains unchanged. These results, though preliminary, indicate that we should anticipate modifications in the set-up of cosmology since changes in the Planck era will be inherited even to the late universe through the framework of Quantum Gravity (or Quantum Field Theory) which utilizes the Planck scale as a fundamental one. More importantly, these corrections will not affect the entropic content of the universe at the Planck time which is a crucial element for one of the basic principles of Quantum Gravity named Holographic Principle.
NASA Astrophysics Data System (ADS)
Mosonyi, Milán; Ogawa, Tomohiro
2015-03-01
We show that the new quantum extension of Rényi's α-relative entropies, introduced recently by Müller-Lennert et al. (J Math Phys 54:122203, 2013) and Wilde et al. (Commun Math Phys 331(2):593-622, 2014), have an operational interpretation in the strong converse problem of quantum hypothesis testing. Together with related results for the direct part of quantum hypothesis testing, known as the quantum Hoeffding bound, our result suggests that the operationally relevant definition of the quantum Rényi relative entropies depends on the parameter α: for α < 1, the right choice seems to be the traditional definition , whereas for α > 1 the right choice is the newly introduced version .On the way to proving our main result, we show that the new Rényi α-relative entropies are asymptotically attainable by measurements for α > 1. From this, we obtain a new simple proof for their monotonicity under completely positive trace-preserving maps.
Controlling quantum information
NASA Astrophysics Data System (ADS)
Landahl, Andrew John
Quantum information science explores ways in which quantum physical laws can be harnessed to control the acquisition, transmission, protection, and processing of information. This field has seen explosive growth in the past several years from progress on both theoretical and experimental fronts. Essential to this endeavor are methods for controlling quantum information. In this thesis, I present three new approaches for controlling quantum information. First, I present a new protocol for continuously protecting unknown quantum states from noise. This protocol combines and expands ideas from the theories of quantum error correction and quantum feedback control. The result can outperform either approach by itself. I generalize this protocol to all known quantum stabilizer codes, and study its application to the three-qubit repetition code in detail via Monte Carlo simulations. Next, I present several new protocols for controlling quantum information that are fault-tolerant. These protocols require only local quantum processing due to the topological properties of the quantum error correcting codes upon which they are built. I show that each protocol's fault-dependence behavior exhibits an order-disorder phase transition when mapped onto an associated statistical-mechanical model. I review the critical error rates of these protocols found by numerical study of the associated models, and I present new analytic bounds for them using a self-avoiding random walk argument. Moreover, I discuss fault-tolerant procedures for encoding, error-correction, computing, and decoding quantum information using these protocols, and calculate the accuracy threshold of fault-tolerant quantum memory for protocols using them. I end by presenting a new class of quantum algorithms that solve combinatorial optimization problems solely by measurement. I compute the running times of these algorithms by establishing an explicit dynamical model for the measurement process. This model, the
Griffiths, Robert B.
2007-12-15
Quantum, in contrast to classical, information theory, allows for different incompatible types (or species) of information which cannot be combined with each other. Distinguishing these incompatible types is useful in understanding the role of the two classical bits in teleportation (or one bit in one-bit teleportation), for discussing decoherence in information-theoretic terms, and for giving a proper definition, in quantum terms, of 'classical information.' Various examples (some updating earlier work) are given of theorems which relate different incompatible kinds of information, and thus have no counterparts in classical information theory.
Similarity between quantum mechanics and thermodynamics: entropy, temperature, and Carnot cycle.
Abe, Sumiyoshi; Okuyama, Shinji
2011-02-01
The similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analog of the quantity of heat, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one. PMID:21405832
Entropy, chaos, and excited-state quantum phase transitions in the Dicke model.
Lóbez, C M; Relaño, A
2016-07-01
We study nonequilibrium processes in an isolated quantum system-the Dicke model-focusing on the role played by the transition from integrability to chaos and the presence of excited-state quantum phase transitions. We show that both diagonal and entanglement entropies are abruptly increased by the onset of chaos. Also, this increase ends in both cases just after the system crosses the critical energy of the excited-state quantum phase transition. The link between entropy production, the development of chaos, and the excited-state quantum phase transition is more clear for the entanglement entropy. PMID:27575109
Relating different quantum generalizations of the conditional Rényi entropy
Tomamichel, Marco; Berta, Mario; Hayashi, Masahito
2014-08-15
Recently a new quantum generalization of the Rényi divergence and the corresponding conditional Rényi entropies was proposed. Here, we report on a surprising relation between conditional Rényi entropies based on this new generalization and conditional Rényi entropies based on the quantum relative Rényi entropy that was used in previous literature. Our result generalizes the well-known duality relation H(A|B) + H(A|C) = 0 of the conditional von Neumann entropy for tripartite pure states to Rényi entropies of two different kinds. As a direct application, we prove a collection of inequalities that relate different conditional Rényi entropies and derive a new entropic uncertainty relation.
Analytic continuation of black hole entropy in Loop Quantum Gravity
NASA Astrophysics Data System (ADS)
Jibril, Ben Achour; Mouchet, Amaury; Noui, Karim
2015-06-01
We define the analytic continuation of the number of black hole microstates in Loop Quantum Gravity to complex values of the Barbero-Immirzi parameter γ. This construction deeply relies on the link between black holes and Chern-Simons theory. Technically, the key point consists in writing the number of microstates as an integral in the complex plane of a holomorphic function, and to make use of complex analysis techniques to perform the analytic continuation. Then, we study the thermodynamical properties of the corresponding system (the black hole is viewed as a gas of indistinguishable punctures) in the framework of the grand canonical ensemble where the energy is defined à la Frodden-Gosh-Perez from the point of view of an observer located close to the horizon. The semi-classical limit occurs at the Unruh temperature T U associated to this local observer. When γ = ± i, the entropy reproduces at the semi-classical limit the area law with quantum corrections. Furthermore, the quantum corrections are logarithmic provided that the chemical potential is fixed to the simple value μ = 2 T U.
Generating functions for black hole entropy in loop quantum gravity
Barbero G, J. Fernando; Villasenor, Eduardo J. S.
2008-06-15
We introduce, in a systematic way, a set of generating functions that solve all the different combinatorial problems that crop up in the study of black hole entropy in loop quantum gravity. Specifically we give generating functions for the following: the different sources of degeneracy related to the spectrum of the area operator, the solutions to the projection constraint, and the black hole degeneracy spectrum. Our methods are capable of handling the different countings proposed and discussed in the literature. The generating functions presented here provide the appropriate starting point to extend the results already obtained for microscopic black holes to the macroscopic regime - in particular those concerning the area law and the appearance of an effectively equidistant area spectrum.
Information entropy of conditionally exactly solvable potentials
Dutta, D.; Roy, P.
2011-03-15
We evaluate Shannon entropy for the position and momentum eigenstates of some conditionally exactly solvable potentials which are isospectral to harmonic oscillator and whose solutions are given in terms of exceptional orthogonal polynomials. The Bialynicki-Birula-Mycielski inequality has also been tested for a number of states.
On phase/current components of entropy/information descriptors of molecular states
NASA Astrophysics Data System (ADS)
Nalewajski, Roman F.
2014-10-01
Quantum-generalised descriptors of the information content of electronic states in molecules are proposed, in which non-classical (current) terms complement classical (probability) functionals of the ordinary information theory. The relation between densities of the familiar classical Fisher and Shannon information/entropy measures is applied to determine their non-classical complements. The quantum supplement of the classical Shannon entropy describes the average magnitude of the phase distribution, while the current term in the Fisher measure accounts for the gradient content of the state phase function. Illustrative applications of these quantum information concepts are presented and thermodynamical analogies are commented upon. The particle-density-constrained (vertical) and -unconstrained (horizontal) equilibria in molecules and their fragments are explored and the corresponding equilibrium 'thermodynamic' phases are determined. A separation of the density (modulus) and current (phase) factors of general many-electron states is effected using the Harriman-Zumbach-Maschke construction of antisymmetric states yielding the specified electron density. The phenomenological framework in spirit of the non-equilibrium thermodynamical description is proposed. It accounts for both the density and current degrees of freedom of molecular states. The associated entropy source in the information continuity equation is derived.
Role of information theoretic uncertainty relations in quantum theory
NASA Astrophysics Data System (ADS)
Jizba, Petr; Dunningham, Jacob A.; Joo, Jaewoo
2015-04-01
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson-Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson-Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.
Role of information theoretic uncertainty relations in quantum theory
Jizba, Petr; Dunningham, Jacob A.; Joo, Jaewoo
2015-04-15
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) Rényi entropy and its related entropy power. This allows us to find a new class of information-theoretic uncertainty relations (ITURs). The potency of such uncertainty relations in quantum mechanics is illustrated with a simple two-energy-level model where they outperform both the usual Robertson–Schrödinger uncertainty relation and Shannon entropy based uncertainty relation. In the continuous case the ensuing entropy power uncertainty relations are discussed in the context of heavy tailed wave functions and Schrödinger cat states. Again, improvement over both the Robertson–Schrödinger uncertainty principle and Shannon ITUR is demonstrated in these cases. Further salient issues such as the proof of a generalized entropy power inequality and a geometric picture of information-theoretic uncertainty relations are also discussed.
PREFACE: Quantum information processing
NASA Astrophysics Data System (ADS)
Briggs, Andrew; Ferry, David; Stoneham, Marshall
2006-05-01
Microelectronics and the classical information technologies transformed the physics of semiconductors. Photonics has given optical materials a new direction. Quantum information technologies, we believe, will have immense impact on condensed matter physics. The novel systems of quantum information processing need to be designed and made. Their behaviours must be manipulated in ways that are intrinsically quantal and generally nanoscale. Both in this special issue and in previous issues (see e.g., Spiller T P and Munro W J 2006 J. Phys.: Condens. Matter 18 V1-10) we see the emergence of new ideas that link the fundamentals of science to the pragmatism of market-led industry. We hope these papers will be followed by many others on quantum information processing in the Journal of Physics: Condensed Matter.
