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Sample records for quantum information entropy

  1. Quantum Entropy and Information

    NASA Astrophysics Data System (ADS)

    Datta, Nilanjana

    As seen in chapter "Classical Information Theory", classical information theory is the mathematical theory of information-processing tasks such as storage and transmission of information. It was born out of a seminal paper by Claude Shannon in 1948.

  2. Information and Entropy in Quantum Theory

    NASA Astrophysics Data System (ADS)

    Maroney, O. J. E.

    2004-11-01

    We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete description of the operation of the Szilard Engine as a quantum system. This enables us to demonstrate that the role of quantum measurement suggested is incorrect, and further, that the use of information theory to resolve Szilard's paradox is both unnecessary and insufficient. Finally we show that, if the concept of 'active information' is extended to cover thermal density matrices, then many of the conceptual problems raised by this paradox appear to be resolved.

  3. 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.

  4. Waveform information from quantum mechanical entropy.

    PubMed

    Funkhouser, Scott; Suski, William; Winn, Andrew

    2016-06-01

    Although the entropy of a given signal-type waveform is technically zero, it is nonetheless desirable to use entropic measures to quantify the associated information. Several such prescriptions have been advanced in the literature but none are generally successful. Here, we report that the Fourier-conjugated 'total entropy' associated with quantum-mechanical probabilistic amplitude functions (PAFs) is a meaningful measure of information in non-probabilistic real waveforms, with either the waveform itself or its (normalized) analytic representation acting in the role of the PAF. Detailed numerical calculations are presented for both adaptations, showing the expected informatic behaviours in a variety of rudimentary scenarios. Particularly noteworthy are the sensitivity to the degree of randomness in a sequence of pulses and potential for detection of weak signals.

  5. The role of relative entropy in quantum information theory

    NASA Astrophysics Data System (ADS)

    Vedral, V.

    2002-01-01

    Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.

  6. 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.

  7. The information-theoretical entropy of some quantum oscillators

    SciTech Connect

    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.

  8. 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.

  9. Quantum Information, Entropy, ALPHA, Hubble Time, and Dark Energy, Linked?

    NASA Astrophysics Data System (ADS)

    Goradia, Shantilal

    2008-03-01

    The postulation of fundamental constants by Newton, Einstein and Planck gave us natural units at Planck scale. Additional postulates may explain coupling constants. About sixty orders of magnitude of Planck times equal Hubble time (W). Substitution of W in Boltzmann's entropy equation (S=k ln W; with Boltzmann constant k = 1 in natural units, and using the natural logarithm to probe nature) equates the statistical entropy (S) of the universe to about 137, the reciprocal of the fine-structure constant (α). Thermodynamic entropy (dS = δQ/T), a consequence of statistical entropy, implies that the fine-structure constant generates heat out of vacuum energy or dark energy. We draw support from the insights of Maxwell's demon (1867), Gamow (1967) and Eddington (1949). In information theory, entropy is linked to a measure of uncertainty, indicating that the fine-structure constant is greater than or equal to the reciprocal of the natural logarithm of the age of the universe: α>=1 / 1 lnW . - lnW. The postulation in [1] (a draft of a 2008 planned review paper) will address further issues. [1] S. Goradia, What is Fine Structure Constant? http://www.arxiv.org/abs/physics/0210040v3 (revised 1/6/2007)

  10. Entropy generation in Gaussian quantum transformations: applying the replica method to continuous-variable quantum information theory

    NASA Astrophysics Data System (ADS)

    Gagatsos, Christos N.; Karanikas, Alexandros I.; Kordas, Georgios; Cerf, Nicolas J.

    2016-02-01

    In spite of their simple description in terms of rotations or symplectic transformations in phase space, quadratic Hamiltonians such as those modelling the most common Gaussian operations on bosonic modes remain poorly understood in terms of entropy production. For instance, determining the quantum entropy generated by a Bogoliubov transformation is notably a hard problem, with generally no known analytical solution, while it is vital to the characterisation of quantum communication via bosonic channels. Here we overcome this difficulty by adapting the replica method, a tool borrowed from statistical physics and quantum field theory. We exhibit a first application of this method to continuous-variable quantum information theory, where it enables accessing entropies in an optical parametric amplifier. As an illustration, we determine the entropy generated by amplifying a binary superposition of the vacuum and a Fock state, which yields a surprisingly simple, yet unknown analytical expression.

  11. Quantum information processing in the radical-pair mechanism: Haberkorn's theory violates the Ozawa entropy bound

    NASA Astrophysics Data System (ADS)

    Mouloudakis, K.; Kominis, I. K.

    2017-02-01

    Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.

  12. Quantum information processing in the radical-pair mechanism: Haberkorn's theory violates the Ozawa entropy bound.

    PubMed

    Mouloudakis, K; Kominis, I K

    2017-02-01

    Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifying the paradigm of quantum biology, satisfies the Ozawa bound as well as the Lanford-Robinson bound on information extraction. By considering Groenewold's information, the quantum information extracted during the reaction, we reproduce the known and unravel other magnetic-field effects not conveyed by reaction yields.

  13. Rigorous relationships among quantum-mechanical kinetic energy and atomic information entropies: Upper and lower bounds

    NASA Astrophysics Data System (ADS)

    Gadre, Shridhar R.; Bendale, Rajeev D.

    1987-08-01

    An uncertainty-type lower bound [I. Bialynicki-Birula and J. Mycielski, Commun. Math. Phys. 44, 129 (1975)] to the information-entropy sum in complementary spaces has recently been reformulated by Gadre et al. [Phys. Rev. A 32, 2602 (1985)] in terms of the respective one-particle probability densities. This bound has been exploited to derive rigorous upper as well as lower bounds to the information entropies and their sum in terms of the corresponding second moments of their distributions. Thus the present work establishes a direct connection, as suggested by Sears, Parr, and Dinur [Israel J. Chem. 19, 165 (1980)], between the quantum-mechanical kinetic energy and information entropy in position space. It has also been demonstrated that given at least one arbitrary moment-type constraint in each space, it is possible to derive an upper bound to the information entropy sum in complementary spaces.

  14. Entropic dynamics: From entropy and information geometry to Hamiltonians and quantum mechanics

    SciTech Connect

    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.

  15. Quantum and Ecosystem Entropies

    NASA Astrophysics Data System (ADS)

    Kirwan, A. D.

    2008-06-01

    Ecosystems and quantum gases share a number of superficial similarities including enormous numbers of interacting elements and the fundamental role of energy in such interactions. A theory for the synthesis of data and prediction of new phenomena is well established in quantum statistical mechanics. The premise of this paper is that the reason a comparable unifying theory has not emerged in ecology is that a proper role for entropy has yet to be assigned. To this end, a phase space entropy model of ecosystems is developed. Specification of an ecosystem phase space cell size based on microbial mass, length, and time scales gives an ecosystem uncertainty parameter only about three orders of magnitude larger than Planck’s constant. Ecosystem equilibria is specified by conservation of biomass and total metabolic energy, along with the principle of maximum entropy at equilibria. Both Bose - Einstein and Fermi - Dirac equilibrium conditions arise in ecosystems applications. The paper concludes with a discussion of some broader aspects of an ecosystem phase space.

  16. 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

  17. Entropy: Order or Information

    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.)

  18. Entropy: Order or Information

    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.)

  19. Quantum thermodynamics and quantum entanglement entropies in an expanding universe

    NASA Astrophysics Data System (ADS)

    Farahmand, Mehrnoosh; Mohammadzadeh, Hosein; Mehri-Dehnavi, Hossein

    2017-05-01

    We investigate an asymptotically spatially flat Robertson-Walker space-time from two different perspectives. First, using von Neumann entropy, we evaluate the entanglement generation due to the encoded information in space-time. Then, we work out the entropy of particle creation based on the quantum thermodynamics of the scalar field on the underlying space-time. We show that the general behavior of both entropies are the same. Therefore, the entanglement can be applied to the customary quantum thermodynamics of the universe. Also, using these entropies, we can recover some information about the parameters of space-time.

  20. On variational definition of quantum entropy

    SciTech Connect

    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.

  1. 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.

  2. Quantum entropies, Schur concavity and dynamical semigroups

    NASA Astrophysics Data System (ADS)

    Aniello, Paolo

    2017-01-01

    Entropy plays a fundamental role in several branches of physics. In the quantum setting, one usually considers the von Neumann entropy, but other useful quantities have been proposed in the literature; e.g., the Rényi and the Tsallis entropies. The evolution of an open quantum system, described by a semigroup of dynamical maps (in short, a dynamical semigroup), may decrease a quantum entropy, for some initial condition. We will discuss various characterizations of those dynamical semigroups that, for every initial condition, do not decrease a general class of quantum entropies, which is defined using the notion of Schur concavity of a function. We will not assume that such a dynamical semigroup be completely positive, the physical justification of this condition being controversial. Therefore, we will consider semigroups of trace-preserving, positive — but not necessarily completely positive — linear maps. We will next focus on a special class of (completely positive) dynamical semigroups, the twirling semigroups, having applications in quantum information science. We will argue that the whole class of dynamical semigroups that do not decrease a quantum entropy can be obtained as a suitable generalization of the twirling semigroups.

  3. Applications of quantum entropy to statistics

    SciTech Connect

    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.

  4. On variational expressions for quantum relative entropies

    NASA Astrophysics Data System (ADS)

    Berta, Mario; Fawzi, Omar; Tomamichel, Marco

    2017-09-01

    Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback-Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki's quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz' conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for α \\in (1/2, ∞) and strictly smaller for α \\in [0,1/2) . The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for α < 1/2 . Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.

  5. Information Entropy of Fullerenes.

    PubMed

    Sabirov, Denis Sh; Ōsawa, Eiji

    2015-08-24

    The reasons for the formation of the highly symmetric C60 molecule under nonequilibrium conditions are widely discussed as it dominates over numerous similar fullerene structures. In such conditions, evolution of structure rather than energy defines the processes. We have first studied the diversity of fullerenes in terms of information entropy. Sorting 2079 structures from An Atlas of Fullerenes [ Fowler , P. W. ; Manolopoulos , D. E. An Atlas of Fullerenes ; Oxford : Clarendon , 1995 . ], we have found that the information entropies of only 14 fullerenes (<1% of the studied structures) lie between the values of C60 and C70, the two most abundant fullerenes. Interestingly, buckminsterfullerene is the only fullerene with zero information entropy, i.e., an exclusive compound among the other members of the fullerene family. Such an efficient sorting demonstrates possible relevance of information entropy to chemical processes. For this reason, we have introduced an algorithm for calculating changes in information entropy at chemical transformations. The preliminary calculations of changes in information entropy at the selected fullerene reactions show good agreement with thermochemical data.

  6. Information entropy in cosmology.

    PubMed

    Hosoya, Akio; Buchert, Thomas; Morita, Masaaki

    2004-04-09

    The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the Kullback-Leibler relative information entropy, expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time evolution of "effective information" and explore some implications. We conjecture that the information content of the Universe-measured by relative information entropy of a cosmological model containing dust matter-is increasing.

  7. Statistical entropy of open quantum systems

    NASA Astrophysics Data System (ADS)

    Durão, L. M. M.; Caldeira, A. O.

    2016-12-01

    Dissipative quantum systems are frequently described within the framework of the so-called "system-plus-reservoir" approach. In this work we assign their description to the Maximum Entropy Formalism and compare the resulting thermodynamic properties with those of the well-established approaches. Due to the non-negligible coupling to the heat reservoir, these systems are nonextensive by nature, and the former task may require the use of nonextensive parameter dependent informational entropies. In doing so, we address the problem of choosing appropriate forms of those entropies in order to describe a consistent thermodynamics for dissipative quantum systems. Nevertheless, even having chosen the most successful and popular forms of those entropies, we have proven our model to be a counterexample where this sort of approach leads us to wrong results.

  8. Relating quantum coherence and correlations with entropy-based measures.

    PubMed

    Wang, Xiao-Li; Yue, Qiu-Ling; Yu, Chao-Hua; Gao, Fei; Qin, Su-Juan

    2017-09-21

    Quantum coherence and quantum correlations are important quantum resources for quantum computation and quantum information. In this paper, using entropy-based measures, we investigate the relationships between quantum correlated coherence, which is the coherence between subsystems, and two main kinds of quantum correlations as defined by quantum discord as well as quantum entanglement. In particular, we show that quantum discord and quantum entanglement can be well characterized by quantum correlated coherence. Moreover, we prove that the entanglement measure formulated by quantum correlated coherence is lower and upper bounded by the relative entropy of entanglement and the entanglement of formation, respectively, and equal to the relative entropy of entanglement for all the maximally correlated states.

  9. Entropy and information optics

    NASA Astrophysics Data System (ADS)

    Yu, Francis T. S.

    2000-03-01

    In this paper we shall begin our discussion with the relationship between optics and humans, in which we see that light has indeed provided us with a very valuable source of information. A general optical communication concept is discussed, in which we see that a picture is indeed worth more than a thousand words. Based on Shannon's information theory, one can show that entropy and information can be simply traded. One of the most intriguing laws of thermodynamics must be the second law, in which we have found that there exists a profound relationship between the physical entropy and information. Without this relationship, information theory would be totally useless in physical science. By applying this relationship, Maxwell and diffraction-limited demons are discussed. And finally, samples of information optics are provided.

  10. On quantum Rényi entropies: A new generalization and some properties

    SciTech Connect

    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.

  11. Axiomatic Relation between Thermodynamic and Information-Theoretic Entropies

    NASA Astrophysics Data System (ADS)

    Weilenmann, Mirjam; Kraemer, Lea; Faist, Philippe; Renner, Renato

    2016-12-01

    Thermodynamic entropy, as defined by Clausius, characterizes macroscopic observations of a system based on phenomenological quantities such as temperature and heat. In contrast, information-theoretic entropy, introduced by Shannon, is a measure of uncertainty. In this Letter, we connect these two notions of entropy, using an axiomatic framework for thermodynamics [E. H. Lieb and J. Yngvason Proc. R. Soc. 469, 20130408 (2013)]. In particular, we obtain a direct relation between the Clausius entropy and the Shannon entropy, or its generalization to quantum systems, the von Neumann entropy. More generally, we find that entropy measures relevant in nonequilibrium thermodynamics correspond to entropies used in one-shot information theory.

  12. Entropy distance: New quantum phenomena

    SciTech Connect

    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.

  13. Quantum geometry and gravitational entropy

    SciTech Connect

    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.

  14. Controlling the Shannon Entropy of Quantum Systems

    PubMed Central

    Xing, Yifan; Wu, Jun

    2013-01-01

    This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking. PMID:23818819

  15. Controlling the shannon entropy of quantum systems.

    PubMed

    Xing, Yifan; Wu, Jun

    2013-01-01

    This paper proposes a new quantum control method which controls the Shannon entropy of quantum systems. For both discrete and continuous entropies, controller design methods are proposed based on probability density function control, which can drive the quantum state to any target state. To drive the entropy to any target at any prespecified time, another discretization method is proposed for the discrete entropy case, and the conditions under which the entropy can be increased or decreased are discussed. Simulations are done on both two- and three-dimensional quantum systems, where division and prediction are used to achieve more accurate tracking.

  16. Biological adaptabilities and quantum entropies.

    PubMed

    Kirby, Kevin G

    2002-01-01

    The entropy-based theory of adaptability set forth by Michael Conrad in the early 1970s continued to appear in his work for over two decades, and was the subject of the only book he published in his lifetime. He applied this theory to a host of subjects ranging from enzyme dynamics to sociology. This paper reviews the formalism of adaptability theory, clarifying some of its mathematical and interpretive difficulties. The theory frames the computational tradeoff principle, a thesis that was the most frequently recurring claim in his work. The formulation of adaptability theory presented here allows the introduction of quantum entropy functions into the theory, revealing an interesting relationship between adaptability and another one of Conrad's deep preoccupations, the role of quantum processes in life.

  17. Trading coherence and entropy by a quantum Maxwell demon

    NASA Astrophysics Data System (ADS)

    Lebedev, A. V.; Oehri, D.; Lesovik, G. B.; Blatter, G.

    2016-11-01

    The second law of thermodynamics states that the entropy of a closed system is nondecreasing. Discussing the second law in the quantum world poses different challenges and provides different opportunities, involving fundamental quantum-information-theoretic questions and interesting quantum-engineered devices. In quantum mechanics, systems with an evolution described by a so-called unital quantum channel evolve with a nondecreasing entropy. Here, we seek the opposite, a system described by a nonunital and, furthermore, energy-conserving channel that describes a system whose entropy decreases with time. We propose a setup involving a mesoscopic four-lead scatterer augmented by a microenvironment in the form of a spin that realizes this goal. Within this nonunital and energy-conserving quantum channel, the microenvironment acts with two noncommuting operations on the system in an autonomous way. We find that the process corresponds to a partial exchange or swap between the system and environment quantum states, with the system's entropy decreasing if the environment's state is more pure. This entropy-decreasing process is naturally expressed through the action of a quantum Maxwell demon and we propose a quantum-thermodynamic engine with four qubits that extracts work from a single heat reservoir when provided with a reservoir of pure qubits. The special feature of this engine, which derives from the energy conservation in the nonunital quantum channel, is its separation into two cycles, a working cycle and an entropy cycle, allowing us to run this engine with no local waste heat.

  18. Experimental device-independent tests of classical and quantum entropy

    NASA Astrophysics Data System (ADS)

    Zhu, Feng; Zhang, Wei; Chen, Sijing; You, Lixing; Wang, Zhen; Huang, Yidong

    2016-12-01

    In quantum information processing, it is important to witness the entropy of the message in the device-independent way which was proposed recently [R. Chaves, J. B. Brask, and N. Brunner, Phys. Rev. Lett. 115, 110501 (2015), 10.1103/PhysRevLett.115.110501]. In this paper, we theoretically obtain the minimal quantum entropy for three widely used linear dimension witnesses, which is considered "a difficult question." Then we experimentally test the classical and quantum entropy in a device-independent manner. The experimental results agree well with the theoretical analysis, demonstrating that entropy is needed in quantum systems that is lower than the entropy needed in classical systems with the given value of the dimension witness.

  19. The relations among Shannon information entropy, quantum discord, concurrence and localization properties of one-dimensional single-electron wave functions

    NASA Astrophysics Data System (ADS)

    Gong, Longyan; Zheng, Yongcui; Wang, Haihong; Cheng, Weiwen; Zhao, Shengmei

    2014-09-01

    Shannon information entropy (SE), concurrence (CC), quantum discord (QD) and localization properties for various one-dimensional one-electron wave functions are intensively studied, respectively. They include Gaussian functions, power-law functions, and functions in the Anderson model and the Harper ones. For all these wave functions, we find that SE, CC and QD increase as the localization length of a wave function increases, respectively. There are linear or quadratic relationships between two of them. Therefore, we can confirm for the analyzed models that SE, CC and QD are statistically equivalent quantities to reflect the localization properties of wave functions though they are different measures of quantum information.

  20. 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.

  1. Multidimensional entropy landscape of quantum criticality

    NASA Astrophysics Data System (ADS)

    Grube, K.; Zaum, S.; Stockert, O.; Si, Q.; Löhneysen, H. V.

    2017-08-01

    The third law of thermodynamics states that the entropy of any system in equilibrium has to vanish at absolute zero temperature. At nonzero temperatures, on the other hand, matter is expected to accumulate entropy near a quantum critical point, where it undergoes a continuous transition from one ground state to another. Here, we determine, based on general thermodynamic principles, the spatial-dimensional profile of the entropy S near a quantum critical point and its steepest descent in the corresponding multidimensional stress space. We demonstrate this approach for the canonical quantum critical compound CeCu 6-xAux near its onset of antiferromagnetic order. We are able to link the directional stress dependence of S to the previously determined geometry of quantum critical fluctuations. Our demonstration of the multidimensional entropy landscape provides the foundation to understand how quantum criticality nucleates novel phases such as high-temperature superconductivity.

  2. Quantum entropy of non-Hermitian entangled systems

    NASA Astrophysics Data System (ADS)

    Zhang, Shi-Yang; Fang, Mao-Fa; Xu, Lan

    2017-10-01

    Non-Hermitian Hamiltonians are an effective tool for describing the dynamics of open quantum systems. Previous research shows that the restrictions of conventional quantum mechanics may be violated in the non-Hermitian cases. We studied the entropy of a system of entangled qubits governed by a local non-Hermitian Hamiltonian operator. We find that local non-Hermitian operation influences the entropies of the two subsystems equally and simultaneously. This indicates that non-Hermitian operators possess the property of non-locality, which makes information exchange possible between subsystems. These information exchanges reduce the uncertainty of outcomes associated with two incompatible quantum measurements.

  3. Gacs quantum algorithmic entropy in infinite dimensional Hilbert spaces

    SciTech Connect

    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.

  4. Entropy, Fisher Information and Variance with Frost-Musulin Potenial

    NASA Astrophysics Data System (ADS)

    Idiodi, J. O. A.; Onate, C. A.

    2016-09-01

    This study presents the Shannon and Renyi information entropy for both position and momentum space and the Fisher information for the position-dependent mass Schrödinger equation with the Frost-Musulin potential. The analysis of the quantum mechanical probability has been obtained via the Fisher information. The variance information of this potential is equally computed. This controls both the chemical properties and physical properties of some of the molecular systems. We have observed the behaviour of the Shannon entropy. Renyi entropy, Fisher information and variance with the quantum number n respectively.

  5. Entropy production of doubly stochastic quantum channels

    SciTech Connect

    Müller-Hermes, Alexander; Stilck França, Daniel Wolf, Michael M.

    2016-02-15

    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.

  6. 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.

  7. 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…

  8. 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…

  9. Quantum estimation via the minimum Kullback entropy principle

    NASA Astrophysics Data System (ADS)

    Olivares, Stefano; Paris, Matteo G. A.

    2007-10-01

    We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state, the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some detail.

  10. Quantum estimation via the minimum Kullback entropy principle

    SciTech Connect

    Olivares, Stefano; Paris, Matteo G. A.

    2007-10-15

    We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state, the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some detail.

  11. Quantum Rényi relative entropies affirm universality of thermodynamics.

    PubMed

    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.

  12. 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.

  13. 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.

  14. Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints

    NASA Astrophysics Data System (ADS)

    Winter, Andreas

    2016-10-01

    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.

  15. Steganography on quantum pixel images using Shannon entropy

    NASA Astrophysics Data System (ADS)

    Laurel, Carlos Ortega; Dong, Shi-Hai; Cruz-Irisson, M.

    2016-07-01

    This paper presents a steganographical algorithm based on least significant bit (LSB) from the most significant bit information (MSBI) and the equivalence of a bit pixel image to a quantum pixel image, which permits to make the information communicate secretly onto quantum pixel images for its secure transmission through insecure channels. This algorithm offers higher security since it exploits the Shannon entropy for an image.

  16. Quantum entropy and special relativity.

    PubMed

    Peres, Asher; Scudo, Petra F; Terno, Daniel R

    2002-06-10

    We consider a single free spin- 1 / 2 particle. The reduced density matrix for its spin is not covariant under Lorentz transformations. The spin entropy is not a relativistic scalar and has no invariant meaning.

  17. Wald entropy formula and loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Bodendorfer, N.; Neiman, Y.

    2014-10-01

    We outline how the Wald entropy formula naturally arises in loop quantum gravity based on recently introduced dimension-independent connection variables. The key observation is that in a loop quantization of a generalized gravity theory, the analog of the area operator turns out to measure, morally speaking, the Wald entropy rather than the area. We discuss the explicit example of (higher-dimensional) Lanczos-Lovelock gravity and comment on recent work on finding the correct numerical prefactor of the entropy by comparing it to a semiclassical effective action.

  18. 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

  19. Measuring entanglement entropy in a quantum many-body system.

    PubMed

    Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus

    2015-12-03

    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.

  20. 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.

  1. Horizon Entropy from Quantum Gravity Condensates.

    PubMed

    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.

  2. 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.

  3. Optimal quantum networks and one-shot entropies

    NASA Astrophysics Data System (ADS)

    Chiribella, Giulio; Ebler, Daniel

    2016-09-01

    We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interative tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game.

  4. Quantum entropy production in phase space

    NASA Astrophysics Data System (ADS)

    Deffner, Sebastian

    2014-03-01

    A fluctuation theorem for the nonequilibrium entropy production in quantum phase space is derived, which enables the consistent thermodynamic description of arbitrary quantum systems, open and closed. The new treatment naturally generalizes classical results to the quantum domain. As an illustration the harmonic oscillator dragged through a thermal bath is solved numerically. Finally, the significance of the new approach is discussed in detail, and the phase space treatment is opposed to the two time energy measurement approach. We acknowledge financial support by a fellowship within the postdoc-program of the German Academic Exchange Service (DAAD, contract No D/11/40955) and from the National Science Foundation (USA) under grant DMR-1206971.

  5. 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.

  6. Comparative analysis of electric field influence on the quantum wells with different boundary conditions.: I. Energy spectrum, quantum information entropy and polarization.

    PubMed

    Olendski, Oleg

    2015-04-01

    Analytical solutions of the Schrödinger equation for the one-dimensional quantum well with all possible permutations of the Dirichlet and Neumann boundary conditions (BCs) in perpendicular to the interfaces uniform electric field [Formula: see text] are used for the comparative investigation of their interaction and its influence on the properties of the system. Limiting cases of the weak and strong voltages allow an easy mathematical treatment and its clear physical explanation; in particular, for the small [Formula: see text], the perturbation theory derives for all geometries a linear dependence of the polarization on the field with the BC-dependent proportionality coefficient being positive (negative) for the ground (excited) states. Simple two-level approximation elementary explains the negative polarizations as a result of the field-induced destructive interference of the unperturbed modes and shows that in this case the admixture of only the neighboring states plays a dominant role. Different magnitudes of the polarization for different BCs in this regime are explained physically and confirmed numerically. Hellmann-Feynman theorem reveals a fundamental relation between the polarization and the speed of the energy change with the field. It is proved that zero-voltage position entropies [Formula: see text] are BC independent and for all states but the ground Neumann level (which has [Formula: see text]) are equal to [Formula: see text] while the momentum entropies [Formula: see text] depend on the edge requirements and the level. Varying electric field changes position and momentum entropies in the opposite directions such that the entropic uncertainty relation is satisfied. Other physical quantities such as the BC-dependent zero-energy and zero-polarization fields are also studied both numerically and analytically. Applications to different branches of physics, such as ocean fluid dynamics and atmospheric and metallic waveguide electrodynamics, are discussed.

  7. Maximum entropy production rate in quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Beretta, Gian Paolo

    2010-06-01

    In the framework of the recent quest for well-behaved nonlinear extensions of the traditional Schrödinger-von Neumann unitary dynamics that could provide fundamental explanations of recent experimental evidence of loss of quantum coherence at the microscopic level, a recent paper [Gheorghiu-Svirschevski 2001 Phys. Rev. A 63 054102] reproposes the nonlinear equation of motion proposed by the present author [see Beretta G P 1987 Found. Phys. 17 365 and references therein] for quantum (thermo)dynamics of a single isolated indivisible constituent system, such as a single particle, qubit, qudit, spin or atomic system, or a Bose-Einstein or Fermi-Dirac field. As already proved, such nonlinear dynamics entails a fundamental unifying microscopic proof and extension of Onsager's reciprocity and Callen's fluctuation-dissipation relations to all nonequilibrium states, close and far from thermodynamic equilibrium. In this paper we propose a brief but self-contained review of the main results already proved, including the explicit geometrical construction of the equation of motion from the steepest-entropy-ascent ansatz and its exact mathematical and conceptual equivalence with the maximal-entropy-generation variational-principle formulation presented in Gheorghiu-Svirschevski S 2001 Phys. Rev. A 63 022105. Moreover, we show how it can be extended to the case of a composite system to obtain the general form of the equation of motion, consistent with the demanding requirements of strong separability and of compatibility with general thermodynamics principles. The irreversible term in the equation of motion describes the spontaneous attraction of the state operator in the direction of steepest entropy ascent, thus implementing the maximum entropy production principle in quantum theory. The time rate at which the path of steepest entropy ascent is followed has so far been left unspecified. As a step towards the identification of such rate, here we propose a possible, well

  8. Entanglement entropy and mutual information of circular entangling surfaces in the 2  +  1-dimensional quantum Lifshitz model

    NASA Astrophysics Data System (ADS)

    Zhou, Tianci; Chen, Xiao; Faulkner, Thomas; Fradkin, Eduardo

    2016-09-01

    We investigate the entanglement entropy (EE) of circular entangling cuts in the 2  +  1-dimensional quantum Lifshitz model. The ground state in this model is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose amplitude is the Gibbs weight of 2D Euclidean free boson. We show that the finite subleading corrections of EE to the area-law term, as well as the mutual information, are conformal invariants and calculate them for cylinder, disk-like and spherical manifolds with various spatial cuts. The subtlety due to the boson compactification in the replica trick is carefully addressed. We find that in the geometry of a punctured plane with many small holes, the constant piece of EE is proportional to the number of holes, indicating the ability of entanglement to detect topological information of the configuration. Finally, we compare the mutual information of two small distant disks with Cardy’s relativistic CFT scaling proposal. We find that in the quantum Lifshitz model, the mutual information also scales at long distance with a power determined by the lowest scaling dimension local operator in the theory.

  9. Book Review: Maxwell's Demon 2: Entropy, classical and quantum information, computing. Harvey Leff and Andrew Rex (Eds.); Institute of Physics, Bristol, 2003, 500pp., US 55, ISBN 0750307595

    NASA Astrophysics Data System (ADS)

    Shenker, Orly R.

    2004-09-01

    In 1867, James Clerk Maxwell proposed a perpetuum mobile of the second kind, that is, a counter example for the Second Law of thermodynamics, which came to be known as "Maxwell's Demon." Unlike any other perpetual motion machine, this one escaped attempts by the best scientists and philosophers to show that the Second Law or its statistical mechanical counterparts are universal after all. "Maxwell's demon lives on. After more than 130 years of uncertain life and at least two pronouncements of death, this fanciful character seems more vibrant than ever." These words of Harvey Leff and Andrew Rex (1990), which open their introduction to Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing (hereafter MD2) are very true: the Demon is as challenging and as intriguing as ever, and forces us to think and rethink about the foundations of thermodynamics and of statistical mechanics.

  10. Covariant entropy bound and loop quantum cosmology

    SciTech Connect

    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.

  11. 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.

  12. Information and entropy in neural networks and interacting systems

    NASA Astrophysics Data System (ADS)

    Shafee, Fariel

    In this dissertation we present a study of certain characteristics of interacting systems that are related to information. The first is periodicity, correlation and other information-related properties of neural networks of integrate-and-fire type. We also form quasiclassical and quantum generalizations of such networks and identify the similarities and differences with the classical prototype. We indicate why entropy may be an important concept for a neural network and why a generalization of the definition of entropy may be required. Like neural networks, large ensembles of similar units that interact also need a generalization of classical information-theoretic concepts. We extend the concept of Shannon entropy in a novel way, which may be relevant when we have such interacting systems, and show how it differs from Shannon entropy and other generalizations, such as Tsallis entropy. We indicate how classical stochasticity may arise in interactions with an entangled environment in a quantum system in terms of Shannon's and generalized entropies and identify the differences. Such differences are also indicated in the use of certain prior probability distributions to fit data as per Bayesian rules. We also suggest possible quantum versions of pattern recognition, which is the principal goal of information processing in most neural networks.

  13. Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions.

    PubMed

    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.

  14. Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions

    NASA Astrophysics Data System (ADS)

    Misra, Avijit; Biswas, Anindya; Pati, Arun K.; SenDe, 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.

  15. Application of non-extensive entropy to study of decoherence of RbCl quantum dot qubit: Tsallis entropy

    NASA Astrophysics Data System (ADS)

    Khordad, R.; Rastegar Sedehi, H. R.

    2017-01-01

    In this work, an electron which is strongly coupled to the LO-phonon in triangular quantum dots with Coulomb impurity is considered. The eigenenergies and eigenfunctions of the ground and the first-excited states of the electron are obtained using the Pekar variational method. We have studied decoherence of RbCl quantum dot qubit using the non-extensive entropy (Tsallis entropy) for different values of Coulomb impurity parameter, polaronic radius and electron-LO phonon coupling strength. Numerical analysis shows that the entropy has the oscillatory periodic evolution as function of the time due to the triangular form of the confinement. It is found that entropy oscillates under a standing wave envelope with increasing the Coulomb impurity parameter, electron-LO phonon coupling strength and polaronic radius. With reducing the non-extensive parameter q, the entropy increases and thereby we can miss information about the system.