Quantum Information Theory for Quantum Communication
NASA Astrophysics Data System (ADS)
Koashi, Masato
This chapter gives a concise description of the fundamental concepts of quantum information and quantum communication, which is pertinent to the discussions in the subsequent chapters. Beginning with the basic set of rules that dictate quantum mechanics, the chapter explains the most general ways to describe quantum states, measurements, and state transformations. Convenient mathematical tools are also presented to provide an intuitive picture of a qubit, which is the simplest unit of quantum information. The chapter then elaborates on the distinction between quantum communication and classical communication, with emphasis on the role of quantum entanglement as a communication resource. Quantum teleportation and dense coding are then explained in the context of optimal resource conversions among quantum channels, classical channels, and entanglement.
NASA Astrophysics Data System (ADS)
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Self-similarity, conservation of entropy/bits and the black hole information puzzle
NASA Astrophysics Data System (ADS)
Singleton, Douglas; Vagenas, Elias C.; Zhu, Tao
2014-05-01
John Wheeler coined the phrase "it from bit" or "bit from it" in the 1980s. However, much of the interest in the connection between information, i.e. "bits", and physical objects, i.e. "its", stems from the discovery that black holes have characteristics of thermodynamic systems having entropies and temperatures. This insight led to the information loss problem — what happens to the "bits" when the black hole has evaporated away due to the energy loss from Hawking radiation? In this essay we speculate on a radical answer to this question using the assumption of self-similarity of quantum correction to the gravitational action and the requirement that the quantum corrected entropy be well behaved in the limit when the black hole mass goes to zero.
Reasonable fermionic quantum information theories require relativity
NASA Astrophysics Data System (ADS)
Friis, Nicolai
2016-03-01
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.
Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP
NASA Astrophysics Data System (ADS)
Anacleto, M. A.; Brito, F. A.; Passos, E.
2015-10-01
In this paper we focus on the Hamilton-Jacobi method to determine the entropy of a self-dual black hole by using linear and quadratic GUPs (generalized uncertainty principles). We have obtained the Bekenstein-Hawking entropy of self-dual black holes and its quantum corrections that are logarithm and also of several other types.
Concentrating Tripartite Quantum Information
NASA Astrophysics Data System (ADS)
Streltsov, Alexander; Lee, Soojoon; Adesso, Gerardo
2015-07-01
We introduce the concentrated information of tripartite quantum states. For three parties Alice, Bob, and Charlie, it is defined as the maximal mutual information achievable between Alice and Charlie via local operations and classical communication performed by Charlie and Bob. We derive upper and lower bounds to the concentrated information, and obtain a closed expression for it on several classes of states including arbitrary pure tripartite states in the asymptotic setting. We show that distillable entanglement, entanglement of assistance, and quantum discord can all be expressed in terms of the concentrated information, thus revealing its role as a unifying informational primitive. We finally investigate quantum state merging of mixed states with and without additional entanglement. The gap between classical and quantum concentrated information is proven to be an operational figure of merit for mixed state merging in the absence of additional entanglement. Contrary to the pure state merging, our analysis shows that classical communication in both directions can provide an advantage for merging of mixed states.
Two faces of entropy and information in biological systems.
Mitrokhin, Yuriy
2014-10-21
The article attempts to overcome the well-known paradox of contradictions between the emerging biological organization and entropy production in biological systems. It is assumed that quality, speculative correlation between entropy and antientropy processes taking place both in the past and today in the metabolic and genetic cellular systems may be perfectly authorized for adequate description of the evolution of biological organization. So far as thermodynamic entropy itself cannot compensate for the high degree of organization which exists in the cell, we discuss the mode of conjunction of positive entropy events (mutations) in the genetic systems of the past generations and the formation of organized structures of current cells. We argue that only the information which is generated in the conditions of the information entropy production (mutations and other genome reorganization) in genetic systems of the past generations provides the physical conjunction of entropy and antientropy processes separated from each other in time generations. It is readily apparent from the requirements of the Second law of thermodynamics. PMID:24956330
Markov property and strong additivity of von Neumann entropy for graded quantum systems
Moriya, Hajime
2006-03-15
The quantum Markov property is equivalent to the strong additivity of von Neumann entropy for graded quantum systems. The additivity of von Neumann entropy for bipartite graded systems implies the statistical independence of states. However, the structure of Markov states for graded systems is different from that for tensor-product systems which have trivial grading. For three-composed graded systems we have U(1)-gauge invariant Markov states whose restriction to the marginal pair of subsystems is nonseparable.
Entropy and complexity analysis of Dirac-delta-like quantum potentials
NASA Astrophysics Data System (ADS)
Bouvrie, P. A.; Angulo, J. C.; Dehesa, J. S.
2011-06-01
The Dirac-delta-like quantum-mechanical potentials are frequently used to describe and interpret numerous phenomena in many scientific fields including atomic and molecular physics, condensed matter and quantum computation. The entropy and complexity properties of potentials with one and two Dirac-delta functions are here analytically calculated and numerically discussed in both position and momentum spaces. We have studied the information-theoretic lengths of Fisher, Rényi and Shannon types as well as the Cramér-Rao, Fisher-Shannon and LMC shape complexities of the lowest-lying stationary states of one-delta and twin-delta. They allow us to grasp and quantify different facets of the spreading of the charge and momentum of the system far beyond the celebrated standard deviation.
Dynamics of Entropy in Quantum-like Model of Decision Making
NASA Astrophysics Data System (ADS)
Basieva, Irina; Khrennikov, Andrei; Asano, Masanari; Ohya, Masanori; Tanaka, Yoshiharu
2011-03-01
We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices. By using this equilibrium point Alice determines her mixed (i.e., probabilistic) strategy with respect to Bob. Thus our model is a model of thinking through decoherence of initially pure mental state. Decoherence is induced by interaction with memory and external environment. In this paper we study (numerically) dynamics of quantum entropy of Alice's state in the process of decision making. Our analysis demonstrates that this dynamics depends nontrivially on the initial state of Alice's mind on her own actions and her prediction state (for possible actions of Bob.)
NASA Astrophysics Data System (ADS)
Sahrai, M.; Arzhang, B.; Taherkhani, D.; Boroojerdi, V. Tahmoorian Askari
2015-03-01
The time evolution of the quantum entropy in a coherently driven triple quantum dot molecule is investigated. The entanglement of the quantum dot molecule and its spontaneous emission field is coherently controlled by the gate voltage and the rate of an incoherent pump field. The degree of entanglement between a triple quantum dot molecule and its spontaneous emission fields is decreased by increasing the tunneling parameter.
Quantum uncertainty of mixed states based on skew information
Luo Shunlong
2006-02-15
The uncertainty of a mixed state has two quite different origins: classical mixing and quantum randomness. While the classical aspect (mixedness) is significantly quantified by the von Neumann entropy, it seems that we still do not have a well accepted measure of quantum uncertainty. In terms of the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurements, we will propose an intrinsic measure for synthesizing quantum uncertainty of a mixed state and investigate its fundamental properties. We illustrate how it arises naturally from a naive hidden-variable approach to entanglement and how it exhibits a simple relation to the notion of negativity, which is an entanglement monotone introduced quite recently. We further show that it has a dramatic nonextensive feature resembling the probability law relating operations of two events. This measure of quantum uncertainty provides an alternative quantity complementary to the von Neumann entropy for studying mixedness and quantum correlations.
Two-site entropy and quantum phase transitions in low-dimensional models.
Legeza, O; Sólyom, J
2006-03-24
We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works equally well for fermionic and spin models, and the two-site entropy is a better indicator of quantum phase transition than calculating gaps, order parameters, or the single-site entropy. The method is especially convenient when the density-matrix renormalization-group algorithm is used. PMID:16605844
Entanglement entropy of disordered quantum chains following a global quench
NASA Astrophysics Data System (ADS)
Zhao, Y.; Andraschko, F.; Sirker, J.
2016-05-01
We numerically investigate the growth of the entanglement entropy Sent(t ) in time t , after a global quench from a product state, in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real-space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density-wave order parameter. We show that multiprecision calculations are required to reach the scaling regime and perform such calculations for specific cases. For interacting models with binary bond disorder we present data based on infinite-size density matrix renormalization group calculations and exact diagonalizations. We obtain numerical evidence of a many-body localized phase in bond-disordered systems where Sent(t ) ˜lnt seems to hold. Our results for bond disorder are contrasted with the well-studied case of potential disorder.
NASA Astrophysics Data System (ADS)
Brukner, Caslav; Zeilinger, Anton
2006-03-01
The violation of local realism is today a well established experimental fact. From it follows that either locality or realism or both cannot provide a foundational basis of Nature. Relaxing the locality condition would essentially not change the epistemological structure of classical physics but only extend its limits. Abandonment of reality, however, would require a radical revision of the conceptual background of all our theories so far. Is a novel conceptual basis of quantum theory feasible, in which the impossibility of defining external reality independent and prior to observation naturally emerges? We suggest the finiteness of information content of a quantum system as providing such basis. Any realistic theory that could arrive at an accurate prediction of a particular event would require the system to carry information as to which specific result will be observed for all possible future measurements. Because the system cannot carry more information than is in principle available, there must exist measurements for which individual events contain an element of irreducible randomness. Quantum entanglement arises from the possibility that information in a composite system resides more in the correlations than in properties of individuals. In the talk we will report on recent efforts towards providing derivations of the elements of the Hilbert space structure from the quantization of information.