  16. Increase of Boltzmann entropy in a quantum forced harmonic oscillator

    NASA Astrophysics Data System (ADS)

    Campisi, Michele

    2008-11-01

    Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.

  17. Increase of Boltzmann entropy in a quantum forced harmonic oscillator.

    PubMed

    Campisi, Michele

    2008-11-01

    Recently, a quantum-mechanical proof of the increase of Boltzmann entropy in quantum systems that are coupled to an external classical source of work has been given. Here we illustrate this result by applying it to a forced quantum harmonic oscillator. We show plots of the actual temporal evolution of work and entropy for various forcing protocols. We note that entropy and work can be partially or even fully returned to the source, although both work and entropy balances are non-negative at all times in accordance with the minimal work principle and the Clausius principle, respectively. A necessary condition for the increase of entropy is that the initial distribution is decreasing (e.g., canonical). We show evidence that for a nondecreasing distribution (e.g., microcanonical), the quantum expectation of entropy may decrease slightly. Interestingly, the classical expectation of entropy cannot decrease, irrespective of the initial distribution, in the forced harmonic oscillator.

  18. Quantum quench and scaling of entanglement entropy

    NASA Astrophysics Data System (ADS)

    Caputa, Paweł; Das, Sumit R.; Nozaki, Masahiro; Tomiya, Akio

    2017-09-01

    Global quantum quench with a finite quench rate which crosses critical points is known to lead to universal scaling of correlation functions as functions of the quench rate. In this work, we explore scaling properties of the entanglement entropy of a subsystem in a harmonic chain during a mass quench which asymptotes to finite constant values at early and late times and for which the dynamics is exactly solvable. When the initial state is the ground state, we find that for large enough subsystem sizes the entanglement entropy becomes independent of size. This is consistent with Kibble-Zurek scaling for slow quenches, and with recently discussed "fast quench scaling" for quenches fast compared to physical scales, but slow compared to UV cutoff scales.

  19. Universal geometric approach to uncertainty, entropy, and information

    NASA Astrophysics Data System (ADS)

    Hall, Michael J. W.

    1999-04-01

    It is shown that a unique measure of volume is associated with any statistical ensemble, which directly quantifies the inherent spread or localization of the ensemble. It is applicable whether the ensemble is classical or quantum, continuous or discrete, and may be derived from a small number of theory-independent geometric postulates. Remarkably, this unique ensemble volume is proportional to the exponential of the ensemble entropy, and hence provides an interesting geometric characterization of the latter quantity. Applications include unified volume-based derivations of results in quantum and classical information theory, a precise geometric interpretation of thermodynamic entropy for equilibrium ensembles, a geometric derivation of semiclassical uncertainty relations, a means for defining classical and quantum localization for arbitrary evolution processes, and a proposed definition for the spot size of an optical beam. Advantages of ensemble volume over other measures of localization (root-mean-square deviation, Renyi entropies, and inverse participation ratio) are discussed.

  20. Entropy Flow in Near-Critical Quantum Circuits

    NASA Astrophysics Data System (ADS)

    Friedan, Daniel

    2017-05-01

    Near-critical quantum circuits close to equilibrium are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from microscopic environmental fluctuations by the renormalization group. Entropy flows in near-critical quantum circuits near equilibrium as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. These "Kirchhoff laws" for entropy flow are the fundamental design constraints for asymptotically large-scale quantum computers. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The quantum entropy current near equilibrium is just the energy current divided by the temperature. The universal properties of the energy-momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: σ S(ω ) = iv2 S/ω T , where ω is the frequency, T the temperature, S the equilibrium entropy density and v the velocity of "light". The thermal conductivity is Re(Tσ S(ω ))=π v2 S δ (ω ). The thermal Drude weight is, universally, v2S. This gives a way to measure the entropy density directly.

  1. Entropy Flow in Near-Critical Quantum Circuits

    NASA Astrophysics Data System (ADS)

    Friedan, Daniel

    2017-03-01

    Near-critical quantum circuits close to equilibrium are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from microscopic environmental fluctuations by the renormalization group. Entropy flows in near-critical quantum circuits near equilibrium as a locally conserved quantum current, obeying circuit laws analogous to the electric circuit laws. These "Kirchhoff laws" for entropy flow are the fundamental design constraints for asymptotically large-scale quantum computers. A quantum circuit made from a near-critical system (of conventional type) is described by a relativistic 1+1 dimensional relativistic quantum field theory on the circuit. The quantum entropy current near equilibrium is just the energy current divided by the temperature. The universal properties of the energy-momentum tensor constrain the entropy flow characteristics of the circuit components: the entropic conductivity of the quantum wires and the entropic admittance of the quantum circuit junctions. For example, near-critical quantum wires are always resistanceless inductors for entropy. A universal formula is derived for the entropic conductivity: σ S(ω ) = iv2 S/ω T , where ω is the frequency, T the temperature, {S the equilibrium entropy density and v the velocity of "light". The thermal conductivity is Re(Tσ S(ω ))=π v2 S δ (ω ) . The thermal Drude weight is, universally, v2S . This gives a way to measure the entropy density directly.

  2. Does horizon entropy satisfy a quantum null energy conjecture?

    NASA Astrophysics Data System (ADS)

    Fu, Zicao; Marolf, Donald

    2016-12-01

    A modern version of the idea that the area of event horizons gives 4G times an entropy is the Hubeny-Rangamani causal holographic information (CHI) proposal for holographic field theories. Given a region R of a holographic QFTs, CHI computes A/4G on a certain cut of an event horizon in the gravitational dual. The result is naturally interpreted as a coarse-grained entropy for the QFT. CHI is known to be finitely greater than the fine-grained Hubeny-Rangamani-Takayanagi (HRT) entropy when \\partial R lies on a Killing horizon of the QFT spacetime, and in this context satisfies other non-trivial properties expected of an entropy. Here we present evidence that it also satisfies the quantum null energy condition (QNEC), which bounds the second derivative of the entropy of a quantum field theory on one side of a non-expanding null surface by the flux of stress-energy across the surface. In particular, we show CHI to satisfy the QNEC in 1  +  1 holographic CFTs when evaluated in states dual to conical defects in AdS3. This surprising result further supports the idea that CHI defines a useful notion of coarse-grained holographic entropy, and suggests unprecedented bounds on the rate at which bulk horizon generators emerge from a caustic. To supplement our motivation, we include an appendix deriving a corresponding coarse-grained generalized second law for 1  +  1 holographic CFTs perturbatively coupled to dilaton gravity.

  3. 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…

  4. The complementarity relations of quantum coherence in quantum information processing

    PubMed Central

    Pan, Fei; Qiu, Liang; Liu, Zhi

    2017-01-01

    We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given. PMID:28272481

  5. The complementarity relations of quantum coherence in quantum information processing.

    PubMed

    Pan, Fei; Qiu, Liang; Liu, Zhi

    2017-03-08

    We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.

  6. The complementarity relations of quantum coherence in quantum information processing

    NASA Astrophysics Data System (ADS)

    Pan, Fei; Qiu, Liang; Liu, Zhi

    2017-03-01

    We establish two complementarity relations for the relative entropy of coherence in quantum information processing, i.e., quantum dense coding and teleportation. We first give an uncertainty-like expression relating local quantum coherence to the capacity of optimal dense coding for bipartite system. The relation can also be applied to the case of dense coding by using unital memoryless noisy quantum channels. Further, the relation between local quantum coherence and teleportation fidelity for two-qubit system is given.

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

    PubMed

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

    2017-04-21

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

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

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

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

  9. Quantum Fokker-Planck-Kramers equation and entropy production.

    PubMed

    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.

  10. 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.

  11. 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…

  12. Entropy Flow Through Near-Critical Quantum Junctions

    NASA Astrophysics Data System (ADS)

    Friedan, Daniel

    2017-03-01

    This is the continuation of Friedan (J Stat Phys, 2017. doi: 10.1007/s10955-017-1752-8). Elementary formulas are derived for the flow of entropy through a circuit junction in a near-critical quantum circuit close to equilibrium, based on the structure of the energy-momentum tensor at the junction. The entropic admittance of a near-critical junction in a bulk-critical circuit is expressed in terms of commutators of the chiral entropy currents. The entropic admittance at low frequency, divided by the frequency, gives the change of the junction entropy with temperature—the entropic "capacitance". As an example, and as a check on the formalism, the entropic admittance is calculated explicitly for junctions in bulk-critical quantum Ising circuits (free fermions, massless in the bulk), in terms of the reflection matrix of the junction. The half-bit of information capacity per end of critical Ising wire is re-derived by integrating the entropic "capacitance" with respect to temperature, from T=0 to T=∞.

  13. Entropy Flow Through Near-Critical Quantum Junctions

    NASA Astrophysics Data System (ADS)

    Friedan, Daniel

    2017-05-01

    This is the continuation of Friedan (J Stat Phys, 2017. doi: 10.1007/s10955-017-1752-8). Elementary formulas are derived for the flow of entropy through a circuit junction in a near-critical quantum circuit close to equilibrium, based on the structure of the energy-momentum tensor at the junction. The entropic admittance of a near-critical junction in a bulk-critical circuit is expressed in terms of commutators of the chiral entropy currents. The entropic admittance at low frequency, divided by the frequency, gives the change of the junction entropy with temperature—the entropic "capacitance". As an example, and as a check on the formalism, the entropic admittance is calculated explicitly for junctions in bulk-critical quantum Ising circuits (free fermions, massless in the bulk), in terms of the reflection matrix of the junction. The half-bit of information capacity per end of critical Ising wire is re-derived by integrating the entropic "capacitance" with respect to temperature, from T=0 to T=∞.

  14. Entanglement entropy near Kondo-destruction quantum critical points

    NASA Astrophysics Data System (ADS)

    Chowdhury, Tathagata; Wagner, Christopher; Ingersent, Kevin; Pixley, Jedediah

    Entanglement entropy is a measure of quantum-mechanical entanglement across the boundary created by partitioning a system into two subsystems. We study this quantity in Kondo impurity models that feature Kondo-destruction quantum critical points (QCPs). Recent work has shown that the entanglement entropy between a Kondo impurity of spin Simp and its environment is pinned at its maximum possible value Se = ln (2Simp + 1) throughout the Kondo phase. In the Kondo-destroyed phase, where the impurity spin acquires a nonzero expectation value Mloc, Se = ln (2Simp + 1) - a (Simp) Mloc2 irrespective of the properties of the host. Here, we report numerical renormalization-group results for Kondo models with a pseudogapped density of states under a different partition that separates the impurity and on-site conduction electrons from the rest of the system. Now, the entanglement entropy is affected by the nature of the environment beyond the information contained in Mloc, but Se still contains a critical part that exhibits power-law behavior in the vicinity of the Kondo-destruction QCP

  15. A note on entanglement entropy and quantum geometry

    NASA Astrophysics Data System (ADS)

    Bodendorfer, N.

    2014-11-01

    It has been argued that the entropy computed in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field, and that the calculation performed is not restricted to horizons. We recall existing work on this issue and explain how recent work on generalizing these computations to arbitrary spacetime dimensions D+1≥slant 3 supports this point of view and makes the duality between entanglement entropy and the entropy computed from counting boundary states manifest. In a certain semiclassical regime in 3+1 dimensions, this entropy is given by the Bekenstein-Hawking formula.

  16. Block entropy and quantum phase transition in the anisotropic Kondo necklace model

    NASA Astrophysics Data System (ADS)

    Mendoza-Arenas, J. J.; Franco, R.; Silva-Valencia, J.

    2010-06-01

    We study the von Neumann block entropy in the Kondo necklace model for different anisotropies η 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 η 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 Δ is included in the Kondo exchange between localized and conduction spins; when Δ diminishes for a fixed value of η, the critical point increases, favoring the antiferromagnetic phase.

  17. Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment

    SciTech Connect

    Rodriquez-Rosario, C.A.; Kimura, G; Imai, H; Aspuru-Guzik, Alan

    2011-02-02

    We find the necessary and sufficient conditions for the entropy rate of the system to be zero under any system-environment Hamiltonian interaction. We call the class of system-environment states that satisfy this condition lazy states. They are a generalization of classically correlated states defined by quantum discord, but based on projective measurements of any rank. The concept of lazy states permits the construction of a protocol for detecting global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the entropy rate, and how to estimate dissipation rates for general non-Markovian open quantum systems.

  18. Sufficient and Necessary Condition for Zero Quantum Entropy Rates under any Coupling to the Environment

    NASA Astrophysics Data System (ADS)

    Rodríguez-Rosario, César A.; Kimura, Gen; Imai, Hideki; Aspuru-Guzik, Alán

    2011-02-01

    We find the necessary and sufficient conditions for the entropy rate of the system to be zero under any system-environment Hamiltonian interaction. We call the class of system-environment states that satisfy this condition lazy states. They are a generalization of classically correlated states defined by quantum discord, but based on projective measurements of any rank. The concept of lazy states permits the construction of a protocol for detecting global quantum correlations using only local dynamical information. We show how quantum correlations to the environment provide bounds to the entropy rate, and how to estimate dissipation rates for general non-Markovian open quantum systems.

  19. Symmetric polynomials in information theory: Entropy and subentropy

    SciTech Connect

    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.

  20. Continuity of the entropy of macroscopic quantum systems.

    PubMed

    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.

  1. 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).

  2. The conditional entropy power inequality for Gaussian quantum states

    SciTech Connect

    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.

  3. Global information balance in quantum measurements.

    PubMed

    Buscemi, Francesco; Hayashi, Masahito; Horodecki, Michał

    2008-05-30

    We perform an information-theoretical analysis of quantum measurement processes and obtain the global information balance in quantum measurements, in the form of a closed chain equation for quantum mutual entropies. Our balance provides a tight and general entropic information-disturbance trade-off, and explains the physical mechanism underlying it. Finally, the single-outcome case, that is, the case of measurements with posts election, is briefly discussed.

  4. The Shannon information entropy of protein sequences.

    PubMed Central

    Strait, B J; Dewey, T G

    1996-01-01

    A comprehensive data base is analyzed to determine the Shannon information content of a protein sequence. This information entropy is estimated by three methods: a k-tuplet analysis, a generalized Zipf analysis, and a "Chou-Fasman gambler." The k-tuplet analysis is a "letter" analysis, based on conditional sequence probabilities. The generalized Zipf analysis demonstrates the statistical linguistic qualities of protein sequences and uses the "word" frequency to determine the Shannon entropy. The Zipf analysis and k-tuplet analysis give Shannon entropies of approximately 2.5 bits/amino acid. This entropy is much smaller than the value of 4.18 bits/amino acid obtained from the nonuniform composition of amino acids in proteins. The "Chou-Fasman" gambler is an algorithm based on the Chou-Fasman rules for protein structure. It uses both sequence and secondary structure information to guess at the number of possible amino acids that could appropriately substitute into a sequence. As in the case for the English language, the gambler algorithm gives significantly lower entropies than the k-tuplet analysis. Using these entropies, the number of most probable protein sequences can be calculated. The number of most probable protein sequences is much less than the number of possible sequences but is still much larger than the number of sequences thought to have existed throughout evolution. Implications of these results for mutagenesis experiments are discussed. PMID:8804598

  5. Remainder terms for some quantum entropy inequalities

    SciTech Connect

    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.

  6. 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.

  7. Image Analysis Using Quantum Entropy Scale Space and Diffusion Concepts

    DTIC Science & Technology

    2009-11-01

    theoretical physics concerned were quantum field theory and quantum statistical mechanics. The PI gave two lectures at the graduate level on Feynman ...sums has been shown important in various areas of theoretical physics , including in support of Feynman diagram calculations. Even more recently, it...quantum and semi-classical entropies of modeled physical systems was also performed. The feasibility of applying forms of generalized quantum search to

  8. 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.

  9. Universal Entanglement Entropy in 2D Conformal Quantum Critical Points

    SciTech Connect

    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.

  10. The Shannon entropy information for mixed Manning Rosen potential in D-dimensional Schrodinger equation

    NASA Astrophysics Data System (ADS)

    Suparmi, A.; Cari, C.; Nur Pratiwi, Beta; Arya Nugraha, Dewanta

    2017-01-01

    D dimensional Schrodinger equation for the mixed Manning Rosen potential was investigated using supersymmetric quantum mechanics. We obtained the energy eigenvalues from radial part solution and wavefunctions in radial and angular parts solution. From the lowest radial wavefunctions, we evaluated the Shannon entropy information using Matlab software. Based on the entropy densities demonstrated graphically, we obtained that the wave of position information entropy density moves right when the value of potential parameter q increases, while its wave moves left with the increase of parameter α. The wave of momentum information entropy densities were expressed in graphs. We observe that its amplitude increase with increasing parameter q and α

  11. Quantum Limits on the Entropy of Bandlimited Radiation

    NASA Astrophysics Data System (ADS)

    Franceschetti, Massimo

    2017-09-01

    Physical limits on the amount of information carried by bandlimited waveforms radiated in one and three dimensions are considered. It is shown that the entropy of radiation can achieve the Bekenstein bound using a "burst" of energy, whose density vanishes as the radiating system expands. In comparison, black body radiation of infinite bandwidth achieves the same entropy scaling, that is proportional to the volume of the space, but requires an energy density that remains constant as the system expands. Rather than following the standard statistical physics approach of counting the number of eigenstates of the Hamiltonian of the quantum wave field, our derivation first considers an optimal subspace approximation, and then determines the number of bits that are required to represent any waveform in the space spanned by this representation with a minimum quantized energy error. This favors a geometric interpretation where the complexity of state counting is replaced by the one of determining the minimum cardinality covering of the signal space by high-dimensional balls, or boxes, whose size is lower bounded by quantum constraints. All derivations are given for both deterministic and stochastic settings.

  12. Effective and fully automatic image segmentation using quantum entropy and pulse-coupled neural networks

    NASA Astrophysics Data System (ADS)

    Du, Songlin; Yan, Yaping; Ma, Yide

    2015-03-01

    A novel image segmentation algorithm which uses quantum entropy and pulse-coupled neural networks (PCNN) is proposed in this paper. Optimal iteration of the PCNN is one of the key factors affecting segmentation accuracy. We borrow quantum entropy from quantum information to act as a criterion in determining optimal iteration of the PCNN. Optimal iteration is captured while total quantum entropy of the segments reaches a maximum. Moreover, compared with other PCNN-employed algorithms, the proposed algorithm works without any manual intervention, because all parameters of the PCNN are set automatically. Experimental results prove that the proposed method can achieve much lower probabilities of error segmentation than other PCNN-based image segmentation algorithms, and this suggests that higher image segmentation quality is achieved by the proposed method.

  13. On Entropy Production of Repeated Quantum Measurements I. General Theory

    NASA Astrophysics Data System (ADS)

    Benoist, T.; Jakšić, V.; Pautrat, Y.; Pillet, C.-A.

    2017-07-01

    We study entropy production (EP) in processes involving repeated quantum measurements of finite quantum systems. Adopting a dynamical system approach, we develop a thermodynamic formalism for the EP and study fine aspects of irreversibility related to the hypothesis testing of the arrow of time. Under a suitable chaoticity assumption, we establish a Large Deviation Principle and a Fluctuation Theorem for the EP.

  14. Quantum Games: Mixed Strategy Nash's Equilibrium Represents Minimum Entropy

    NASA Astrophysics Data System (ADS)

    Jiménez, Edward

    2003-12-01

    This paper introduces Hermite's polynomials, in the description of quantum games. Hermite's polynomials are associated with gaussian probability density. The gaussian probability density represents minimum dispersion. I introduce the concept of minimum entropy as a paradigm of both Nash's equilibrium (maximum utility MU) and Hayek equilibrium (minimum entropy ME). The ME concept is related to Quantum Games. Some questions arise after carrying out this exercise: i) What does Heisenberg's uncertainty principle represent in Game Theory and Time Series?, and ii) What do the postulates of Quantum Mechanics indicate in Game Theory and Economics?.

  15. What is Quantum Information?

    NASA Astrophysics Data System (ADS)

    Lombardi, Olimpia; Fortin, Sebastian; Holik, Federico; López, Cristian

    2017-04-01

    Preface; Introduction; Part I. About the Concept of Information: 1. About the concept of information Sebastian Fortin and Olimpia Lombardi; 2. Representation, information, and theories of information Armond Duwell; 3. Information, communication, and manipulability Olimpia Lombardi and Cristian López; Part II. Information and quantum mechanics: 4. Quantum versus classical information Jeffrey Bub; 5. Quantum information and locality Dennis Dieks; 6. Pragmatic information in quantum mechanics Juan Roederer; 7. Interpretations of quantum theory: a map of madness Adán Cabello; Part III. Probability, Correlations, and Information: 8. On the tension between ontology and epistemology in quantum probabilities Amit Hagar; 9. Inferential versus dynamical conceptions of physics David Wallace; 10. Classical models for quantum information Federico Holik and Gustavo Martin Bosyk; 11. On the relative character of quantum correlations Guido Bellomo and Ángel Ricardo Plastino; Index.

  16. 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.

  17. 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.

  18. 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.

  19. Reply to "Comment on 'Quantum Kaniadakis entropy under projective measurement' ".

    PubMed

    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.

  20. 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

  1. 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.

  2. 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.

  3. Philosophy of Quantum Information and Entanglement

    NASA Astrophysics Data System (ADS)

    Bokulich, Alisa; Jaeger, Gregg

    2010-06-01

    Preface; Introduction; Part I. Quantum Entanglement and Nonlocality: 1. Nonlocality beyond quantum mechanics Sandu Popescu; 2. Entanglement and subsystems, entanglement beyond subsystems, and all that Lorenza Viola and Howard Barnum; 3. Formalism locality in quantum theory and quantum gravity Lucien Hardy; Part II. Quantum Probability: 4. Bell's inequality from the contextual probabilistic viewpoint Andrei Khrennikov; 5. Probabilistic theories: what is special about quantum mechanics? Giacomo Mauro D'Ariano; 6. What probabilities tell about quantum systems, with application to entropy and entanglement John Myers and Hadi Madjid; 7. Bayesian updating and information gain in quantum measurements Leah Henderson; Part III. Quantum Information: 8. Schumacher information and the philosophy of physics Arnold Duwell; 9. From physics to information theory and back Wayne Myrvold; 10. Information, immaterialism, and instrumentalism: old and new in quantum information Chris Timpson; Part IV. Quantum Communication and Computing: 11. Quantum computation: where does the speed-up come from? Jeff Bub; 12. Quantum mechanics, quantum computing and quantum cryptography Tai Wu.

  4. 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.

  5. Entropy evolution of moving mirrors and the information loss problem

    NASA Astrophysics Data System (ADS)

    Chen, Pisin; Yeom, Dong-han

    2017-07-01

    We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semiclassical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semiclassical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semiclassical quantum field theory.

  6. 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.

  7. Quantum information causality.

    PubMed

    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.

  8. Entanglement entropy after selective measurements in quantum chains

    NASA Astrophysics Data System (ADS)

    Najafi, Khadijeh; Rajabpour, M. A.

    2016-12-01

    We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.

  9. 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.

  10. Fluctuations and entropy in models of quantum optical resonance

    NASA Astrophysics Data System (ADS)

    Phoenix, S. J. D.; Knight, P. L.

    1988-09-01

    We use variances, entropy, and the Shannon entropy to analyse the fluctuations and quantum evolution of various simple models of quantum optical resonance. We discuss at length the properties of the single-mode radiation field coupled to a single two-level atom, and then extend our analysis to describe the micromaser in which a cavity mode is repeatedly pumped by a succession of atoms passing through the cavity. We also discuss the fluctuations in the single-mode laser theory of Scully and Lamb.

  11. Information propagation in isolated quantum systems

    NASA Astrophysics Data System (ADS)

    Luitz, David J.; Bar Lev, Yevgeny

    2017-07-01

    Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time evolution we show that for weakly disordered nonintegrable systems information propagates behind a ballistically moving front, and the entanglement entropy growths linearly in time. For stronger disorder the motion of the information front is algebraic and subballistic and is characterized by an exponent, which depends on the strength of the disorder, similarly to the sublinear growth of the entanglement entropy. We show that the dynamical exponent associated with the information front coincides with the exponent of the growth of the entanglement entropy for both weak and strong disorder. We also demonstrate that the temporal dependence of the OTOC is characterized by a fast nonexponential growth, followed by a slow saturation after the passage of the information front. Finally, we discuss the implications of this behavioral change on the growth of the entanglement entropy.

  12. Life, Information, Entropy, and Time

    PubMed Central

    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

  13. Gaussian quantum information

    NASA Astrophysics Data System (ADS)

    Weedbrook, Christian; Pirandola, Stefano; García-Patrón, Raúl; Cerf, Nicolas J.; Ralph, Timothy C.; Shapiro, Jeffrey H.; Lloyd, Seth

    2012-04-01

    The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography, and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any combination of Gaussian states, Gaussian operations, and Gaussian measurements. Interestingly, such a restriction to the Gaussian realm comes with various benefits, since on the theoretical side, simple analytical tools are available and, on the experimental side, optical components effecting Gaussian processes are readily available in the laboratory. Yet, Gaussian quantum information processing opens the way to a wide variety of tasks and applications, including quantum communication, quantum cryptography, quantum computation, quantum teleportation, and quantum state and channel discrimination. This review reports on the state of the art in this field, ranging from the basic theoretical tools and landmark experimental realizations to the most recent successful developments.

  14. Bounds to information entropies for atomic systems

    NASA Astrophysics Data System (ADS)

    Tao, Jianmin; Li, Guobao; Li, Jianmin

    1997-07-01

    Bounds to atomic information entropies and their sum in position and momentum spaces have been derived in terms of radial and momentum expectation values and . Numerical studies on atomic systems show that the bounds presented in terms of and , the first moments of the position and momentum space densities are sharper than those given by Gadre and Bendale in terms of and , the second moments of the position and momentum space densities. Within the BKCM procedure due to Burkhardt, Kónya, Coulson, and March, several relationships between the information entropies and the average electron densities <ρ> and <γ> in position and momentum spaces have been established.

  15. 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.

  16. Metric on the space of quantum states from relative entropy. Tomographic reconstruction

    NASA Astrophysics Data System (ADS)

    Man'ko, Vladimir I.; Marmo, Giuseppe; Ventriglia, Franco; Vitale, Patrizia

    2017-08-01

    In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a suitably defined coordinate free differential calculus. The cases N=2, N=3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher-Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.

  17. Three faces of entropy for complex systems: Information, thermodynamics, and the maximum entropy principle

    NASA Astrophysics Data System (ADS)

    Thurner, Stefan; Corominas-Murtra, Bernat; Hanel, Rudolf

    2017-09-01

    There are at least three distinct ways to conceptualize entropy: entropy as an extensive thermodynamic quantity of physical systems (Clausius, Boltzmann, Gibbs), entropy as a measure for information production of ergodic sources (Shannon), and entropy as a means for statistical inference on multinomial processes (Jaynes maximum entropy principle). Even though these notions represent fundamentally different concepts, the functional form of the entropy for thermodynamic systems in equilibrium, for ergodic sources in information theory, and for independent sampling processes in statistical systems, is degenerate, H (p ) =-∑ipilogpi . For many complex systems, which are typically history-dependent, nonergodic, and nonmultinomial, this is no longer the case. Here we show that for such processes, the three entropy concepts lead to different functional forms of entropy, which we will refer to as SEXT for extensive entropy, SIT for the source information rate in information theory, and SMEP for the entropy functional that appears in the so-called maximum entropy principle, which characterizes the most likely observable distribution functions of a system. We explicitly compute these three entropy functionals for three concrete examples: for Pólya urn processes, which are simple self-reinforcing processes, for sample-space-reducing (SSR) processes, which are simple history dependent processes that are associated with power-law statistics, and finally for multinomial mixture processes.

  18. Quantum maximum entropy principle for a system of identical particles

    SciTech Connect

    Trovato, M.; Reggiani, L.

    2010-02-15

    By introducing a functional of the reduced density matrix, we generalize the definition of a quantum entropy which incorporates the indistinguishability principle of a system of identical particles. With the present definition, the principle of quantum maximum entropy permits us to solve the closure problem for a quantum hydrodynamic set of balance equations corresponding to an arbitrary number of moments in the framework of extended thermodynamics. The determination of the reduced Wigner function for equilibrium and nonequilibrium conditions is found to become possible only by assuming that the Lagrange multipliers can be expanded in powers of (Planck constant/2pi){sup 2}. Quantum contributions are expressed in powers of (Planck constant/2pi){sup 2} while classical results are recovered in the limit (Planck constant/2pi)->0.

  19. Entanglement entropy of the Q≥4 quantum Potts chain.

    PubMed

    Lajkó, Péter; Iglói, Ferenc

    2017-01-01

    The entanglement entropy S is an indicator of quantum correlations in the ground state of a many-body quantum system. At a second-order quantum phase-transition point in one dimension S generally has a logarithmic singularity. Here we consider quantum spin chains with a first-order quantum phase transition, the prototype being the Q-state quantum Potts chain for Q>4 and calculate S across the transition point. According to numerical, density matrix renormalization group results at the first-order quantum phase transition point S shows a jump, which is expected to vanish for Q→4^{+}. This jump is calculated in leading order as ΔS=lnQ[1-4/Q-2/(QlnQ)+O(1/Q^{2})].

  20. Chain rules for quantum Rényi entropies

    SciTech Connect

    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.

  1. Measuring Renyi entanglement entropy in quantum Monte Carlo simulations.

    PubMed

    Hastings, Matthew B; González, Iván; Kallin, Ann B; Melko, Roger G

    2010-04-16

    We develop a quantum Monte Carlo procedure, in the valence bond basis, to measure the Renyi entanglement entropy of a many-body ground state as the expectation value of a unitary Swap operator acting on two copies of the system. An improved estimator involving the ratio of Swap operators for different subregions enables convergence of the entropy in a simulation time polynomial in the system size. We demonstrate convergence of the Renyi entropy to exact results for a Heisenberg chain. Finally, we calculate the scaling of the Renyi entropy in the two-dimensional Heisenberg model and confirm that the Néel ground state obeys the expected area law for systems up to linear size L=32.

  2. Quantum information and computation

    SciTech Connect

    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}.

  3. GENERAL: Mutual Information and Relative Entropy of Sequential Effect Algebras

    NASA Astrophysics Data System (ADS)

    Wang, Jia-Mei; Wu, Jun-De; Cho, Minhyung

    2010-08-01

    In this paper, we introduce and investigate the mutual information and relative entropy on the sequential effect algebra, we also give a comparison of these mutual information and relative entropy with the classical ones by the venn diagrams. Finally, a nice example shows that the entropies of sequential effect algebra depend extremely on the order of its sequential product.

  4. 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.

  5. 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.

  6. 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.

  7. Random matrix techniques in quantum information theory

    SciTech Connect

    Collins, Benoît; Nechita, Ion

    2016-01-15

    The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.

  8. Random matrix techniques in quantum information theory

    NASA Astrophysics Data System (ADS)

    Collins, Benoît; Nechita, Ion

    2016-01-01

    The purpose of this review is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review and of more detailed examples—coming mainly from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.

  9. Uniform Additivity in Classical and Quantum Information

    NASA Astrophysics Data System (ADS)

    Cross, Andrew; Li, Ke; Smith, Graeme

    2017-01-01

    Information theory quantifies the optimal rates of resource interconversions, usually in terms of entropies. However, nonadditivity often makes evaluating entropic formulas intractable. In a few auspicious cases, additivity allows a full characterization of optimal rates. We study uniform additivity of formulas, which is easily evaluated and captures all known additive quantum formulas. Our complete characterization of uniform additivity exposes an intriguing new additive quantity and identifies a remarkable coincidence—the classical and quantum uniformly additive functions with one auxiliary variable are identical.

  10. Quantum Information Processing

    DTIC Science & Technology

    2007-11-02

    preparation, indicating, to our surprise, that standard quantum teleportation is *not* optimal for the transmission of states from Alice to Bob if...1 August 1998-1 August. 2001 4. TITLE AND SUBTITLE Quantum Information Processing 5. FUNDING NUMBERS DAAG55-98-C-0041 6. AUTHOR(S) David P... quantum entanglement in which the transmitted quantum state is known to Alice. Very recently, with A. Winter, a new, more efficient protocol for RSP has

  11. de Sitter Tunneling, Emission Spectrum and Entropy/Area Quantum

    NASA Astrophysics Data System (ADS)

    Jiang, Qing-Quan

    2012-08-01

    The Banerjee—Majhi's recent work shows that the Hawking radiation and entropy/area quantum of the black hole horizon (EH) can be well described in the tunneling picture. In this paper, we develop this idea to the case of a de Sitter tunneling from the cosmological horizon (CH), and obtain the Hawking emission spectrum and entropy/area spectroscopy from the CH of the purely de Sitter black hole as well as the Schwarzschild-de Sitter black hole. It is interestingly found that the area of the CH is quantized by ΔA = 4l2pl, as was given by Hod for the area quantum of -the EH by considering the Heisenberg uncertainty principle and Schwinger-type emission process. Also, we conclude from our derivation that the entropy/area quantum of the CH is universal in the sense that it is independent of the black hole parameters. This realization implies that, (at least) at a semiclassical level, the de Sitter gravity shares the similar quantum behavior as the usual gravity without presence of a cosmological constant.