Theory of entropy production in quantum many-body systems
NASA Astrophysics Data System (ADS)
Solano-Carrillo, E.; Millis, A. J.
2016-06-01
We define the entropy operator as the negative of the logarithm of the density matrix, give a prescription for extracting its thermodynamically measurable part, and discuss its dynamics. For an isolated system we derive the first, second, and third laws of thermodynamics. For weakly coupled subsystems of an isolated system, an expression for the long-time limit of the expectation value of the rate of change of the thermodynamically measurable part of the entropy operator is derived and interpreted in terms of entropy production and entropy transport terms. The interpretation is justified by comparison to the known expression for the entropy production in an aged classical Markovian system with Gaussian fluctuations and by a calculation of the current-induced entropy production in a conductor with electron-phonon scattering.
NASA Astrophysics Data System (ADS)
Mohammad-Djafari, Ali
2015-01-01
The main object of this tutorial article is first to review the main inference tools using Bayesian approach, Entropy, Information theory and their corresponding geometries. This review is focused mainly on the ways these tools have been used in data, signal and image processing. After a short introduction of the different quantities related to the Bayes rule, the entropy and the Maximum Entropy Principle (MEP), relative entropy and the Kullback-Leibler divergence, Fisher information, we will study their use in different fields of data and signal processing such as: entropy in source separation, Fisher information in model order selection, different Maximum Entropy based methods in time series spectral estimation and finally, general linear inverse problems.
Irreversible information loss: Fundamental notions and entropy costs
NASA Astrophysics Data System (ADS)
Anderson, Neal G.
2014-09-01
Landauer's Principle (LP) associates an entropy increase with the irreversible loss of information from a physical system. Clear statement, unambiguous interpretation, and proper application of LP requires precise, mutually consistent, and sufficiently general definitions for a set of interlocking fundamental notions and quantities (entropy, information, irreversibility, erasure). In this work, we critically assess some common definitions and quantities used or implied in statements of LP, and reconsider their definition within an alternative “referential” approach to physical information theory that embodies an overtly relational conception of physical information. We prove an inequality on the entropic cost of irreversible information loss within this context, as well as “referential analogs” of LP and its more general restatement by Bennett. Advantages of the referential approach for establishing fundamental limits on the physical costs of irreversible information loss in communication and computing systems are discussed throughout.
Competition between Homophily and Information Entropy Maximization in Social Networks
Zhao, Jichang; Liang, Xiao; Xu, Ke
2015-01-01
In social networks, it is conventionally thought that two individuals with more overlapped friends tend to establish a new friendship, which could be stated as homophily breeding new connections. While the recent hypothesis of maximum information entropy is presented as the possible origin of effective navigation in small-world networks. We find there exists a competition between information entropy maximization and homophily in local structure through both theoretical and experimental analysis. This competition suggests that a newly built relationship between two individuals with more common friends would lead to less information entropy gain for them. We demonstrate that in the evolution of the social network, both of the two assumptions coexist. The rule of maximum information entropy produces weak ties in the network, while the law of homophily makes the network highly clustered locally and the individuals would obtain strong and trust ties. A toy model is also presented to demonstrate the competition and evaluate the roles of different rules in the evolution of real networks. Our findings could shed light on the social network modeling from a new perspective. PMID:26334994
Competition between Homophily and Information Entropy Maximization in Social Networks.
Zhao, Jichang; Liang, Xiao; Xu, Ke
2015-01-01
In social networks, it is conventionally thought that two individuals with more overlapped friends tend to establish a new friendship, which could be stated as homophily breeding new connections. While the recent hypothesis of maximum information entropy is presented as the possible origin of effective navigation in small-world networks. We find there exists a competition between information entropy maximization and homophily in local structure through both theoretical and experimental analysis. This competition suggests that a newly built relationship between two individuals with more common friends would lead to less information entropy gain for them. We demonstrate that in the evolution of the social network, both of the two assumptions coexist. The rule of maximum information entropy produces weak ties in the network, while the law of homophily makes the network highly clustered locally and the individuals would obtain strong and trust ties. A toy model is also presented to demonstrate the competition and evaluate the roles of different rules in the evolution of real networks. Our findings could shed light on the social network modeling from a new perspective. PMID:26334994
Quantum entanglement and informational activities of biomolecules
NASA Astrophysics Data System (ADS)
Al-Shargi, Hanan; Berkovich, Simon
2009-03-01
Our model of holographic Universe [1] explains the surprising property of quantum entanglement and reveals its biological implications. The suggested holographic mechanism handles 2D slices of the physical world as a whole. Fitting this simple holistic process in the Procrustean bed of individual particles interactions leads to intricacies of quantum theory with an unintelligible protrusion of distant correlations. Holographic medium imposes dependence of quantum effects on absolute positioning. Testing this prediction for a non-exponential radioactive decay could resolutely point to outside ``memory.'' The essence of Life is in the sophistication of macromolecules. Distinctions in biological information processing of nucleotides in DNA and amino acids in proteins are related to entropies of their structures. Randomness of genetic configurations as exposed by their maximal entropy is characteristic of passive identification rather than active storage functionality. Structural redundancy of proteins shows their operability, of which different foldings of prions is most indicative. Folding of one prion can reshape another prion without a direct contact appearing like ``quantum entanglement,'' or ``teleportation.'' Testing the surmised influence of absolute orientation on the prion reshaping can uncover the latency effects in the ``mad cow'' disease. 1. Simon Berkovich, TR-GWU-CS-07-006, http://www.cs.gwu.edu/research/reports.php
Canonical energy is quantum Fisher information
NASA Astrophysics Data System (ADS)
Lashkari, Nima; Van Raamsdonk, Mark
2016-04-01
In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In gravitational physics, Canonical Energy defines a natural metric on the space of perturbations to spacetimes with a Killing horizon. In this paper, we show that the Fisher information metric for perturbations to the vacuum density matrix of a ball-shaped region B in a holographic CFT is dual to the canonical energy metric for perturbations to a corresponding Rindler wedge R B of Anti-de-Sitter space. Positivity of relative entropy at second order implies that the Fisher information metric is positive definite. Thus, for physical perturbations to anti-de-Sitter spacetime, the canonical energy associated to any Rindler wedge must be positive. This second-order constraint on the metric extends the first order result from relative entropy positivity that physical perturbations must satisfy the linearized Einstein's equations.
Quantum Markov chains, sufficiency of quantum channels, and Rényi information measures
NASA Astrophysics Data System (ADS)
Datta, Nilanjana; Wilde, Mark M.
2015-12-01
A short quantum Markov chain is a tripartite state {ρ }{ABC} such that system A can be recovered perfectly by acting on system C of the reduced state {ρ }{BC}. Such states have conditional mutual information I(A;B| C) equal to zero and are the only states with this property. A quantum channel {N} is sufficient for two states ρ and σ if there exists a recovery channel using which one can perfectly recover ρ from {N}(ρ ) and σ from {N}(σ ). The relative entropy difference D(ρ \\parallel σ )-D({N}(ρ )\\parallel {N}(σ )) is equal to zero if and only if {N} is sufficient for ρ and σ. In this paper, we show that these properties extend to Rényi generalizations of these information measures which were proposed in (Berta et al 2015 J. Math. Phys. 56 022205; Seshadreesan et al 2015 J. Phys. A: Math. Theor. 48 395303), thus providing an alternate characterization of short quantum Markov chains and sufficient quantum channels. These results give further support to these quantities as being legitimate Rényi generalizations of the conditional mutual information and the relative entropy difference. Along the way, we solve some open questions of Ruskai and Zhang, regarding the trace of particular matrices that arise in the study of monotonicity of relative entropy under quantum operations and strong subadditivity of the von Neumann entropy.
Relative entropies in conformal field theory.
Lashkari, Nima
2014-08-01
Relative entropy is a measure of distinguishability for quantum states, and it plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include, as special cases, most entropy measures used in quantum information theory. We construct a Euclidean path-integral approach to Renyi relative entropies in conformal field theory, then compute the fidelity and the relative entropy of states in one spatial dimension at zero and finite temperature using a replica trick. In contrast to the entanglement entropy, the relative entropy is free of ultraviolet divergences, and is obtained as a limit of certain correlation functions. The relative entropy of two states provides an upper bound on their trace distance. PMID:25126908
Maximal entanglement versus entropy for mixed quantum states
Wei, T.-C.; Goldbart, Paul M.; Kwiat, Paul G.; Nemoto, Kae; Munro, William J.; Verstraete, Frank
2003-02-01
Maximally entangled mixed states are those states that, for a given mixedness, achieve the greatest possible entanglement. For two-qubit systems and for various combinations of entanglement and mixedness measures, the form of the corresponding maximally entangled mixed states is determined primarily analytically. As measures of entanglement, we consider entanglement of formation, relative entropy of entanglement, and negativity; as measures of mixedness, we consider linear and von Neumann entropies. We show that the forms of the maximally entangled mixed states can vary with the combination of (entanglement and mixedness) measures chosen. Moreover, for certain combinations, the forms of the maximally entangled mixed states can change discontinuously at a specific value of the entropy. Along the way, we determine the states that, for a given value of entropy, achieve maximal violation of Bell's inequality.