  12. 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.

  13. Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution.

    PubMed

    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.

  14. Gravitational correlation, black hole entropy, and information conservation

    NASA Astrophysics Data System (ADS)

    He, DongShan; Cai, QingYu

    2017-04-01

    When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.

  15. Gravitational correlation, black hole entropy, and information conservation

    NASA Astrophysics Data System (ADS)

    He, DongShan; Cai, QingYu

    2017-04-01

    When two objects have gravitational interaction between them, they are no longer independent of each other. In fact, there exists gravitational correlation between these two objects. Inspired by Verlinde's paper, we first calculate the entropy change of a system when gravity does positive work on this system. Based on the concept of gravitational correlation entropy, we prove that the entropy of a Schwarzschild black hole originates from the gravitational correlations between the interior matters of the black hole. By analyzing the gravitational correlation entropies in the process of Hawking radiation in a general context, we prove that the reduced entropy of a black hole is exactly carried away by the radiation and the gravitational correlations between these radiating particles, and the entropy or information is conserved at all times during Hawking radiation. Finally, we attempt to give a unified description of the non-extensive black-hole entropy and the extensive entropy of ordinary matter.

  16. Structural information in two-dimensional patterns: entropy convergence and excess entropy.

    PubMed

    Feldman, David P; Crutchfield, James P

    2003-05-01

    We develop information-theoretic measures of spatial structure and pattern in more than one dimension. As is well known, the entropy density of a two-dimensional configuration can be efficiently and accurately estimated via a converging sequence of conditional entropies. We show that the manner in which these conditional entropies converge to their asymptotic value serves as a measure of global correlation and structure for spatial systems in any dimension. We compare and contrast entropy convergence with mutual-information and structure-factor techniques for quantifying and detecting spatial structure.

  17. Hybrid quantum information processing

    SciTech Connect

    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.

  18. Information Entropy of Influenza A Segment 7

    NASA Astrophysics Data System (ADS)

    Thompson, William A.; Fan, Shaohua; Weltman, Joel K.

    2008-12-01

    Information entropy (H) is a measure of uncertainty at each position within in a sequence of nucleotides.H was used to characterize a set of influenza A segment 7 nucleotide sequences. Nucleotide locations of high entropy were identified near the 5’ start of all of the sequences and the sequences were assigned to subsets according to synonymous nucleotide variants at those positions: either uracil at position six (U6), cytosine at position six (C6), adenine (A12) at position 12, guanine at position 12 (G12), adenine at position 15 (A15) or cytosine (C15) at position 15. H values were found to be correlated/corresponding (Kendall tau) along the lengths of the nucleotide segments of the subset pairs at each position. However, the H values of each subset of sequences were statistically distinguishable from those of the other member of the pair (Kolmogorov-Smirnov test). The joint probability of uncorrelated distributions of U6 and C6 sequences to viral subtypes and to viral host species was 34 times greater than for the A12:G12 subset pair and 214 times greater than for the A15:C15 pair. This result indicates that the high entropy position six of segment 7 is either a reporter or a sentinel location. The fact that not one of the H5N1 sequences in the dataset was a member of the C6 subset, but all 125 H5N1 sequences are members of the U6 subset suggests a non-random sentinel function.

  19. Heat engine driven by purely quantum information.

    PubMed

    Park, Jung Jun; Kim, Kang-Hwan; Sagawa, Takahiro; Kim, Sang Wook

    2013-12-06

    The key question of this Letter is whether work can be extracted from a heat engine by using purely quantum mechanical information. If the answer is yes, what is its mathematical formula? First, by using a bipartite memory we show that the work extractable from a heat engine is bounded not only by the free energy change and the sum of the entropy change of an individual memory but also by the change of quantum mutual information contained inside the memory. We then find that the engine can be driven by purely quantum information, expressed as the so-called quantum discord, forming a part of the quantum mutual information. To confirm it, as a physical example we present the Szilard engine containing a diatomic molecule with a semipermeable wall.

  20. Toward explaining black hole entropy quantization in loop quantum gravity

    NASA Astrophysics Data System (ADS)

    Sahlmann, Hanno

    2007-11-01

    In a remarkable numerical analysis of the spectrum of states for a spherically symmetric black hole in loop quantum gravity, Corichi, Diaz-Polo and Fernandez-Borja found that the entropy of the black hole horizon increases in what resembles discrete steps as a function of area. In the present article we reformulate the combinatorial problem of counting horizon states in terms of paths through a certain space. This formulation sheds some light on the origins of this steplike behavior of the entropy. In particular, using a few extra assumptions we arrive at a formula that reproduces the observed step length to a few tenths of a percent accuracy. However, in our reformulation the periodicity ultimately arises as a property of some complicated process, the properties of which, in turn, depend on the properties of the area spectrum in loop quantum gravity in a rather opaque way. Thus, in some sense, a deep explanation of the observed periodicity is still lacking.

  1. 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.

  2. Quantum Liouville theory and BTZ black hole entropy

    NASA Astrophysics Data System (ADS)

    Chen, Yujun

    In this thesis I give an explicit conformal field theory description of (2+1)-dimensional BTZ black hole entropy. In the boundary Liouville field theory I investigate the reducible Verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra Uq(sl2) ⊙ Uq̂(sl2). I show that there are states that decouple from these reducible Verma modules in a similar fashion to the decoupling of null states in minimal models. Because of the nonstandard form of the Ward identity for the two-point correlation functions in quantum Liouville field theory, these decoupling states have positive-definite norms. The unitary representations built on these decoupling states give the Bekenstein-Hawking entropy of the BTZ black hole.

  3. Entropy and correlation functions of a driven quantum spin chain

    SciTech Connect

    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.

  4. 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.

  5. Entanglement entropy in quantum spin chains with broken reflection symmetry

    SciTech Connect

    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.

  6. Quantum Information, Computation and Communication

    NASA Astrophysics Data System (ADS)

    Jones, Jonathan A.; Jaksch, Dieter

    2012-07-01

    Part I. Quantum Information: 1. Quantum bits and quantum gates; 2. An atom in a laser field; 3. Spins in magnetic fields; 4. Photon techniques; 5. Two qubits and beyond; 6. Measurement and entanglement; Part II. Quantum Computation: 7. Principles of quantum computing; 8. Elementary quantum algorithms; 9. More advanced quantum algorithms; 10. Trapped atoms and ions; 11. Nuclear magnetic resonance; 12. Large scale quantum computers; Part III. Quantum Communication: 13. Basics of information theory; 14. Quantum information; 15. Quantum communication; 16. Testing EPR; 17. Quantum cryptography; Appendixes; References; Index.

  7. Entanglement entropy near Kondo-destruction quantum critical points

    NASA Astrophysics Data System (ADS)

    Pixley, J. H.; Chowdhury, Tathagata; Miecnikowski, M. T.; Stephens, Jaimie; Wagner, Christopher; Ingersent, Kevin

    2015-06-01

    We study the impurity entanglement entropy Se in quantum impurity models that feature a Kondo-destruction quantum critical point (QCP) arising from a pseudogap in the conduction-band density of states or from coupling to a bosonic bath. On the local-moment (Kondo-destroyed) side of the QCP, the entanglement entropy contains a critical component that can be related to the order parameter characterizing the quantum phase transition. In Kondo models describing a spin-Simp,Se assumes its maximal value of ln(2 Simp+1 ) at the QCP and throughout the Kondo phase, independent of features such as particle-hole symmetry and under- or overscreening. In Anderson models, Se is nonuniversal at the QCP and, at particle-hole symmetry, rises monotonically on passage from the local-moment phase to the Kondo phase; breaking this symmetry can lead to a cusp peak in Se due to a divergent charge susceptibility at the QCP. Implications of these results for quantum critical systems and quantum dots are discussed.

  8. Relative Entropy Bounds on Quantum, Private and Repeater Capacities

    NASA Astrophysics Data System (ADS)

    Christandl, Matthias; Müller-Hermes, Alexander

    2017-07-01

    We find a strong-converse bound on the private capacity of a quantum channel assisted by unlimited two-way classical communication. The bound is based on the max-relative entropy of entanglement and its proof uses a new inequality for the sandwiched Rényi divergences based on complex interpolation techniques. We provide explicit examples of quantum channels where our bound improves upon both the transposition bound (on the quantum capacity assisted by classical communication) and the bound based on the squashed entanglement. As an application, we study a repeater version of the private capacity assisted by classical communication and provide an example of a quantum channel with high private capacity but negligible private repeater capacity.

  9. Quantum Entanglement and Information

    NASA Astrophysics Data System (ADS)

    Zeilinger, Anton

    2002-04-01

    The development of quantum entanglement presents a very interesting and typical case how fundamental reasearch leads to new technologically interesting concepts. Initially it was introduced by Einstein and Schroedinger because of its philosophical interest. This, together with Bell's theorem, led to experiments beginning in the early 1970-s which also were only motivated by their importance for the foundations of physics. Most remarkably, in recent years people discovered that quantum entanglement can be useful in completely novel ways of transmitting and processing of information with no analog in classical physics. Here the most developed areas are quantum communication, quantum cryptography, quantum teleportation and quantum computation. In the talk I will present the basics of these applications of entanglement and I will discuss some existing experimental realisations. Finally I will argue that, while it is impossible to foresee where the present development will lead us, it is very likely that in the end a novel kind of information technology will emerge.

  10. Experimental Rectification of Entropy Production by Maxwell's Demon in a Quantum System

    NASA Astrophysics Data System (ADS)

    Camati, Patrice A.; Peterson, John P. S.; Batalhão, Tiago B.; Micadei, Kaonan; Souza, Alexandre M.; Sarthour, Roberto S.; Oliveira, Ivan S.; Serra, Roberto M.

    2016-12-01

    Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1 /2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1 /2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility in a nonequilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.

  11. 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.

  12. Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism

    SciTech Connect

    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.

  13. Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism.

    PubMed

    Trovato, M; Reggiani, L

    2011-12-01

    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(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 → 0.

  14. 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

  15. Types of quantum information

    SciTech Connect

    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.

  16. Relativistic quantum information

    NASA Astrophysics Data System (ADS)

    Mann, R. B.; Ralph, T. C.

    2012-11-01

    Over the past few years, a new field of high research intensity has emerged that blends together concepts from gravitational physics and quantum computing. Known as relativistic quantum information, or RQI, the field aims to understand the relationship between special and general relativity and quantum information. Since the original discoveries of Hawking radiation and the Unruh effect, it has been known that incorporating the concepts of quantum theory into relativistic settings can produce new and surprising effects. However it is only in recent years that it has become appreciated that the basic concepts involved in quantum information science undergo significant revision in relativistic settings, and that new phenomena arise when quantum entanglement is combined with relativity. A number of examples illustrate that point. Quantum teleportation fidelity is affected between observers in uniform relative acceleration. Entanglement is an observer-dependent property that is degraded from the perspective of accelerated observers moving in flat spacetime. Entanglement can also be extracted from the vacuum of relativistic quantum field theories, and used to distinguish peculiar motion from cosmological expansion. The new quantum information-theoretic framework of quantum channels in terms of completely positive maps and operator algebras now provides powerful tools for studying matters of causality and information flow in quantum field theory in curved spacetimes. This focus issue provides a sample of the state of the art in research in RQI. Some of the articles in this issue review the subject while others provide interesting new results that will stimulate further research. What makes the subject all the more exciting is that it is beginning to enter the stage at which actual experiments can be contemplated, and some of the articles appearing in this issue discuss some of these exciting new developments. The subject of RQI pulls together concepts and ideas from

  17. 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.

  18. Comment on "Quantum Kaniadakis entropy under projective measurement".

    PubMed

    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)PLEEE81539-375510.1103/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.

  19. Fisher Information and Shannon Entropy in Confined 1D Harmonic Oscillator

    SciTech Connect

    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.

  20. Classicality condition on a system observable in a quantum measurement and a relative-entropy conservation law

    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.

  1. Single particle in quantum gravity and Braunstein-Ghosh-Severini entropy of a spin network

    SciTech Connect

    Rovelli, Carlo; Vidotto, Francesca

    2010-02-15

    Passerini and Severini have recently shown that the Braunstein-Ghosh-Severini (BGS) entropy S{sub {Gamma}}=-Tr[{rho}{sub {Gamma}}log{rho}{sub {Gamma}}] of a certain density matrix {rho}{sub {Gamma}} naturally associated to a graph {Gamma}, is maximized, among all graphs with a fixed number of links and nodes, by regular graphs. We ask if this result can play a role in quantum gravity, and be related to the apparent regularity of the physical geometry of space. We show that in loop quantum gravity the matrix {rho}{sub {Gamma}} is precisely the Hamiltonian operator (suitably normalized) of a nonrelativistic quantum particle interacting with the quantum gravitational field, if we restrict elementary area and volume eigenvalues to a fixed value. This operator provides a spectral characterization of the physical geometry, and can be interpreted as a state describing the spectral information about the geometry available when geometry is measured by its physical interaction with matter. It is then tempting to interpret its BGS entropy S{sub {Gamma}} as a genuine physical entropy: we discuss the appeal and the difficulties of this interpretation.

  2. Changes in the Entropy and Information Difference During Self-Organization of Nonextensive Systems in Parastatistics

    NASA Astrophysics Data System (ADS)

    Zaripov, R. G.

    2017-09-01

    On the basis of the method of Bose quantum states in parastatistics for quantum nonextensive systems, the evolution of the parametric entropy and the information difference under induced transitions between stationary states in the space of control parameters during self-organization is considered. S and I theorems on changes in renormalized measures under the Gibbs condition on the constancy of the total energy and the total number of particles are proven.

  3. Topological Rényi entropy after a quantum quench.

    PubMed

    Halász, Gábor B; Hamma, Alioscia

    2013-04-26

    We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Rényi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Rényi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.

  4. What is quantum information?

    NASA Astrophysics Data System (ADS)

    Lombardi, Olimpia; Holik, Federico; Vanni, Leonardo

    2016-11-01

    In the present article we address the question 'What is quantum information?' from a conceptual viewpoint. In particular, we argue that there seems to be no sufficiently good reasons to accept that quantum information is qualitatively different from classical information. The view that, in the communicational context, there is only one kind of information, physically neutral, which can be encoded by means of classical or quantum states has, in turn, interesting conceptual advantages. First, it dissolves the widely discussed puzzles of teleportation without the need to assume a particular interpretation of information. Second, and from a more general viewpoint, it frees the attempts to reconstruct quantum mechanics on the basis of informational constraints from any risk of circularity; furthermore, it endows them with a strong conceptual appealing and, derivatively, opens the way to the possibility of a non-reductive unification of physics. Finally, in the light of the idea of the physical neutrality of information, the wide field of research about classical models for quantum information acquires a particular conceptual and philosophical interest.

  5. Quantum information theory of the Bell-state quantum eraser

    NASA Astrophysics Data System (ADS)

    Glick, Jennifer R.; Adami, Christoph

    2017-01-01

    Quantum systems can display particle- or wavelike properties, depending on the type of measurement that is performed on them. The Bell-state quantum eraser is an experiment that brings the duality to the forefront, as a single measurement can retroactively be made to measure particlelike or wavelike properties (or anything in between). Here we develop a unitary information-theoretic description of this and several related quantum measurement situations that sheds light on the trade-off between the quantum and classical features of the measurement. In particular, we show that both the coherence of the quantum state and the classical information obtained from it can be described using only quantum-information-theoretic tools and that those two measures satisfy an equality on account of the chain rule for entropies. The coherence information and the which-path information have simple interpretations in terms of state preparation and state determination and suggest ways to account for the relationship between the classical and the quantum world.

  6. 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

  7. 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.

  8. Effects of correlated variability on information entropies in nonextensive systems

    NASA Astrophysics Data System (ADS)

    Hasegawa, Hideo

    2008-08-01

    We have calculated the Tsallis entropy and Fisher information matrix (entropy) of spatially correlated nonextensive systems, by using an analytic non-Gaussian distribution obtained by the maximum entropy method. The effects of the correlated variability on the Fisher information matrix are shown to be different from those on the Tsallis entropy. The Fisher information is increased (decreased) by a positive (negative) correlation, whereas the Tsallis entropy is decreased with increasing absolute magnitude of the correlation, independently of its sign. This fact arises from the difference in their characteristics. It implies from the Cramér-Rao inequality that the accuracy of an unbiased estimate of fluctuation is improved by a negative correlation. A critical comparison is made between the present study and previous ones employing the Gaussian approximation for the correlated variability due to multiplicative noise.

  9. Correlations and diagonal entropy after quantum quenches in XXZ chains

    NASA Astrophysics Data System (ADS)

    Piroli, Lorenzo; Vernier, Eric; Calabrese, Pasquale; Rigol, Marcos

    2017-02-01

    We study quantum quenches in the XXZ spin-1 /2 Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasilocal conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble, finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we use exact diagonalization to compute the diagonal entropy in the postquench steady state. We show that the Yang-Yang entropy for the complete GGE is consistent with twice the value of the diagonal entropy in the largest chains or the extrapolated result in the thermodynamic limit. Finally, the complete GGE is quantitatively contrasted with the GGE built using only the local conserved charges (local GGE). The predictions of the two ensembles are found to differ significantly in the case of ferromagnetic initial states. Such initial states are better suited than others considered in the literature to experimentally test the validity of the complete GGE and contrast it to the failure of the local GGE.

  10. Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

    DOE PAGES

    Ferrie, Christopher; Blume-Kohout, Robin

    2016-03-04

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

  11. Minimax Quantum Tomography: Estimators and Relative Entropy Bounds

    SciTech Connect

    Ferrie, Christopher; Blume-Kohout, Robin

    2016-03-04

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

  12. Quantum Information Science Using Photons

    NASA Astrophysics Data System (ADS)

    Bouwmeester, D.; Howell, J. C.; Lamas-Linares, A.

    Contents: 1 Introduction 1.1 A Humble Point of View 1.2 Quantum Mystery 1.3 Maxwell's Demon 1.4 Shannon Entropy 1.5 Von Neumann Entropy 2 Einstein-Podolsky-Rosen Paradox and Bell's Inequalities 3 Producing Entangled Particles 3.1 Introduction 3.2 Parametric Down-Conversion 3.3 Franson's Proposal 3.4 Polarization Entanglement 4 The Beam Splitter Action on a Two-Photon State 4.1 Beamsplitter Transformation 4.2 Bell-State Analyzer 5 No-Cloning Theorem 6 Quantum Cryptography 7 Quantum Dense Coding 7.1 Theoretical Scheme 7.2 Experimental Dense Coding with Qubits 8 Quantum Teleportation 8.1 Theoretical Scheme 8.2 Experimental Quantum Teleportation of Qubits 8.3 Teleportation of Entanglement 8.4 A Two-Particle Scheme for Quantum Teleportation 9 Teleportation of Continuous Quantum Variables 9.1 Theoretical Scheme 9.2 Quantum Optical Implementation 10 Quantum Error Detection and Correction 10.1 Introduction 10.2 Quantum Error Detection 10.3 Avoiding Controlled-NOT Operations 10.4 Post-selection 11 Stimulated Entanglement 11.1 Theory 12 Bohm-Type Spin-s Entanglements

  13. Loop quantum gravity, exact holographic mapping, and holographic entanglement entropy

    NASA Astrophysics Data System (ADS)

    Han, Muxin; Hung, Ling-Yan

    2017-01-01

    The relation between loop quantum gravity (LQG) and tensor networks is explored from the perspectives of the bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space Σ with boundary ∂Σ is an exact holographic mapping similar to the proposal in [X.-L. Qi, Exact holographic mapping and emergent space-time geometry, arXiv:1309.6282]. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse-graining procedure of spin networks. Furthermore, when a region A and its complement A ¯ are specified on the boundary ∂Σ , we show that the boundary entanglement entropy S (A ) of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e., S (A ) is proportional to the minimal area of the bulk surface attached to the boundary of A in ∂Σ .

  14. Concentrating Tripartite Quantum Information.

    PubMed

    Streltsov, Alexander; Lee, Soojoon; Adesso, Gerardo

    2015-07-17

    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.

  15. 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.

  16. Quantum Gravity corrections and entropy at the Planck time

    SciTech Connect

    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.

  17. Quantum criticality from Fisher information

    NASA Astrophysics Data System (ADS)

    Song, Hongting; Luo, Shunlong; Fu, Shuangshuang

    2017-04-01

    Quantum phase transition is primarily characterized by a qualitative sudden change in the ground state of a quantum system when an external or internal parameter of the Hamiltonian is continuously varied. Investigating quantum criticality using information-theoretic methods has generated fruitful results. Quantum correlations and fidelity have been exploited to characterize the quantum critical phenomena. In this work, we employ quantum Fisher information to study quantum criticality. The singular or extremal point of the quantum Fisher information is adopted as the estimated thermal critical point. By a significant model constructed in Quan et al. (Phys Rev Lett 96: 140604, 2006), the effectiveness of this method is illustrated explicitly.

  18. Quantum Hypothesis Testing and the Operational Interpretation of the Quantum Rényi Relative Entropies

    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.

  19. Violating the quantum focusing conjecture and quantum covariant entropy bound in d ⩾ 5 dimensions

    NASA Astrophysics Data System (ADS)

    Fu, Zicao; Koeller, Jason; Marolf, Donald

    2017-09-01

    We study the quantum focussing conjecture (QFC) in curved spacetime. Noting that quantum corrections from integrating out massive fields generally induce a Gauss-Bonnet term, we study Einstein-Hilbert-Gauss-Bonnet gravity and show for d≥slant 5 spacetime dimensions that weakly-curved solutions can violate the associated QFC for either sign of the Gauss-Bonnet coupling. The nature of the violation shows that—so long as the Gauss-Bonnet coupling is non-zero—it will continue to arise for local effective actions containing arbitrary further higher curvature terms, and when gravity is coupled to generic d≥slant 5 theories of massive quantum fields. The argument also implies violations of a recently-conjectured form of the generalized covariant entropy bound. The possible validity of the QFC and covariant entropy bound in d≤slant 4 spacetime dimensions remains open.

  20. Similarity between quantum mechanics and thermodynamics: entropy, temperature, and Carnot cycle.

    PubMed

    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.

  1. Entropy, chaos, and excited-state quantum phase transitions in the Dicke model.

    PubMed

    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.

  2. 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.

  3. Role of information theoretic uncertainty relations in quantum theory

    SciTech Connect

    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.

  4. Relating different quantum generalizations of the conditional Rényi entropy

    SciTech Connect

    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.

  5. Tsallis entropy and general polygamy of multiparty quantum entanglement in arbitrary dimensions

    NASA Astrophysics Data System (ADS)

    Kim, Jeong San

    2016-12-01

    We establish a unified view of the polygamy of multiparty quantum entanglement in arbitrary dimensions. Using quantum Tsallis-q entropy, we provide a one-parameter class of polygamy inequalities of multiparty quantum entanglement. This class of polygamy inequalities reduces to the known polygamy inequalities based on tangle and entanglement of assistance for a selective choice of the parameter q . We further provide one-parameter generalizations of various quantum correlations based on Tsallis-q entropy. By investigating the properties of the generalized quantum correlations, we provide a sufficient condition on which the Tsallis-q polygamy inequalities hold in multiparty quantum systems of arbitrary dimensions.

  6. Entanglement entropy of U (1) quantum spin liquids

    NASA Astrophysics Data System (ADS)

    Pretko, Michael; Senthil, T.

    2016-09-01

    We here investigate the entanglement structure of the ground state of a (3 +1 )-dimensional U (1 ) quantum spin liquid, which is described by the deconfined phase of a compact U (1 ) gauge theory. A gapless photon is the only low-energy excitation, with matter existing as deconfined but gapped excitations of the system. It is found that, for a given bipartition of the system, the elements of the entanglement spectrum can be grouped according to the electric flux between the two regions, leading to a useful interpretation of the entanglement spectrum in terms of electric charges living on the boundary. The entanglement spectrum is also given additional structure due to the presence of the gapless photon. Making use of the Bisognano-Wichmann theorem and a local thermal approximation, these two contributions to the entanglement (particle and photon) are recast in terms of boundary and bulk contributions, respectively. Both pieces of the entanglement structure give rise to universal subleading terms (relative to the area law) in the entanglement entropy, which are logarithmic in the system size (logL ), as opposed to the subleading constant term in gapped topologically ordered systems. The photon subleading logarithm arises from the low-energy conformal field theory and is essentially local in character. The particle subleading logarithm arises due to the constraint of closed electric loops in the wave function and is shown to be the natural generalization of topological entanglement entropy to the U (1 ) spin liquid. This contribution to the entanglement entropy can be isolated by means of the Grover-Turner-Vishwanath construction (which generalizes the Kitaev-Preskill scheme to three dimensions).

  7. Quantum statistical gravity: time dilation due to local information in many-body quantum systems

    NASA Astrophysics Data System (ADS)

    Sels, Dries; Wouters, Michiel

    2017-08-01

    We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at constant probability. This definition is motivated by the analysis of entropic forces in classical systems.

  8. Information Entropy Exchange in the Path Integral Formulation of Transition Amplitudes

    NASA Astrophysics Data System (ADS)

    Deeter, Daniel; Petridis, Athanasios

    2016-09-01

    The quantum mechanical transition amplitude for a free particle is calculated using the path integral formalism. This amplitude is the kernel of the Schrödinger equation. A Wick rotation of the time increment transforms the kernel into a partition function that depends on the space and time intervals of the transition, with the temperature being proportional to the inverse of the time increment. The information entropy exchange between the system and the observer during the transition is calculated from the partition function. The requirement that this be real-valued leads to uncertainty-type relations. Furthermore, the transition exhibits positive information entropy exchange for small time intervals and negative entropy for large ones. The related statistical weight is inversely proportional to the square root of the time interval. Calculations for interacting systems are in progress.

  9. Quantum mechanics and quantum information theory

    NASA Astrophysics Data System (ADS)

    van Camp, Wesley William

    The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches -- that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism -- fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel

  10. Precise Evaluation of Leaked Information with Secure Randomness Extraction in the Presence of Quantum Attacker

    NASA Astrophysics Data System (ADS)

    Hayashi, Masahito

    2015-01-01

    We treat secret key extraction when the eavesdropper has correlated quantum states. We propose quantum privacy amplification theorems different from Renner's, which are based on quantum conditional Rényi entropy of order 1 + s. Using those theorems, we derive an exponential rate of decrease for leaked information and the asymptotic equivocation rate, which have not been derived hitherto in the quantum setting.

  11. Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states

    NASA Astrophysics Data System (ADS)

    Yurischev, M. A.

    2017-10-01

    For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy S_{cond} as a function of measurement angle θ \\in [0,π /2]. Numerical calculations show that the function S_{cond}(θ ) for X states can have at most one local extremum in the open interval from zero to π /2 (unimodality property). If the extremum is a minimum, the quantum discord displays region with variable (state-dependent) optimal measurement angle θ ^*. Such θ -regions (phases, fractions) are very tiny in the space of X-state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval (0,π /2). It is remarkable that the maxima exist in surprisingly wide regions, and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum.

  12. Sharp continuity bounds for entropy and conditional entropy

    NASA Astrophysics Data System (ADS)

    Chen, ZhiHua; Ma, ZhiHao; Nikoufar, Ismail; Fei, Shao-Ming

    2017-02-01

    The Renyi entropy plays an essential role in quantum information theory. We study the continuity estimation of the Renyi entropy. An inequality relating the Renyi entropy difference of two quantum states to their trace norm distance is derived. This inequality is shown to be tight in the sense that equality can be attained for every prescribed value of the trace norm distance. It includes the sharp Fannes inequality for von Neumann entropy as a special case.

  13. Quantum hairs’ and entropy of the quantum isolated horizon from Chern-Simons theory

    NASA Astrophysics Data System (ADS)

    Majhi, Abhishek; Majumdar, Parthasarathi

    2014-10-01

    We articulate the fact that the loop quantum gravity (LQG) description of the quantum macrostates of black hole horizons, modeled as quantum isolated horizons (QIHs), is completely characterized in terms of two independent integer-valued ‘quantum hairs’, viz, the coupling constant (k) of the quantum SU(2) Chern-Simons (CS) theory describing QIH dynamics, and the number of punctures (N) produced by the bulk spin network edges piercing the isolated horizon (which act as pointlike sources for the CS fields). We demonstrate that the microcanonical entropy of macroscopic (both parameters assuming very large values) QIHs can be obtained directly from the microstates of this CS theory using standard statistical mechanical methods, without having to additionally postulate the horizon as an ideal gas of punctures, or incorporate any additional classical or semiclassical input from general relativity vis-a-vis the functional dependence of the isolated horizon mass on its area, or indeed, without having to restrict to any special class of spins. Requiring the validity of the Bekenstein-Hawking area law relates these two parameters (as an equilibrium ‘equation of state’), and consequently allows the Barbero-Immirzi parameter to take any real and positive value depending on the value of k/N. The logarithmic correction to the area law obtained a decade ago by R Kaul and one of us (PM), ensues straightforwardly, with precisely the coefficient -3/2, making it a signature of the LQG approach to black hole entropy.

  14. Informational power of quantum measurements

    SciTech Connect

    Dall'Arno, Michele; D'Ariano, Giacomo Mauro; Sacchi, Massimiliano F.

    2011-06-15

    We introduce the informational power of a quantum measurement as the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We prove the additivity by showing that the informational power corresponds to the classical capacity of a quantum-classical channel. We restate the problem of evaluating the informational power as the maximization of the accessible information of a suitable ensemble. We provide a numerical algorithm to find an optimal ensemble and quantify the informational power.

  15. Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential

    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.

  16. Quantum statistical entropy for Kerr de Sitter black hole

    NASA Astrophysics Data System (ADS)

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

    2004-06-01

    Improving the membrane model by which the entropy of the black hole is studied, we study the entropy of the black hole in the non-thermal equilibrium state. To give the problem stated here widespread meaning, we discuss the (n+2)-dimensional de Sitter spacetime. Through discussion, we obtain that the black hole's entropy which contains two horizons (a black hole's horizon and a cosmological horizon) in the non-thermal equilibrium state comprises the entropy corresponding to the black hole's horizon and the entropy corresponding to the cosmological horizon. Furthermore, the entropy of the black hole is a natural property of the black hole. The entropy is irrelevant to the radiation field out of the horizon. This deepens the understanding of the relationship between black hole's entropy and horizon's area. A way to study the bosonic and fermionic entropy of the black hole in high non-thermal equilibrium spacetime is given.

  17. Two faces of entropy and information in biological systems.

    PubMed

    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. Copyright © 2014 Elsevier Ltd. All rights reserved.

  18. Statistical mechanical expression of entropy production for an open quantum system

    NASA Astrophysics Data System (ADS)

    Majima, Hiroki; Suzuki, Akira

    2013-02-01

    A quantum statistical expression for the entropy of a nonequilibrium system is defined so as to be consistent with Gibbs' relation, and is shown to corresponds to dynamical variable by introducing analogous to the Heisenberg picture in quantum mechanics. The general relation between system-reservoir interactions and an entropy change operator in an open quantum system, relying just on the framework of statistical mechanics and the definition of von Neumann entropy. By using this formula, we can obtain the correct entropy production in the linear response framework. The present derivation of entropy production is directly based on the first principle of microscopic time-evolution, while the previous standard argument is due to the thermodynamic energy balance.

  19. Strategy based on information entropy for optimizing stochastic functions.

    PubMed

    Schmidt, Tobias Christian; Ries, Harald; Spirkl, Wolfgang

    2007-02-01

    We propose a method for the global optimization of stochastic functions. During the course of the optimization, a probability distribution is built up for the location and the value of the global optimum. The concept of information entropy is used to make the optimization as efficient as possible. The entropy measures the information content of a probability distribution, and thus gives a criterion for decisions: From several possibilities we choose the one which yields the most information concerning location and value of the global maximum sought.