Effects of Shannon entropy and electric field on polaron in RbCl triangular quantum dot
NASA Astrophysics Data System (ADS)
M, Tiotsop; A, J. Fotue; S, C. Kenfack; N, Issofa; H, Fotsin; L, C. Fai
2016-04-01
In this paper, the time evolution of the quantum mechanical state of a polaron is examined using the Pekar type variational method on the condition of the electric-LO-phonon strong-coupling and polar angle in RbCl triangular quantum dot. We obtain the eigenenergies, and the eigenfunctions of the ground state, and the first excited state respectively. This system in a quantum dot can be treated as a two-level quantum system qubit and the numerical calculations are performed. The effects of Shannon entropy and electric field on the polaron in the RbCl triangular quantum dot are also studied.
Entropy, fidelity, and double orthogonality for resonance states in two-electron quantum dots
Pont, Federico M.; Osenda, Omar; Serra, Pablo; Toloza, Julio H.
2010-04-15
Resonance states of a two-electron quantum dots are studied using a variational expansion with both real basis-set functions and complex scaling methods. The two-electron entanglement (linear entropy) is calculated as a function of the electron repulsion at both sides of the critical value, where the ground (bound) state becomes a resonance (unbound) state. The linear entropy and fidelity and double orthogonality functions are compared as methods for the determination of the real part of the energy of a resonance. The complex linear entropy of a resonance state is introduced using complex scaling formalism.
Shannon entropy and decoherence of bound magnetopolaron in a modified cylindrical quantum dot
NASA Astrophysics Data System (ADS)
Fotue, A. J.; Kenfack, S. C.; Tiotsop, M.; Issofa, N.; Wirngo, A. V.; Tabue Djemmo, M. P.; Fotsin, H.; Fai, L. C.
2015-12-01
In this paper, we calculate the time evolution of the quantum mechanical state of a bound magnetopolaron in a modified cylindrical quantum dot. In the condition of strong coupling, we investigate the eigen energies and the eigenfunctions of the ground state and the first excited state, respectively. This system may be employed as a two-level quantum system qubit and therefore be helpful for storage of information. The Shannon entropy is used to investigate the decoherence of the qubit when the latter is in the superposition state of the ground and the first excited states. We also study the influence of the electric field, the magnetic field and the Coulomb potential on the decoherence time, eigen energies of the ground state, and the first excited state. It is shown that, the phonon spontaneous emission causes the decoherence of the qubit. We plot the decay of the density matrix of the qubit and the coherent term of the density matrix element p01 (or p10) in a function of time for different coupling strengths, confinement lengths and dispersion coefficient.
Isobaric yield ratio difference and Shannon information entropy
NASA Astrophysics Data System (ADS)
Ma, Chun-Wang; Wei, Hui-Ling; Wang, Shan-Shan; Ma, Yu-Gang; Wada, Ryoichi; Zhang, Yan-Li
2015-03-01
The Shannon information entropy theory is used to explain the recently proposed isobaric yield ratio difference (IBD) probe which aims to determine the nuclear symmetry energy. Theoretically, the difference between the Shannon uncertainties carried by isobars in two different reactions (ΔIn21), is found to be equivalent to the difference between the chemical potentials of protons and neutrons of the reactions [the IBD probe, IB- Δ(βμ)21, with β the reverse temperature]. From the viewpoints of Shannon information entropy, the physical meaning of the above chemical potential difference is interpreted by ΔIn21 as denoting the nuclear symmetry energy or density difference between neutrons and protons in reactions more concisely than from the statistical ablation-abrasion model.
On entropy/information continuity in molecular electronic states
NASA Astrophysics Data System (ADS)
Nalewajski, Roman F.
2016-04-01
ARRAY(0x2421ba0) This article is dedicated to Prof. Andreas Savin on the occasion of his 65th birthday.Throughout the article x denotes a scalar quantity, x stands for the row- or column-vector, and x represents a square or rectangular matrix. The natural logarithm log = ln used in the Shannon entropy expresses the amount of information in nats (natural units): 1 nat = 1.44 bits.
Quantum Mutual Entropy for a Multilevel Atom Interacting with a Cavity Field
NASA Astrophysics Data System (ADS)
Abdel-Aty, M.; Wahiddin, M. R. B.; Obada, A.-S. F.
2007-04-01
We derive an explicit formula for the quantum mutual entropy as a measure of the total correlations in a multi-level atom interacting with a cavity field. We describe its theoretical basis and discuss its practical relevance. The effect of the number of levels involved on the quantum mutual entropy is demonstrated via examples of three-, four- and five-level atom. Numerical calculations under current experimental conditions are performed and it is found that the number of levels present changes the general features of the correlations dramatically.
Characterizing the dynamical semigroups that do not decrease a quantum entropy
NASA Astrophysics Data System (ADS)
Aniello, Paolo; Chruściński, Dariusz
2016-08-01
In finite dimensions, we provide characterizations of the quantum dynamical semigroups that do not decrease the von Neumann, the Tsallis and the Rényi entropies, as well as a family of functions of density operators strictly related to the Schatten norms. A few remarkable consequences—in particular, a description of the associated infinitesimal generators—are derived, and some significant examples are discussed. Extensions of these results to semigroups of trace-preserving positive (i.e., not necessarily completely positive) maps and to a more general class of quantum entropies are also considered.
NASA Astrophysics Data System (ADS)
Bousso, Raphael
2016-07-01
We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focusing and area loss can be computed perturbatively on a Minkowski background, yielding entropy bounds in terms of the energy flux of the outgoing radiation. In the asymptotic limit, we obtain boundary versions of the quantum null energy condition, of the generalized Second Law, and of the quantum Bousso bound.
Spickermann, Christian; Lehmann, Sebastian B C; Kirchner, Barbara
2008-06-28
In the present study, we employ quantum cluster equilibrium calculations on a small water cluster set in order to derive thermochemical equilibrium properties of the liquid phase as well as the liquid-vapor phase transition. The focus is set on the calculation of liquid phase entropies, from which entropies of vaporization at the normal boiling point of water are derived. Different electronic structure methods are compared and the influences of basis set size and of cooperative effects are discussed. In line with a previous study on the subject [B. Kirchner, J. Chem. Phys. 123, 204116 (2005)], we find that the neglect of cooperativity leads to large errors in the equilibrium cluster populations as well as in the obtained entropy values. In contrast, a correct treatment of the intermolecular many-body interaction yields liquid phase entropies and phase transition entropies being in very good agreement with the experimental reference, thus demonstrating that the quantum cluster equilibrium partition function intrinsically accounts for the shortcomings of the ideal gas partition function often employed in first principles entropy calculations. Comparing the calculated vaporization entropies to the value predicted by Trouton's rule, it is observed that for entropy calculations the consideration of intracluster cooperative effects is more important than the explicit treatment of the intercluster association even in a highly associated liquid such as water. The decomposition of entropy into contributions due to different degrees of freedom implies the need for the accurate treatment of particle indistinguishability and free volume of translation, whereas minor influences should be expected from the vibrational and rotational degrees of freedom and none from the electronic degrees of freedom. PMID:18618941
Indirect Acquisition of Information in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Ballesteros, M.; Fraas, M.; Fröhlich, J.; Schubnel, B.
2016-02-01
Long sequences of successive direct (projective) measurements or observations of just a few "uninteresting" physical quantities pertaining to a quantum system, such as clicks of some detectors, may reveal indirect, but precise and unambiguous information on the values of some very "interesting" observables of the system. In this paper, the mathematics underlying this claim is developed; i.e., we attempt to contribute to a mathematical theory of indirect and, in particular, non-demolition observations and measurements in quantum mechanics. Our attempt leads us to make some novel uses of classical notions and results of probability theory, such as the "algebra of functions measurable at infinity", the Central Limit Theorem, results concerning relative entropy and its role in the theory of large deviations, etc.
Measuring entanglement entropy of a generic many-body system with a quantum switch.
Abanin, Dmitry A; Demler, Eugene
2012-07-13
Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Rényi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order. PMID:23030142
Automatic detection of marine mammals using information entropy.
Erbe, Christine; King, Andrew R
2008-11-01
This article describes an automatic detector for marine mammal vocalizations. Even though there has been previous research on optimizing automatic detectors for specific calls or specific species, the detection of any type of call by a diversity of marine mammal species still poses quite a challenge--and one that is faced more frequently as the scope of passive acoustic monitoring studies and the amount of data collected increase. Information (Shannon) entropy measures the amount of information in a signal. A detector based on spectral entropy surpassed two commonly used detectors based on peak-energy detection. Receiver operating characteristic curves were computed for performance comparison. The entropy detector performed considerably faster than real time. It can be used as a first step in an automatic signal analysis yielding potential signals. It should be followed by automatic classification, recognition, and identification algorithms to group and identify signals. Examples are shown from underwater recordings in the Western Canadian Arctic. Calls of a variety of cetacean and pinniped species were detected. PMID:19045771
Characteristic features of Shannon information entropy of confined atoms
NASA Astrophysics Data System (ADS)
Sen, K. D.
2005-08-01
The Shannon information entropy of 1-normalized electron density in position and momentum space Sr and Sp, and the sum ST, respectively, are reported for the ground-state H, He+, Li2+, H-, He, Li+, Li, and B atoms confined inside an impenetrable spherical boundary defined by radius R. We find new characteristic features in ST denoted by well-defined minimum and maximum as a function of confinement. The results are analyzed in the background of the irreducible lower bound stipulated by the entropy uncertainty principle [I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975)]. The spherical confinement model leads to the ST values which satisfy the lower bound up to the limits of extreme confinements with the interesting new result displaying regions over which a set of upper and lower bounds to the information entropy sum can be locally prescribed. Similar calculations on the H atom in 2s excited states are presented and their novel characteristics are discussed.
Min-entropy and quantum key distribution: Nonzero key rates for ''small'' numbers of signals
Bratzik, Sylvia; Mertz, Markus; Kampermann, Hermann; Bruss, Dagmar
2011-02-15
We calculate an achievable secret key rate for quantum key distribution with a finite number of signals by evaluating the quantum conditional min-entropy explicitly. The min-entropy for a classical random variable is the negative logarithm of the maximal value in its probability distribution. The quantum conditional min-entropy can be expressed in terms of the guessing probability, which we calculate for d-dimensional systems. We compare these key rates to previous approaches using the von Neumann entropy and find nonzero key rates for a smaller number of signals. Furthermore, we improve the secret key rates by modifying the parameter estimation step. Both improvements taken together lead to nonzero key rates for only 10{sup 4}-10{sup 5} signals. An interesting conclusion can also be drawn from the additivity of the min-entropy and its relation to the guessing probability: for a set of symmetric tensor product states, the optimal minimum-error discrimination (MED) measurement is the optimal MED measurement on each subsystem.
NASA Astrophysics Data System (ADS)
Shastry, Abhay; Stafford, Charles A.
2015-12-01
We consider a question motivated by the third law of thermodynamics: Can there be a local temperature arbitrarily close to absolute zero in a nonequilibrium quantum system? We consider nanoscale quantum conductors with the source reservoir held at finite temperature and the drain held at or near absolute zero, a problem outside the scope of linear response theory. We obtain local temperatures close to absolute zero when electrons originating from the finite temperature reservoir undergo destructive quantum interference. The local temperature is computed by numerically solving a nonlinear system of equations describing equilibration of a scanning thermoelectric probe with the system, and we obtain excellent agreement with analytic results derived using the Sommerfeld expansion. A local entropy for a nonequilibrium quantum system is introduced and used as a metric quantifying the departure from local equilibrium. It is shown that the local entropy of the system tends to zero when the probe temperature tends to zero, consistent with the third law of thermodynamics.
An entropy-based measure of founder informativeness.
Reyes-Valdés, M Humberto; Williams, Claire G
2005-02-01
Optimizing quantitative trait locus (QTL) mapping experiments requires a generalized measure of marker informativeness because variable information is obtained from different marker systems, marker distribution and pedigree types. Such a measure can be derived from the concept of Shannon entropy, a central concept in information theory. Here we introduce entropy-based founder informativeness (EFI), a new measure of information content generalized across pedigrees, maps, marker systems and mating configurations. We derived equations for inbred- and outbred-derived mapping populations. Mathematical properties of EFI include enhanced sensitivity to mapping population type and extension to any number of founders. To illustrate the use of EFI, we compared experimental designs for QTL mapping for three examples: (i) different marker systems for an F2 pedigree, (ii) different marker densities and sampling sizes for a BC1 pedigree and (iii) a comparison of haplotypic versus zygotic analyses of an outbred pedigree. As an a priori generalized measure of information content, EFI does not require phenotypic data for optimizing experimental designs for QTL mapping. PMID:16089038
Quantum Information: Opportunities and Challenges
Bennink, Ryan S
2008-01-01
Modern society is shaped by the ability to transmit, manipulate, and store large amounts of information. Although we tend to think of information as abstract, information is physical, and computing is a physical process. How then should we understand information in a quantum world, in which physical systems may exist in multiple states at once and are altered by the very act of observation? This question has evolved into an exciting new field of research called Quantum Information (QI). QI challenges many accepted rules and practices in computer science. For example, a quantum computer would turn certain hard problems into soft problems, and would render common computationally-secure encryption methods (such as RSA) insecure. At the same time, quantum communication would provide an unprecedented kind of intrinsic information security at the level of the smallest physical objects used to store or transmit the information. This talk provides a general introduction to the subject of quantum information and its relevance to cyber security. In the first part, two of the stranger aspects of quantum physics namely, superposition and uncertainty are explained, along with their relation to the concept of information. These ideas are illustrated with a few examples: quantum ID cards, quantum key distribution, and Grover s quantum search algorithm. The state-of-the-art in quantum computing and communication hardware is then discussed, along with the daunting technological challenges that must be overcome. Relevant experimental and theoretical efforts at ORNL are highlighted. The talk concludes with speculations on the short- and long-term impact of quantum information on cyber security.
Thermodynamical properties of triangular quantum wires: entropy, specific heat, and internal energy
NASA Astrophysics Data System (ADS)
Khordad, R.
2016-07-01
In the present work, thermodynamical properties of a GaAs quantum wire with equilateral triangle cross section are studied. First, the energy levels of the system are obtained by solving the Schrödinger equation. Second, the Tsallis formalism is applied to obtain entropy, internal energy, and specific heat of the system. We have found that the specific heat and entropy have certain physically meaningful values, which mean thermodynamic properties cannot take any continuous value, unlike classical thermodynamics in which they are considered as continuous quantities. Maximum of entropy increases with increasing the wire size. The specific heat is zero at special temperatures. Specific heat decreases with increasing temperature. There are several peaks in specific heat, and these are dependent on quantum wire size.
Nonadditive entropy reconciles the area law in quantum systems with classical thermodynamics.
Caruso, Filippo; Tsallis, Constantino
2008-08-01
The Boltzmann-Gibbs-von Neumann entropy of a large part (of linear size L ) of some (much larger) d -dimensional quantum systems follows the so-called area law (as for black holes), i.e., it is proportional to Ld-1. Here we show, for d=1,2 , that the (nonadditive) entropy Sq satisfies, for a special value of q not equal to 1, the classical thermodynamical prescription for the entropy to be extensive, i.e., Sq proportional variant Ld. Therefore, we reconcile with classical thermodynamics the area law widespread in quantum systems. Recently, a similar behavior was exhibited in mathematical models with scale-invariant correlations [C. Tsallis, M. Gell-Mann, and Y. Sato, Proc. Natl. Acad. Sci. U.S.A.102 15377 (2005)]. Finally, we find that the system critical features are marked by a maximum of the special entropic index q. PMID:18850781
Informational derivation of quantum theory
NASA Astrophysics Data System (ADS)
Chiribella, Giulio; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2011-07-01
We derive quantum theory from purely informational principles. Five elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—define a broad class of theories of information processing that can be regarded as standard. One postulate—purification—singles out quantum theory within this class.
Entropy of conditional tomographic probability distributions for classical and quantum systems
NASA Astrophysics Data System (ADS)
Man'ko, Margarita A.; Man'ko, Vladimir I.
2013-06-01
The possibility to describe hybrid systems containing classical and quantum subsystems by means of conditional tomographic probability distributions (tomograms) is discussed. Tomographic Shannon and Rényi entropies associated with the tomograms are studied, and new tomographic uncertainty relations are obtained.
NASA Astrophysics Data System (ADS)
Obregón, Octavio; Cabo Bizet, Nana Geraldine
2016-03-01
Generalized information (entanglement) entropy(ies) that depend only on the probability (the density matrix) will be exhibited. It will be shown that these generalized information entropy(ies) are obtained by means of the superstatistics proposal and they correspond to generalized entanglement entropy(ies) that are at the same time a consequence of generalizing the Replica trick. Following the entropic force formulation, these generalized entropy(ies) provide a modified Newtońs law of gravitation. We discuss the difficulties to get an associated theory of gravity. Moreover, our results show corrections to the von Neumann entropy S0 that are larger than the usual UV ones and also than the corrections to the length dependent AdS3 entropy which result comparable to the UV ones. The correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT and the gravitational AdS3 entropies.
Lateral Quantum Dots for Quantum Information Processing
NASA Astrophysics Data System (ADS)
House, Matthew Gregory
The possibility of building a computer that takes advantage of the most subtle nature of quantum physics has been driving a lot of research in atomic and solid state physics for some time. It is still not clear what physical system or systems can be used for this purpose. One possibility that has been attracting significant attention from researchers is to use the spin state of an electron confined in a semiconductor quantum dot. The electron spin is magnetic in nature, so it naturally is well isolated from electrical fluctuations that can a loss of quantum coherence. It can also be manipulated electrically, by taking advantage of the exchange interaction. In this work we describe several experiments we have done to study the electron spin properties of lateral quantum dots. We have developed lateral quantum dot devices based on the silicon metal-oxide-semiconductor transistor, and studied the physics of electrons confined in these quantum dots. We measured the electron spin excited state lifetime, which was found to be as long as 30 ms at the lowest magnetic fields that we could measure. We fabricated and characterized a silicon double quantum dot. Using this double quantum dot design, we fabricated devices which combined a silicon double quantum dot with a superconducting microwave resonator. The microwave resonator was found to be sensitive to two-dimensional electrons in the transistor channel, which we measured and characterized. We developed a new method for extracting information from random telegraph signals, which are produced when we observe thermal fluctuations of electrons in quantum dots. The new statistical method, based on the hidden Markov model, allows us to detect spin-dependent effects in such fluctuations even though we are not able to directly observe the electron spin. We use this analysis technique on data from two experiments involving gallium arsenide quantum dots and use it to measure spin-dependent tunneling rates. Our results advance the
How an autonomous quantum Maxwell demon can harness correlated information
NASA Astrophysics Data System (ADS)
Chapman, Adrian; Miyake, Akimasa
2015-12-01
We study an autonomous quantum system which exhibits refrigeration under an information-work trade-off like a Maxwell demon. The system becomes correlated as a single "demon" qubit interacts sequentially with memory qubits while in contact with two heat reservoirs of different temperatures. Using strong subadditivity of the von Neumann entropy, we derive a global Clausius inequality to show thermodynamic advantages from access to correlated information. It is demonstrated, in a matrix product density operator formalism, that our demon can simultaneously realize refrigeration against a thermal gradient and erasure of information from its memory, which is impossible without correlations. The phenomenon can be even enhanced by the presence of quantum coherence.