  20. Entropy Bounds and Entanglement

    NASA Astrophysics Data System (ADS)

    Fisher, Zachary

    The generalized covariant entropy bound, or Bousso bound, is a holographic bound on the entropy of a region of space in a gravitational theory. It bounds the entropy passing through certain null surfaces. The bound remains non-trivial in the weak-gravity limit, and provides non-trivial constraints on the entropy of ordinary quantum states even in a regime where gravity is negligible. In the first half of this thesis, we present a proof of the Bousso bound in the weak-gravity regime within the framework of quantum field theory. The bound uses techniques from quantum information theory which relate the energy and entropy of quantum states. We present two proofs of the bound in free and interacting field theory. In the second half, we present a generalization of the Bousso bound called the quantum focussing conjecture. Our conjecture is a bound on the rate of entropy generation in a quantum field theory coupled semiclassically to gravity. The conjecture unifies and generalizes several ideas in holography. In particular, the quantum focussing conjecture implies a bound on entropies which is similar to, but subtly different from, the Bousso bound proven in the first half. The quantum focussing conjecture implies a novel non-gravitational energy condition, the quantum null energy condition, which gives a point-wise lower bound on the null-null component of the stress tensor of quantum matter. We give a proof of this bound in the context of free and superrenormalizable bosonic quantum field theory.

  1. Fisher information and Rényi entropies in dynamical systems

    NASA Astrophysics Data System (ADS)

    Godó, B.; Nagy, Á.

    2017-07-01

    The link between the Fisher information and Rényi entropies is explored. The relationship is based on a thermodynamical formalism based on Fisher information with a parameter, β, which is interpreted as the inverse temperature. The Fisher heat capacity is defined and found to be sensitive to changes of higher order than the analogous quantity in the conventional formulation.

  2. Optimization of Secondary Concentrators with the Continuous Information Entropy Strategy

    NASA Astrophysics Data System (ADS)

    Schmidt, Tobias Christian; Ries, Harald

    2010-10-01

    In this contribution, a method for global optimization of noisy functions, the Continuous Information Entropy Strategy (CIES), is explained and its applicability for the optimization of solar concentrators is shown. The CIES is efficient because all decisions made during optimizations are based on criteria that are derived from the concept of information entropy. Two secondary concentrators have been optimized with the CIES. The optimized secondary concentrators convert circular light distributions of round focal spots to square light distributions to match with the shape of square PV cells. The secondary concentrators are highly efficient and have geometrical concentration ratios of 2.25 and 8 respectively. Part of this material has been published in: T. C. Schmidt, "Information Entropy-Based Decision Making in Optimization", Ph.D. Thesis, Philipps University Marburg, 2010.

  3. 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.

  4. Quantum Information and Nepal

    NASA Astrophysics Data System (ADS)

    Brady, Adam; Chapagain, Nirdosh; Simkhada, Prashanna

    2011-10-01

    Quantum Information (QI) is a relatively young science with exciting research opportunities. Nepal has an untapped reserve of motivated students with scientific research potential. Based on our educational experience in Nepal and in the US and based on our exposure to QI, we explore the possibility of developing QI research in Nepal. In this poster we lay out basic facts on physics and physics education in Nepal, report on an introductory QI class experiment at BYU, and use what we have learned to envision a QI future in Nepal.

  5. Markov property and strong additivity of von Neumann entropy for graded quantum systems

    SciTech Connect

    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.

  6. Physical basis of information and the relation to entropy

    NASA Astrophysics Data System (ADS)

    Ebeling, W.

    2017-01-01

    We discuss the relation between entropy and information from the physicists point of view differing between bound and free information. The quantitative physical aspects of information flow are given by flows of entropy, which are closely related to the reduction of uncertainty and the predictability of events. Free information is considered as a quantity, which has intrinsic non - physical components, and is originally created by selforganization and evolution. Bound and free information are both represented by a matter carrier but not as tight - bounded like mass or energy. Free information is connected with information - processing; it is introduced as a binary relation between a sender and a receiver, which may have different carriers, it is essentially characterized by symbolic representations. Processing free information is originally created by selforganization on the early earth and is connected with the origin of life, therefore it is always at least indirectly related to living systems.

  7. Remarks on the information entropy maximization method and extended thermodynamics

    NASA Astrophysics Data System (ADS)

    Eu, Byung Chan

    1998-04-01

    The information entropy maximization method was applied by Jou et al. [J. Phys. A 17, 2799 (1984)] to heat conduction in the past. Advancing this method one more step, Nettleton [J. Chem. Phys. 106, 10311 (1997)] combined the method with a projection operator technique to derive a set of evolution equations for macroscopic variables from the Liouville equation for a simple liquid, and a claim was made that the method provides a statistical mechanical theory basis of irreversible processes and, in particular, of extended thermodynamics which is consistent with the laws of thermodynamics. This line of information entropy maximization method is analyzed from the viewpoint of the laws of thermodynamics in this paper.

  8. 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.)

  9. The use of the information-theoretic entropy in thermodynamics

    NASA Astrophysics Data System (ADS)

    Ladyman, James; Presnell, Stuart; Short, Anthony J.

    When considering controversial thermodynamic scenarios such as Maxwell's demon, it is often necessary to consider probabilistic mixtures of macrostates. This raises the question of how, if at all, to assign entropy to them. The information-theoretic entropy is often used in such cases; however, no general proof of the soundness of doing so has been given, and indeed some arguments against doing so have been presented. We offer a general proof of the applicability of the information-theoretic entropy to probabilistic mixtures of macrostates that is based upon a probabilistic generalisation of the Kelvin statement of the second law. We defend the latter and make clear the other assumptions on which our main result depends. We also briefly discuss the interpretation of our result.

  10. Entropy and Information Transmission in Causation and Retrocausation

    NASA Astrophysics Data System (ADS)

    Moddel, Garret

    2006-10-01

    Although experimental evidence for retrocausation exists, there are clearly subtleties to the phenomenon. The bilking paradox, in which one intervenes to eliminate a subsequent cause after a preceding effect has occurred, appears on the surface to show that retrocausation is logically impossible. In a previous paper, the second law of thermodynamics was invoked to show that the entropy in each process of a psi interaction (presentience, telepathy, remote perception, and psychokinesis) cannot decrease, prohibiting psi processes in which signals condense from background fluctuations. Here it is shown, perhaps contrary to one's intuition, that reversible processes cannot be influenced through retrocausation, but irreversible processes can. The increase in thermodynamic entropy in irreversible processes — which are generally described by Newtonian mechanics but not Lagrangian dynamics and Hamilton's Principle — is required for causation. Thermodynamically reversible processes cannot be causal and hence also cannot be retrocausal. The role of entropy in psi interactions is extended by using the bilking paradox to consider information transmission in retroactive psychokinesis (PK). PK efficiency, ηPK, is defined. A prediction of the analysis is that ηPK ⩽ H/H0, where H is the information uncertainty or entropy in the retro-PK agent's knowledge of the event that is to be influenced retrocausally. The information entropy can provide the necessary ingredient for non-reversibility, and hence retrocausation. Noise and bandwidth limitations in the communication to the agent of the outcome of the event increase the maximum PK efficiency. Avoidance of the bilking paradox does not bar a subject from using the premonition of an event to prevent it from occurring. The necessity for large information entropy, which is the expected value of the surprisal, is likely to be essential for any successful PK process, not just retro-PK processes. Hence uncertainty in the

  11. Quantum coherence via skew information and its polygamy

    NASA Astrophysics Data System (ADS)

    Yu, Chang-shui

    2017-04-01

    Quantifying coherence is a key task in both quantum-mechanical theory and practical applications. Here, a reliable quantum coherence measure is presented by utilizing the quantum skew information of the state of interest subject to a certain broken observable. This coherence measure is proven to fulfill all the criteria (especially the strong monotonicity) recently introduced in the resource theories of quantum coherence. The coherence measure has an analytic expression and an obvious operational meaning related to quantum metrology. In terms of this coherence measure, the distribution of the quantum coherence, i.e., how the quantum coherence is distributed among the multiple parties, is studied and a corresponding polygamy relation is proposed. As a further application, it is found that the coherence measure forms the natural upper bounds for quantum correlations prepared by incoherent operations. The experimental measurements of our coherence measure as well as the relative-entropy coherence and lp-norm coherence are studied finally.

  12. Universal boundary entropies in conformal field theory: A quantum Monte Carlo study

    NASA Astrophysics Data System (ADS)

    Tang, Wei; Chen, Lei; Li, Wei; Xie, X. C.; Tu, Hong-Hao; Wang, Lei

    2017-09-01

    Recently, entropy corrections on nonorientable manifolds such as the Klein bottle are proposed as a universal characterization of critical systems with an emergent conformal field theory (CFT). We show that entropy correction on the Klein bottle can be interpreted as a boundary effect via transforming the Klein bottle into an orientable manifold with nonlocal boundary interactions. The interpretation reveals the conceptual connection of the Klein bottle entropy with the celebrated Affleck-Ludwig entropy in boundary CFT. We propose a generic scheme to extract these universal boundary entropies from quantum Monte Carlo calculation of partition function ratios in lattice models. Our numerical results on the Affleck-Ludwig entropy and Klein bottle entropy for the q -state quantum Potts chains with q =2 ,3 show excellent agreement with the CFT predictions. For the quantum Potts chain with q =4 , the Klein bottle entropy slightly deviates from the CFT prediction, which is possibly due to marginally irrelevant terms in the low-energy effective theory.

  13. Atomistic-level non-equilibrium model for chemically reactive systems based on steepest-entropy-ascent quantum thermodynamics

    NASA Astrophysics Data System (ADS)

    Li, Guanchen; Al-Abbasi, Omar; von Spakovsky, Michael R.

    2014-10-01

    This paper outlines an atomistic-level framework for modeling the non-equilibrium behavior of chemically reactive systems. The framework called steepest- entropy-ascent quantum thermodynamics (SEA-QT) is based on the paradigm of intrinsic quantum thermodynamic (IQT), which is a theory that unifies quantum mechanics and thermodynamics into a single discipline with wide applications to the study of non-equilibrium phenomena at the atomistic level. SEA-QT is a novel approach for describing the state of chemically reactive systems as well as the kinetic and dynamic features of the reaction process without any assumptions of near-equilibrium states or weak-interactions with a reservoir or bath. Entropy generation is the basis of the dissipation which takes place internal to the system and is, thus, the driving force of the chemical reaction(s). The SEA-QT non-equilibrium model is able to provide detailed information during the reaction process, providing a picture of the changes occurring in key thermodynamic properties (e.g., the instantaneous species concentrations, entropy and entropy generation, reaction coordinate, chemical affinities, reaction rate, etc). As an illustration, the SEA-QT framework is applied to an atomistic-level chemically reactive system governed by the reaction mechanism F + H2 leftrightarrow FH + H.

  14. Competition between Homophily and Information Entropy Maximization in Social Networks

    PubMed Central

    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

  15. Competition between Homophily and Information Entropy Maximization in Social Networks.

    PubMed

    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.

  16. Information entropy analysis of leopard seal vocalization bouts

    NASA Astrophysics Data System (ADS)

    Buck, John R.; Rogers, Tracey L.; Cato, Douglas H.

    2004-05-01

    Leopard seals (Hydrurga leptonyx) are solitary pinnipeds who are vocally active during their brief breeding season. The seals produce vocal bouts consisting of a sequence of distinct sounds, with an average length of roughly ten sounds. The sequential structure of the bouts is thought to be individually distinctive. Bouts recorded from five leopard seals during 1992-1994 were analyzed using information theory. The first-order Markov model entropy estimates were substantially smaller than the independent, identically distributed model entropy estimates for all five seals, indicative of constraints on the sequential structure of each seal's bouts. Each bout in the data set was classified using maximum-likelihood estimates from the first-order Markov model for each seal. This technique correctly classified 85% of the bouts, comparable to results in Rogers and Cato [Behaviour (2002)]. The relative entropies between the Markov models were found to be infinite in 18/20 possible cross-comparisons, indicating there is no probability of misclassifying the bouts in these 18 comparisons in the limit of long data sequences. One seal has sufficient data to compare a nonparametric entropy estimate with the Markov entropy estimate, finding only a small difference. This suggests that the first-order Markov model captures almost all the sequential structure in this seal's bouts.

  17. 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.

  18. Shannon information entropy in the canonical genetic code.

    PubMed

    Nemzer, Louis R

    2017-02-21

    The Shannon entropy measures the expected information value of messages. As with thermodynamic entropy, the Shannon entropy is only defined within a system that identifies at the outset the collections of possible messages, analogous to microstates, that will be considered indistinguishable macrostates. This fundamental insight is applied here for the first time to amino acid alphabets, which group the twenty common amino acids into families based on chemical and physical similarities. To evaluate these schemas objectively, a novel quantitative method is introduced based the inherent redundancy in the canonical genetic code. Each alphabet is taken as a separate system that partitions the 64 possible RNA codons, the microstates, into families, the macrostates. By calculating the normalized mutual information, which measures the reduction in Shannon entropy, conveyed by single nucleotide messages, groupings that best leverage this aspect of fault tolerance in the code are identified. The relative importance of properties related to protein folding - like hydropathy and size - and function, including side-chain acidity, can also be estimated. This approach allows the quantification of the average information value of nucleotide positions, which can shed light on the coevolution of the canonical genetic code with the tRNA-protein translation mechanism. Copyright © 2016 Elsevier Ltd. All rights reserved.

  19. Information and Entropy Flow in the Kalman?Bucy Filter

    NASA Astrophysics Data System (ADS)

    Mitter, Sanjoy K.; Newton, Nigel J.

    2005-01-01

    We investigate the information theoretic properties of Kalman-Bucy filters in continuous time, developing notions of information supply, storage and dissipation. Introducing a concept of energy, we develop a physical analogy in which the unobserved signal describes a statistical mechanical system interacting with a heat bath. The abstract `universe' comprising the signal and the heat bath obeys a non-increase law of entropy; however, with the introduction of partial observations, this law can be violated. The Kalman-Bucy filter behaves like a Maxwellian demon in this analogy, returning signal energy to the heat bath without causing entropy increase. This is made possible by the steady supply of new information. In a second analogy the signal and filter interact, setting up a stationary non-equilibrium state, in which energy flows between the heat bath, the signal and the filter without causing any overall entropy increase. We introduce a rate of interactive entropy flow that isolates the statistical mechanics of this flow from marginal effects. Both analogies provide quantitative examples of Landauer's Principle.

  20. Quantum information of cosmological correlations

    NASA Astrophysics Data System (ADS)

    Lim, Eugene A.

    2015-04-01

    It has been shown that the primordial perturbations sourced by inflation are driven to classicality by unitary evolution alone. However, their coupling with the environment such as photons and subsequent decoherence renders the cosmological correlations quantum, losing primordial information in the process. We argue that the quantumness of the resulting cosmological correlations is given by quantum discord, which captures nonclassical behavior beyond quantum entanglement. By considering the environment as a quantum channel in which primordial information contained in the perturbations is transmitted to us, we can then ask how much of this information is inaccessible. We show that this amount of information is given by the discord of the joint primordial perturbations-environment system. To illustrate these points, we model the joint system as a mixed bimodal Gaussian state, and show that quantum discord is dependent on the basis which decoherence occurs.

  1. 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.

  2. Eigen solutions, Shannon entropy and fisher information under the Eckart Manning Rosen potential model

    NASA Astrophysics Data System (ADS)

    Onate, C. A.; Onyeaju, M. C.; Ikot, A. N.; Idiodi, J. O. A.; Ojonubah, J. O.

    2017-02-01

    We solved the Schrödinger equation with a certain approximation to the centrifugal term for an arbitrary angular momentum state with the Eckart Manning Rosen potential. The bound-state energy eigenvalues and the corresponding wave functions have been approximately obtained using the parametric Nikiforov Uvarov method. The solutions of the Schrödinger equation for the Eckart potential, Manning Rosen potential, and Hulthén potential have been obtained using a certain transformation. The concepts of the Shannon entropy and the Fisher information of a system under the Eckart Manning Rosen potential are investigated in detail. The behavior of the screening parameter and the quantum number n for Fisher information and the Shannon entropy are also investigated.

  3. Quantum Information: Opportunities and Challenges

    SciTech Connect

    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.

  4. Information entropy of a time-dependent three-level trapped ion interacting with a laser field

    NASA Astrophysics Data System (ADS)

    Abdel-Aty, Mahmoud

    2005-10-01

    Trapped and laser-cooled ions are increasingly used for a variety of modern high-precision experiments, frequency standard applications and quantum information processing. Therefore, in this communication we present a comprehensive analysis of the pattern of information entropy arising in the time evolution of an ion interacting with a laser field. A general analytic approach is proposed for a three-level trapped-ion system in the presence of the time-dependent couplings. By working out an exact analytic solution, we conclusively analyse the general properties of the von Neumann entropy and quantum information entropy. It is shown that the information entropy is affected strongly by the time-dependent coupling and exhibits long time periodic oscillations. This feature attributed to the fact that in the time-dependent region Rabi oscillation is time dependent. Using parameters corresponding to a specific three-level ionic system, a single beryllium ion in a RF-(Paul) trap, we obtain illustrative examples of some novel aspects of this system in the dynamical evolution. Our results establish an explicit relation between the exact information entropy and the entanglement between the multi-level ion and the laser field. We show that different nonclassical effects arise in the dynamics of the ionic population inversion, depending on the initial states of the vibrational motion/field and on the values of Lamb-Dicke parameter η.