Optical Hybrid Quantum Information Processing
NASA Astrophysics Data System (ADS)
Takeda, Shuntaro; Furusawa, Akira
Historically, two complementary approaches to optical quantum information processing have been pursued: qubits and continuous-variables, each exploiting either particle or wave nature of light. However, both approaches have pros and cons. In recent years, there has been a significant progress in combining both approaches with a view to realizing hybrid protocols that overcome the current limitations. In this chapter, we first review the development of the two approaches with a special focus on quantum teleportation and its applications. We then introduce our recent research progress in realizing quantum teleportation by a hybrid scheme, and mention its future applications to universal and fault-tolerant quantum information processing.
NASA Astrophysics Data System (ADS)
Dupuis, Frédéric; Wilde, Mark M.
2016-03-01
This paper introduces "swiveled Rényi entropies" as an alternative to the Rényi entropic quantities put forward in Berta et al. (Phys Rev A 91(2):022333, 2015). What distinguishes the swiveled Rényi entropies from the prior proposal of Berta et al. is that there is an extra degree of freedom: an optimization over unitary rotations with respect to particular fixed bases (swivels). A consequence of this extra degree of freedom is that the swiveled Rényi entropies are ordered, which is an important property of the Rényi family of entropies. The swiveled Rényi entropies are, however, generally discontinuous at α =1 and do not converge to the von Neumann entropy-based measures in the limit as α rightarrow 1, instead bounding them from above and below. Particular variants reduce to known Rényi entropies, such as the Rényi relative entropy or the sandwiched Rényi relative entropy, but also lead to ordered Rényi conditional mutual information and ordered Rényi generalizations of a relative entropy difference. Refinements of entropy inequalities such as monotonicity of quantum relative entropy and strong subadditivity follow as a consequence of the aforementioned properties of the swiveled Rényi entropies. Due to the lack of convergence at α =1, it is unclear whether the swiveled Rényi entropies would be useful in one-shot information theory, so that the present contribution represents partial progress toward this goal.
Creation of a low-entropy quantum gas of polar molecules in an optical lattice.
Moses, Steven A; Covey, Jacob P; Miecnikowski, Matthew T; Yan, Bo; Gadway, Bryce; Ye, Jun; Jin, Deborah S
2015-11-01
Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena. However, realizing a highly degenerate quantum gas of molecules with a low entropy per particle is challenging. We report the synthesis of a low-entropy quantum gas of potassium-rubidium molecules (KRb) in a three-dimensional optical lattice. We simultaneously load into the optical lattice a Mott insulator of bosonic Rb atoms and a single-band insulator of fermionic K atoms. Then, using magnetoassociation and optical state transfer, we efficiently produce ground-state molecules in the lattice at those sites that contain one Rb and one K atom. The achieved filling fraction of 25% should enable future studies of transport and entanglement propagation in a many-body system with long-range dipolar interactions. PMID:26542566
Creation of a low-entropy quantum gas of polar molecules in an optical lattice
NASA Astrophysics Data System (ADS)
Moses, Steven A.; Covey, Jacob P.; Miecnikowski, Matthew T.; Yan, Bo; Gadway, Bryce; Ye, Jun; Jin, Deborah S.
2015-11-01
Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena. However, realizing a highly degenerate quantum gas of molecules with a low entropy per particle is challenging. We report the synthesis of a low-entropy quantum gas of potassium-rubidium molecules (KRb) in a three-dimensional optical lattice. We simultaneously load into the optical lattice a Mott insulator of bosonic Rb atoms and a single-band insulator of fermionic K atoms. Then, using magnetoassociation and optical state transfer, we efficiently produce ground-state molecules in the lattice at those sites that contain one Rb and one K atom. The achieved filling fraction of 25% should enable future studies of transport and entanglement propagation in a many-body system with long-range dipolar interactions.
Shannon information entropy in position space for two-electron atomic systems
NASA Astrophysics Data System (ADS)
Lin, Chien-Hao; Ho, Yew Kam
2015-07-01
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited states in helium-like systems. In this work, we adopt another entropic measure, Shannon entropy, to probe the nature of correlation effects. Besides the results of the Shannon entropy in coordinate space for the singlet ground states of helium-like systems including positronium negative ion, hydrogen negative ion, helium atom, and lithium positive ion, we also show results for systems with nucleus charge around the ionization threshold.
Hybrid quantum information processing
NASA Astrophysics Data System (ADS)
Furusawa, Akira
2013-03-01
There are two types of schemes for quantum information processing (QIP). One is based on qubits, and the other is based on continuous variables (CVs), where the computational basis for qubit QIP is { | 0 > , | 1 > } and that for CV QIP is { | x > } (- ∞ < x < ∞). A universal gate set for qubit QIP is {`bit flip'σx, `phase flip'σz, `Hadamard gate'H, ` π / 8 gate', `controlled NOT (CNOT) gate'}. Similarly, a universal gate set for CV QIP is {` x-displacement' D& circ; (x) , ` p-displacement' D& circ; (ip) , `Fourier gate' F& circ;, `cubic phase gate'e ikxcirc;3, `quantum non-demolition (QND) gate'}. There is one-to-one correspondence between them. CV version of `bit flip'σx is ` x-displacement' D& circ; (x) , which changes the value of the computational basis. Similarly, CV version of `phase flip'σz is ` p-displacement' D& circ; (ip) , where `phase flip'σz switches the ``value'' of `conjugate basis' of qubit { | + > , | - > } (| +/- > = (| 0 > +/- | 1 >) / √{ 2}) and ` p-displacement' D& circ; (ip) changes the value of CV conjugate basis { | p > }. `Hadamard' and `Fourier' gates transform computational bases to respective conjugate bases. CV version of ` π / 8 gate' is a `cubic phase gate'e ikxcirc;3, and CV version of CNOT gate is a QND gate. However, the origin of nonlinearity for QIP is totally different, here the very basic nonlinear operation is calculation of multiplication and of course it is the heart of information processing. The nonlinearity of qubit QIP comes from a CNOT gate, while that of CV QIP comes from a cubic phase gate. Since nonlinear operations are harder to realize compared to linear operations, the most difficult operation for qubit is a CNOT gate, while the counter part, a QND gate, is not so difficult. CNOT and QND gates are both entangling gates, it follows that creating entanglement is easier for CV QIP compared to qubit QIP. Here, creating entanglement is the heart of QIP. So, it is a big advantage of CV QIP. On
Quantum information to the home
NASA Astrophysics Data System (ADS)
Choi, Iris; Young, Robert J.; Townsend, Paul D.
2011-06-01
Information encoded on individual quanta will play an important role in our future lives, much as classically encoded digital information does today. Combining quantum information carried by single photons with classical signals encoded on strong laser pulses in modern fibre-to-the-home (FTTH) networks is a significant challenge, the solution to which will facilitate the global distribution of quantum information to the home and with it a quantum internet [1]. In real-world networks, spontaneous Raman scattering in the optical fibre would induce crosstalk between the high-power classical channels and a single-photon quantum channel, such that the latter is unable to operate. Here, we show that the integration of quantum and classical information on an FTTH network is possible by performing quantum key distribution (QKD) on a network while simultaneously transferring realistic levels of classical data. Our novel scheme involves synchronously interleaving a channel of quantum data with the Raman scattered photons from a classical channel, exploiting the periodic minima in the instantaneous crosstalk and thereby enabling secure QKD to be performed.
Models, Entropy and Information of Temporal Social Networks
NASA Astrophysics Data System (ADS)
Zhao, Kun; Karsai, Márton; Bianconi, Ginestra
Temporal social networks are characterized by heterogeneous duration of contacts, which can either follow a power-law distribution, such as in face-to-face interactions, or a Weibull distribution, such as in mobile-phone communication. Here we model the dynamics of face-to-face interaction and mobile phone communication by a reinforcement dynamics, which explains the data observed in these different types of social interactions. We quantify the information encoded in the dynamics of these networks by the entropy of temporal networks. Finally, we show evidence that human dynamics is able to modulate the information present in social network dynamics when it follows circadian rhythms and when it is interfacing with a new technology such as the mobile-phone communication technology.
Entanglement entropy and mutual information in Bose-Einstein condensates
Ding Wenxin; Yang Kun
2009-07-15
In this paper we study the entanglement properties of free nonrelativistic Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system and find that it diverges logarithmically with the particle number in the subsystem. For finite temperatures, we study the mutual information between the two blocks. We first analytically study an infinite-range hopping model, then numerically study a set of long-range hopping models in one dimension that exhibit Bose-Einstein condensation. In both cases we find that a Bose-Einstein condensate, if present, makes a divergent contribution to the mutual information which is proportional to the logarithm of the number of particles in the condensate in the subsystem. The prefactor of the logarithmic divergent term is model dependent.
Thermodynamics of Maximum Transition Entropy for Quantum Assemblies
NASA Astrophysics Data System (ADS)
Rogers, David
2015-03-01
We present one possible unifying framework for the statistics of driven quantum systems in terms of a stochastic propagator for the density matrix. Its classical limit [Rogers, Beck and Rempe, J. Stat. Phys 145:385, 2011] takes the form of a Langevin equation with an associated large-deviation functional intimately related to the partition function of statistical mechanics. Surprising results of this quantum theory are that work is a measurable quantity, and that a precise form of the second law of thermodynamics can be stated for dynamical systems. Numerical results are presented for the time-course of work and heat production for trapped 1D particles. Properties of the large deviation functional are discussed in the context of the quantum measurement problem.
Note on a Family of Monotone Quantum Relative Entropies
NASA Astrophysics Data System (ADS)
Deuchert, Andreas; Hainzl, Christian; Seiringer, Robert
2015-10-01
Given a convex function and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691-705, 2014) the relative entropy defined by . Among other things, they prove that the so-defined quantity is monotone if and only if is operator monotone. The monotonicity is then used to properly define for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections with strongly, the limit is shown to exist and to be independent of the sequence of projections . The question whether this sequence converges to its "obvious" limit, namely , has been left open. We answer this question in principle affirmatively and show that . If the operators A and B are regular enough, that is ( A - B), and are trace-class, the identity holds.
Quantum Tomograms and Their Application in Quantum Information Science
NASA Astrophysics Data System (ADS)
Fedorov, Aleksey K.; Yurchenko, Stanislav O.
2013-02-01
This note is devoted to quantum tomograms application in quantum information science. Representation for quantum tomograms of continuous variables via Feynman path integrals is considered. Due to this construction quantum tomograms of harmonic oscillator are obtained. Application tomograms in causal analysis of quantum states is presented. Two qubit maximum entangled and "quantum-classical" states have been analyzed by tomographic causal analysis of quantum states.
Information entropy of Gegenbauer polynomials and Gaussian quadrature
NASA Astrophysics Data System (ADS)
Sánchez-Ruiz, Jorge
2003-05-01
In a recent paper (Buyarov V S, López-Artés P, Martínez-Finkelshtein A and Van Assche W 2000 J. Phys. A: Math. Gen. 33 6549-60), an efficient method was provided for evaluating in closed form the information entropy of the Gegenbauer polynomials C(lambda)n(x) in the case when lambda = l in Bbb N. For given values of n and l, this method requires the computation by means of recurrence relations of two auxiliary polynomials, P(x) and H(x), of degrees 2l - 2 and 2l - 4, respectively. Here it is shown that P(x) is related to the coefficients of the Gaussian quadrature formula for the Gegenbauer weights wl(x) = (1 - x2)l-1/2, and this fact is used to obtain the explicit expression of P(x). From this result, an explicit formula is also given for the polynomial S(x) = limnrightarrowinfty P(1 - x/(2n2)), which is relevant to the study of the asymptotic (n rightarrow infty with l fixed) behaviour of the entropy.
Unification of quantum information theory
NASA Astrophysics Data System (ADS)
Abeyesinghe, Anura
We present the unification of many previously disparate results in noisy quantum Shannon theory and the unification of all of noiseless quantum Shannon theory. More specifically we deal here with bipartite, unidirectional, and memoryless quantum Shannon theory. We find all the optimal protocols and quantify the relationship between the resources used, both for the one-shot and for the ensemble case, for what is arguably the most fundamental task in quantum information theory: sharing entangled states between a sender and a receiver. We find that all of these protocols are derived from our one-shot superdense coding protocol and relate nicely to each other. We then move on to noisy quantum information theory and give a simple, direct proof of the "mother" protocol, or rather her generalization to the Fully Quantum Slepian-Wolf protocol (FQSW). FQSW simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim, and Winter as well as a new class of distributed compression protocols for correlated quantum sources, which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.
First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy
NASA Astrophysics Data System (ADS)
Westermann, Till; Manthe, Uwe
2012-05-01
A new concept to describe the quantum dynamics in complex systems is suggested. It extends established schemes based on the Dirac-Frenkel variation principle, e.g., the multi-configurational time-dependent Hartree (MCTDH) approach. The concept is based on a correlation-based von Neumann entropy (CvN-entropy) definition measuring the complexity of the wavefunction. Equations of motion are derived using a CvN-entropy constraint in the variational principle and result in a generally applicable effective Hamiltonian. It consists of the standard Hamilton operator and an additional nonlinear operator which limits the complexity of the wavefunction. Effectively, this nonlinear operator absorbs complex structures which are emerging in the wavefunction and allows one to introduce non-norm conserving equations of motion. Important aspects of the new concept are outlined studying the wave packet propagation on the diabatic B2 potential energy surfaces of NO2. First, it is demonstrated that during standard wave packet propagation the CvN-entropy increases strongly with time roughly independent of the coordinate systems employed. Second, one finds that employing CvN-entropy constrained MCTDH propagation yields improved wave function accuracy on longer time scales while compromising on the short time accuracy. Third, the loss of the wavefunction's norm is directly related to the overlap with the exact wavefunction. This provides an error estimate available without knowing an exact reference.
First principle nonlinear quantum dynamics using a correlation-based von Neumann entropy.
Westermann, Till; Manthe, Uwe
2012-05-28
A new concept to describe the quantum dynamics in complex systems is suggested. It extends established schemes based on the Dirac-Frenkel variation principle, e.g., the multi-configurational time-dependent Hartree (MCTDH) approach. The concept is based on a correlation-based von Neumann entropy (CvN-entropy) definition measuring the complexity of the wavefunction. Equations of motion are derived using a CvN-entropy constraint in the variational principle and result in a generally applicable effective Hamiltonian. It consists of the standard Hamilton operator and an additional nonlinear operator which limits the complexity of the wavefunction. Effectively, this nonlinear operator absorbs complex structures which are emerging in the wavefunction and allows one to introduce non-norm conserving equations of motion. Important aspects of the new concept are outlined studying the wave packet propagation on the diabatic B(2) potential energy surfaces of NO(2). First, it is demonstrated that during standard wave packet propagation the CvN-entropy increases strongly with time roughly independent of the coordinate systems employed. Second, one finds that employing CvN-entropy constrained MCTDH propagation yields improved wave function accuracy on longer time scales while compromising on the short time accuracy. Third, the loss of the wavefunction's norm is directly related to the overlap with the exact wavefunction. This provides an error estimate available without knowing an exact reference. PMID:22667549
Quantum key distribution with finite resources: Secret key rates via Renyi entropies
Abruzzo, Silvestre; Kampermann, Hermann; Mertz, Markus; Bruss, Dagmar
2011-09-15
A realistic quantum key distribution (QKD) protocol necessarily deals with finite resources, such as the number of signals exchanged by the two parties. We derive a bound on the secret key rate which is expressed as an optimization problem over Renyi entropies. Under the assumption of collective attacks by an eavesdropper, a computable estimate of our bound for the six-state protocol is provided. This bound leads to improved key rates in comparison to previous results.
Detecting topological entanglement entropy in a lattice of quantum harmonic oscillators
NASA Astrophysics Data System (ADS)
Demarie, Tommaso F.; Linjordet, Trond; Menicucci, Nicolas C.; Brennen, Gavin K.
2014-08-01
The Kitaev surface code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy (TEE), but due to low signal to noise, it is extremely difficult to observe in these systems, and one usually resorts to measuring anyonic statistics of excitations or non-local string operators to reveal the order. We describe a continuous-variable analog to the surface code using quantum harmonic oscillators on a two-dimensional lattice, which has the distinctive property of needing only two-body nearest-neighbor interactions for its creation. Though such a model is gapless, it satisfies an area law and the ground state can be simply prepared by measurements on a finitely squeezed and gapped two-dimensional cluster-state without topological order. Asymptotically, the continuous variable surface code TEE grows linearly with the squeezing parameter and a recently discovered non-local quantity, the topological logarithmic negativity, behaves analogously. We also show that the mixed-state generalization of the TEE, the topological mutual information, is robust to some forms of state preparation error and can be detected simply using single-mode quadrature measurements. Finally, we discuss scalable implementation of these methods using optical and circuit-QED technology.
NASA Astrophysics Data System (ADS)
Whitney, Robert S.
2015-03-01
We investigate the nonlinear scattering theory for quantum systems with strong Seebeck and Peltier effects, and consider their use as heat engines and refrigerators with finite power outputs. This paper gives detailed derivations of the results summarized in a previous paper [R. S. Whitney, Phys. Rev. Lett. 112, 130601 (2014), 10.1103/PhysRevLett.112.130601]. It shows how to use the scattering theory to find (i) the quantum thermoelectric with maximum possible power output, and (ii) the quantum thermoelectric with maximum efficiency at given power output. The latter corresponds to a minimal entropy production at that power output. These quantities are of quantum origin since they depend on system size over electronic wavelength, and so have no analog in classical thermodynamics. The maximal efficiency coincides with Carnot efficiency at zero power output, but decreases with increasing power output. This gives a fundamental lower bound on entropy production, which means that reversibility (in the thermodynamic sense) is impossible for finite power output. The suppression of efficiency by (nonlinear) phonon and photon effects is addressed in detail; when these effects are strong, maximum efficiency coincides with maximum power. Finally, we show in particular limits (typically without magnetic fields) that relaxation within the quantum system does not allow the system to exceed the bounds derived for relaxation-free systems, however, a general proof of this remains elusive.
NASA Astrophysics Data System (ADS)
Maghrebi, Mohammad F.; Jaffe, Robert L.; Kardar, Mehran
2014-07-01
We study the implications of quantum fluctuations of a dispersive medium, under steady rotation, either in or out of thermal equilibrium with its environment. A rotating object exhibits a quantum instability by dissipating its mechanical motion via spontaneous emission of photons, as well as internal heat generation. Universal relations are derived for the radiated energy and angular momentum as trace formulas involving the object's scattering matrix. We also compute the quantum noise by deriving the full statistics of the radiated photons out of thermal and/or dynamic equilibrium. The (entanglement) entropy generation is quantified and the total entropy is shown to be always increasing. Furthermore, we derive a Fokker-Planck equation governing the stochastic angular motion resulting from the fluctuating backreaction frictional torque. As a result, we find a quantum limit on the uncertainty of the object's angular velocity in steady rotation. Finally, we show in some detail that a rotating object drags nearby objects, making them spin parallel to its axis of rotation. A scalar toy model is introduced to simplify the technicalities and ease the conceptual complexities and then a detailed discussion of quantum electrodynamics is presented.
NASA Astrophysics Data System (ADS)
Salimi, S.; Haseli, S.; Khorashad, A. S.; Adabi, F.
2016-05-01
The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.
NASA Astrophysics Data System (ADS)
Salimi, S.; Haseli, S.; Khorashad, A. S.; Adabi, F.
2016-09-01
The interaction between system and environment is a fundamental concept in the theory of open quantum systems. As a result of the interaction, an amount of correlation (both classical and quantum) emerges between the system and the environment. In this work, we recall the quantity that will be very useful to describe the emergence of the correlation between the system and the environment, namely, the total entropy production. Appearance of total entropy production is due to the entanglement production between the system and the environment. In this work, we discuss about the role of the total entropy production for detecting the non-Markovianity. By utilizing the relation between the total entropy production and total correlation between subsystems, one can see a temporary decrease of total entropy production is a signature of non-Markovianity. We apply our criterion for the special case, where the composite system has initial correlation with environment.
Resource Letter QI-1: Quantum Information
NASA Astrophysics Data System (ADS)
Strauch, Frederick W.
2016-07-01
This Resource Letter surveys the history and modern developments in the field of quantum information. It is written to guide advanced undergraduates, beginning graduate students, and other new researchers to the theoretical and experimental aspects of this field. The topics covered include quantum states and processes, quantum coding and cryptography, quantum computation, the experimental implementation of quantum information processing, and the role of quantum information in the fundamental properties and foundations of physical theories.
Quantum Information with Structured Light
NASA Astrophysics Data System (ADS)
Mirhosseini, Mohammad
Quantum information science promises dramatic progress in a variety of fields such as cryptography, computation, and metrology. Although the proof-of-principle attempts for implementing quantum protocols have often relied on only a few qubits, the utilization of more sophisticated quantum systems is required for practical applications. In this thesis, we investigate the emerging role of high-dimensional optical states as a resource for encoding quantum information. We begin the first chapter with a review of orbital angular momentum (OAM) as a prime candidate for realizing multilevel quantum states and follow with a brief introduction to the quantum measurement theory. The second and the third chapters are dedicated to the application of OAM modes in quantum cryptography. In the second chapter, we discuss the challenges of projective measurement of OAM at the single-photon level, a crucial task required for quantum information processing. We then present our development of an efficient and accurate mode-sorting device that is capable of projectively measuring the orbital angular momentum of single photons. In the third chapter, we discuss the role of OAM modes in increasing the information capacity of quantum cryptography. We start this chapter by establishing the merits of encoding information on the quantum index of OAM modes in a free-space link. We then generalizing the BB-84 QKD protocol to the Hilbert space spanned by a finite number of OAM modes and outline our experimental realization. The last two chapters are dedicated to the tomography of structured light fields. We start the fourth chapter by applying the recently found method of direct measurement to the characterization of OAM superpositions. We find the quantum state in the Hilbert space spanned by 27 OAM modes by performing a weak measurement of orbital angular momentum (OAM) followed by a strong measurement of azimuthal angle. We then introduce the concept of compressive direct measurement (CDM
Information Entropy Analysis of the H1N1 Genetic Code
NASA Astrophysics Data System (ADS)
Martwick, Andy
2010-03-01
During the current H1N1 pandemic, viral samples are being obtained from large numbers of infected people world-wide and are being sequenced on the NCBI Influenza Virus Resource Database. The information entropy of the sequences was computed from the probability of occurrence of each nucleotide base at every position of each set of sequences using Shannon's definition of information entropy, [ H=∑bpb,2( 1pb ) ] where H is the observed information entropy at each nucleotide position and pb is the probability of the base pair of the nucleotides A, C, G, U. Information entropy of the current H1N1 pandemic is compared to reference human and swine H1N1 entropy. As expected, the current H1N1 entropy is in a low entropy state and has a very large mutation potential. Using the entropy method in mature genes we can identify low entropy regions of nucleotides that generally correlate to critical protein function.
Information gain and information leak in quantum measurements
NASA Astrophysics Data System (ADS)
Xi, Zhengjun
2016-05-01
We discuss the relationships among various quantities of information during the process of an efficient quantum measurement, e.g., information gain, quantum loss, Holevo information, and coherent information. In particular, we give an uncertaintylike relation between information gain and coherent information. We also investigate the information gain by local measurements and quantum correlations in bipartite quantum systems. Moreover, we discuss two cases of information leak according to whether the observer of the environment possesses extra information about the measured system.
Structural information content of networks: graph entropy based on local vertex functionals.
Dehmer, Matthias; Emmert-Streib, Frank
2008-04-01
In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating j-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. PMID:18243802
Eeg Transfer Entropy Tracks Changes in Information Transfer on the Onset of Vision
NASA Astrophysics Data System (ADS)
Madulara, M. D.; Francisco, P. A. B.; Nawang, S.; Arogancia, D. C.; Cellucci, C. J.; Rapp, P. E.; Albano, A. M.
We investigate the pairwise mutual information and transfer entropy of ten-channel, free-running electroencephalographs measured from thirteen subjects under two behavioral conditions: eyes open resting and eyes closed resting. Mutual information measures nonlinear correlations; transfer entropy determines the directionality of information transfer. For all channel pairs, mutual information is generally lower with eyes open compared to eyes closed indicating that EEG signals at different scalp sites become more dissimilar as the visual system is engaged. On the other hand, transfer entropy increases on average by almost two-fold when the eyes are opened. The largest one-way transfer entropies are to and from the Oz site consistent with the involvement of the occipital lobe in vision. The largest net transfer entropies are from F3 and F4 to almost all the other scalp sites.
NASA Astrophysics Data System (ADS)
Mona, Khare; Shraddha, Roy
2008-09-01
The purpose of the present paper is to study the entropy hs(Φ) of a quantum dynamical systems Φ = (L,s,phi), where s is a bayessian state on an orthomodular lattice L. Having introduced the notion of entropy hs(phi,Script A) of partition Script A of a Boolean algebra B with respect to a state s and a state preserving homomorphism phi, we prove a few results on that, define the entropy of a dynamical system hs(Φ), and show its invariance. The concept of sufficient families is also given and we establish that hs(Φ) comes out to be equal to the supremum of hs(phi,Script A), where Script A varies over any sufficient family. The present theory has then been extended to the quantum dynamical system (L,s,phi), which as an effect of the theory of commutators and Bell inequalities can equivalently be replaced by the dynamical system (B,s0,phi), where B is a Boolean algebra and s0 is a state on B.
NASA Astrophysics Data System (ADS)
Ghafourian, M.; Hassanabadi, H.
2016-06-01
The Shannon information entropies for the Klein-Gordon equations are evaluated for the Poschl-Teller potential, and the position-space information entropies for the ground and the excited states are calculated.
Practicality of quantum information processing
NASA Astrophysics Data System (ADS)
Lau, Hoi-Kwan
Quantum Information Processing (QIP) is expected to bring revolutionary enhancement to various technological areas. However, today's QIP applications are far from being practical. The problem involves both hardware issues, i.e., quantum devices are imperfect, and software issues, i.e., the functionality of some QIP applications is not fully understood. Aiming to improve the practicality of QIP, in my PhD research I have studied various topics in quantum cryptography and ion trap quantum computation. In quantum cryptography, I first studied the security of position-based quantum cryptography (PBQC). I discovered a wrong assumption in the previous literature that the cheaters are not allowed to share entangled resources. I proposed entanglement attacks that could cheat all known PBQC protocols. I also studied the practicality of continuous-variable (CV) quantum secret sharing (QSS). While the security of CV QSS was considered by the literature only in the limit of infinite squeezing, I found that finitely squeezed CV resources could also provide finite secret sharing rate. Our work relaxes the stringent resources requirement of implementing QSS. In ion trap quantum computation, I studied the phase error of quantum information induced by dc Stark effect during ion transportation. I found an optimized ion trajectory for which the phase error is the minimum. I also defined a threshold speed, above which ion transportation would induce significant error. In addition, I proposed a new application for ion trap systems as universal bosonic simulators (UBS). I introduced two architectures, and discussed their respective strength and weakness. I illustrated the implementations of bosonic state initialization, transformation, and measurement by applying radiation fields or by varying the trap potential. When comparing with conducting optical experiments, the ion trap UBS is advantageous in higher state initialization efficiency and higher measurement accuracy. Finally, I
Vallverdú, Montserrat; Clariá, Francesc; Melia, Umberto; Bayés de Luna, Antonio; Caminal, Pere
2015-08-01
The Shannon entropy theory was applied to the Choi-Williams time-frequency distribution (CWD) of cardiac time series (RR series) in order to extract entropy information in both time and frequency domains. From this distribution, four indexes were defined: (1) instantaneous partial entropy; (2) spectral partial entropy; (3) instantaneous complete entropy; (4) spectral complete entropy. These indexes were used for analyzing the heart rate variability of ischemic cardiomyopathy patients (ICM) with different sudden cardiac death risk. The results have shown that the values of these indexes tend to decrease, with different proportion, when the severity of pathological condition increases. Statistical differences (p-value < 0.0005) of these indexes were found comparing low risk and high risk of cardiac death during night and between daytime and nighttime periods of ICM patients. Finally, these indexes have demonstrated to be useful tools to quantify the different complex components of the cardiac time series. PMID:26736628
NASA Astrophysics Data System (ADS)
El-Menoufi, Basem Kamal
2016-05-01
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.