  5. Husimi-Wehrl entropy in the quantum chaotic system -An efficient calculational method-

    NASA Astrophysics Data System (ADS)

    Tsukiji, Hidekazu; Iida, Hideaki; Kunihiro, Teiji; Ohnishi, Akira

    2014-09-01

    Early thermalization in heavy ion collisions still remains a theoretical challenge. It was suggested in the hydrodynamical analyses of the relativistic heavy-ion collisions at RHIC and later at LHC. There are many proposals for pinning down the underlying mechanism for it. Quantum fluctuations on top of the classical configurations (glasma) are found to induce instabilities. It may trigger the chaotic behavior of the gauge field and eventually give rise to entropy production. In this work, we investigate thermalization of glasma by using the Husimi-Wehrl entropy. Quasi-distribution function defined in phase space should be useful to describe possible chaotic behavior of a quantum system. We adopt the Husimi distribution function to discuss entropy production of quantum systems. Husimi function is a minimally coarse-grained Wigner function and semi-positive definite. As a first stage of the study, we calculate the Husimi-Wehrl (H-W) entropy of a quantum Yang-Mills system [Tsai, Muller (2012)] with two-degrees of freedom. We propose a Monte-Carlo method to numerically calculate the time evolution of the Husimi function and the H-W entropy. We also discuss an extension of the method to quantum field theories.

  6. 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.

  7. Studies in quantum information theory

    NASA Astrophysics Data System (ADS)

    Menicucci, Nicolas C.

    Quantum information theory started as the backdrop for quantum computing and is often considered only in relation to this technology, which is still in its infancy. But quantum information theory is only partly about quantum computing. While much of the interest in this field is spurred by the possible use of quantum computers for code breaking using fast factoring algorithms, to a physicist interested in deeper issues, it presents an entirely new set of questions based on an entirely different way of looking at the quantum world. This thesis is an exploration of several topics in quantum information theory. But it is also more than this. This thesis explores the new paradigm brought about by quantum information theory---that of physics as the flow of information. The thesis consists of three main parts. The first part describes my work on continuous-variable cluster states, a new platform for quantum computation. This begins with background material discussing classical and quantum computation and emphasizing the physical underpinnings of each, followed by a discussion of two recent unorthodox models of quantum computation. These models are combined into an original proposal for quantum computation using continuous-variable cluster states, including a proposed optical implementation. These are followed by a mathematical result radically simplifying the optical construction. Subsequent work simplifies this connection even further and provides a constructive proposal for scalable generation of large-scale cluster states---necessary if there is to be any hope of using this method in practical quantum computation. Experimental implementation is currently underway by my collaborators at The University of Virginia. The second part describes my work related to the physics of trapped ions, starting with an overview of the basic theory of linear ion traps. Although ion traps are often discussed in terms of their potential use for quantum computation, my work looks at their

  8. 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.

  9. Quantum information with Rydberg atoms

    SciTech Connect

    Saffman, M.; Walker, T. G.; Moelmer, K.

    2010-07-15

    Rydberg atoms with principal quantum number n>>1 have exaggerated atomic properties including dipole-dipole interactions that scale as n{sup 4} and radiative lifetimes that scale as n{sup 3}. It was proposed a decade ago to take advantage of these properties to implement quantum gates between neutral atom qubits. The availability of a strong long-range interaction that can be coherently turned on and off is an enabling resource for a wide range of quantum information tasks stretching far beyond the original gate proposal. Rydberg enabled capabilities include long-range two-qubit gates, collective encoding of multiqubit registers, implementation of robust light-atom quantum interfaces, and the potential for simulating quantum many-body physics. The advances of the last decade are reviewed, covering both theoretical and experimental aspects of Rydberg-mediated quantum information processing.

  10. Quantum mutual information along unitary orbits

    NASA Astrophysics Data System (ADS)

    Jevtic, Sania; Jennings, David; Rudolph, Terry

    2012-05-01

    Motivated by thermodynamic considerations, we analyze the variation of the quantum mutual information on a unitary orbit of a bipartite system's state with and without global constraints such as energy conservation. We solve the full optimization problem for the smallest system of two qubits and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward for equal-sized subsystems, however their minimization displays nontrivial structures. We characterize a set of separable states in which the minimally correlated state resides: a collection of classically correlated states admitting a particular “Young tableau” form. Furthermore, a partial order exists on this set with respect to individual marginal entropies, and the presence of a “see-saw effect” for these entropies forces a finer analysis to determine the optimal tableau.

  11. Preservation of a quantum Rényi relative entropy implies existence of a recovery map

    NASA Astrophysics Data System (ADS)

    Jenčová, Anna

    2017-02-01

    It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched Rényi relative α-entropy with α >1 is also equivalent to this property. For the proof, we use an interpolating family of L p -norms with respect to a state.

  12. Local Stereo Matching Based on Information Entropy of Image

    NASA Astrophysics Data System (ADS)

    Geng, Yingnan

    2016-09-01

    Adaptive support-window algorithm is one of the simplest local algorithms for stereo matching. An important problem for adaptive support-window algorithm is to determine the appropriate support-window size, which is always hard to do and limits the validity of adaptive support-window algorithm. An appropriate support-window size must be selected adaptively based on image features. In this paper, information entropy of image is defined for stereo matching in the RGB vector space. Based on adaptive support-window, a new support-window selection algorithm, which uses information entropy of image to quantify image features such as illumination color and number of object contained in an image, is proposed. Experimental results evaluated on the Middlebury stereo benchmark show that our algorithm outperforms the conventional adaptive support-window algorithms.

  13. Rigorous bounds to information entropies for atomic systems

    NASA Astrophysics Data System (ADS)

    Tao, Jianmin; Li, Guobao; Li, Jianmin

    1997-09-01

    Rigorous bounds to atomic information entropies and their sum in position and momentum spaces have been derived in terms of radial and momentum expectation values langrnrang and langpnrang. Numerical studies on atomic systems show that the bounds presented in terms of langrrang and langprang, the first moments of the position and momentum - space densities are sharper than those given by Gadre and Bendale in terms of langr2rang and langp2rang, the second moments of the position and momentum-space densities. Within the BKCM procedure, several relationships between the information entropies and the average electron densities langρrang and langγrang in position and momentum spaces have been established.

  14. Quantum Information Theory - an Invitation

    NASA Astrophysics Data System (ADS)

    Werner, Reinhard F.

    Quantum information and quantum computers have received a lot of public attention recently. Quantum computers have been advertised as a kind of warp drive for computing, and indeed the promise of the algorithms of Shor and Grover is to perform computations which are extremely hard or even provably impossible on any merely ``classical'' computer.In this article I shall give an account of the basic concepts of quantum information theory is given, staying as much as possible in the area of general agreement.The article is divided into two parts. The first (up to the end of Sect. 2.5) is mostly in plain English, centered around the exploration of what can or cannot be done with quantum systems as information carriers. The second part, Sect. 2.6, then gives a description of the mathematical structures and of some of the tools needed to develop the theory.

  15. Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations.

    PubMed

    Inglis, Stephen; Melko, Roger G

    2013-01-01

    We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.

  16. The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems

    NASA Astrophysics Data System (ADS)

    Amigó, José M.; Kennel, Matthew B.; Kocarev, Ljupco

    2005-10-01

    Permutation entropy quantifies the diversity of possible orderings of the values a random or deterministic system can take, as Shannon entropy quantifies the diversity of values. We show that the metric and permutation entropy rates-measures of new disorder per new observed value-are equal for ergodic finite-alphabet information sources (discrete-time stationary stochastic processes). With this result, we then prove that the same holds for deterministic dynamical systems defined by ergodic maps on n-dimensional intervals. This result generalizes a previous one for piecewise monotone interval maps on the real line [C. Bandt, G. Keller, B. Pompe, Entropy of interval maps via permutations, Nonlinearity 15 (2002) 1595-1602.] at the expense of requiring ergodicity and using a definition of permutation entropy rate differing modestly in the order of two limits. The case of non-ergodic finite-alphabet sources is also studied and an inequality developed. Finally, the equality of permutation and metric entropy rates is extended to ergodic non-discrete information sources when entropy is replaced by differential entropy in the usual way.

  17. 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.

  18. 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.

  19. Maximum information entropy: a foundation for ecological theory.

    PubMed

    Harte, John; Newman, Erica A

    2014-07-01

    The maximum information entropy (MaxEnt) principle is a successful method of statistical inference that has recently been applied to ecology. Here, we show how MaxEnt can accurately predict patterns such as species-area relationships (SARs) and abundance distributions in macroecology and be a foundation for ecological theory. We discuss the conceptual foundation of the principle, why it often produces accurate predictions of probability distributions in science despite not incorporating explicit mechanisms, and how mismatches between predictions and data can shed light on driving mechanisms in ecology. We also review possible future extensions of the maximum entropy theory of ecology (METE), a potentially important foundation for future developments in ecological theory. Copyright © 2014 Elsevier Ltd. All rights reserved.

  20. Quantum communication and information processing

    NASA Astrophysics Data System (ADS)

    Beals, Travis Roland

    Quantum computers enable dramatically more efficient algorithms for solving certain classes of computational problems, but, in doing so, they create new problems. In particular, Shor's Algorithm allows for efficient cryptanalysis of many public-key cryptosystems. As public key cryptography is a critical component of present-day electronic commerce, it is crucial that a working, secure replacement be found. Quantum key distribution (QKD), first developed by C.H. Bennett and G. Brassard, offers a partial solution, but many challenges remain, both in terms of hardware limitations and in designing cryptographic protocols for a viable large-scale quantum communication infrastructure. In Part I, I investigate optical lattice-based approaches to quantum information processing. I look at details of a proposal for an optical lattice-based quantum computer, which could potentially be used for both quantum communications and for more sophisticated quantum information processing. In Part III, I propose a method for converting and storing photonic quantum bits in the internal state of periodically-spaced neutral atoms by generating and manipulating a photonic band gap and associated defect states. In Part II, I present a cryptographic protocol which allows for the extension of present-day QKD networks over much longer distances without the development of new hardware. I also present a second, related protocol which effectively solves the authentication problem faced by a large QKD network, thus making QKD a viable, information-theoretic secure replacement for public key cryptosystems.

  1. Tight informationally complete quantum measurements

    NASA Astrophysics Data System (ADS)

    Scott, A. J.

    2006-10-01

    We introduce a class of informationally complete positive-operator-valued measures which are, in analogy with a tight frame, 'as close as possible' to orthonormal bases for the space of quantum states. These measures are distinguished by an exceptionally simple state-reconstruction formula which allows 'painless' quantum state tomography. Complete sets of mutually unbiased bases and symmetric informationally complete positive-operator-valued measures are both members of this class, the latter being the unique minimal rank-one members. Recast as ensembles of pure quantum states, the rank-one members are in fact equivalent to weighted 2-designs in complex projective space. These measures are shown to be optimal for quantum cloning and linear quantum state tomography.

  2. Quantum entropies in extreme dilaton black hole backgrounds

    NASA Astrophysics Data System (ADS)

    Wei, Yi-Huan; Wang, Yongcheng; Zhao, Zheng

    2002-06-01

    For spinor fields, the entropies from the spin-1/2- and spin-1/2+ components, Sq-ext and Sq+ext, are quite different, though the former is 7/8 times the scalar entropy and the latter contains an extra term. The brick wall model is applicable to both NEBH and EBH. For the EDBH with 0≺a2≺1, using the brick wall model with the cutoff ɛ being given by ɛ(1- a2)/(1+a2)=(1+a2)κm2/ (1+a2) and κ the surface gravity on the event horizon, at the Hawking temperature TH=κ/2π, the scalar and spinor entropies are Sqext=S0/(1- a2)(1+a2)2 with S0=1/135 and SqFext=7/2Sqext+[1/6(1- a2)], respectively. For the EGHSDBH, the spin-1/2- and spin-1/2+ fields contribute the entropies Sq- ext=7/8Sqext, Sq+ext=7/8Sqext+(πm/6β) ln(L/ɛ), respectively; at the Hawking temperature, the spinor entropy is SqFext=(7/2+30)Sqext with Sqext=1/360 ln(L/ɛ).

  3. Measuring entanglement entropy of a generic many-body system with a quantum switch.

    PubMed

    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.

  4. Physics as quantum information processing

    NASA Astrophysics Data System (ADS)

    Mauro D'Ariano, Giacomo

    2011-10-01

    The experience from Quantum Information has lead us to look at Quantum Theory (QT) and the whole Physics from a different angle. The information-theoretical paradigm—It from Bit— prophesied by John Archibald Wheeler is relentlessly advancing. Recently it has been shown that QT is derivable from pure informational principles. The possibility that there is only QT at the foundations of Physics has been then considered, with space-time, Relativity, quantization rules and Quantum Field Theory (QFT) emerging from a quantum-information processing. The resulting theory is a discrete version of QFT with automatic relativistic invariance, and without fields, Hamiltonian, and quantization rules. In this paper I review some recent advances on these lines. In particular: i) How space-time and relativistic covariance emerge from the quantum computation; ii) The derivation of the Dirac equation as free information flow, without imposing Lorentz covariance; iii) the information-theoretical meaning of inertial mass and Planck constant; iv) An observable consequence of the theory: a mass-dependent refraction index of vacuum. I will then conclude with two possible routes to Quantum Gravity.

  5. 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.

  6. Skein theory and topological quantum registers: Braiding matrices and topological entanglement entropy of non-Abelian quantum Hall states

    SciTech Connect

    Hikami, Kazuhiro

    2008-07-15

    We study topological properties of quasi-particle states in the non-Abelian quantum Hall states. We apply a skein-theoretic method to the Read-Rezayi state whose effective theory is the SU(2){sub K} Chern-Simons theory. As a generalization of the Pfaffian (K = 2) and the Fibonacci (K = 3) anyon states, we compute the braiding matrices of quasi-particle states with arbitrary spins. Furthermore we propose a method to compute the entanglement entropy skein-theoretically. We find that the entanglement entropy has a nontrivial contribution called the topological entanglement entropy which depends on the quantum dimension of non-Abelian quasi-particle intertwining two subsystems.

  7. Min-entropy and quantum key distribution: Nonzero key rates for ''small'' numbers of signals

    SciTech Connect

    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.

  8. Updating Darwin: Information and entropy drive the evolution of life.

    PubMed

    Cohen, Irun R

    2016-01-01

    The evolution of species, according to Darwin, is driven by struggle - by competition between variant autonomous individuals for survival of the fittest and reproductive advantage; the outcome of this struggle for survival is natural selection. The Neo-Darwinians reframed natural selection in terms of DNA: inherited genotypes directly encode expressed phenotypes; a fit phenotype means a fit genotype - thus the evolution of species is the evolution of selfish, reproducing individual genotypes.              Four general characteristics of advanced forms of life are not easily explained by this Neo-Darwinian paradigm: 1) Dependence on cooperation rather than on struggle, manifested by the microbiome, ecosystems and altruism; 2) The pursuit of diversity rather than optimal fitness, manifested by sexual reproduction; 3) Life's investment in programmed death, rather then in open-ended survival; and 4) The acceleration of complexity, despite its intrinsic fragility.               Here I discuss two mechanisms that can resolve these paradoxical features; both mechanisms arise from viewing life as the evolution of information. Information has two inevitable outcomes; it increases by autocatalyis and it is destroyed by entropy. On the one hand, the autocalalysis of information inexorably drives the evolution of complexity, irrespective of its fragility. On the other hand, only those strategic arrangements that accommodate the destructive forces of entropy survive - cooperation, diversification, and programmed death result from the entropic selection of evolving species. Physical principles of information and entropy thus fashion the evolution of life.

  9. Updating Darwin: Information and entropy drive the evolution of life

    PubMed Central

    Cohen, Irun R.

    2016-01-01

    The evolution of species, according to Darwin, is driven by struggle – by competition between variant autonomous individuals for survival of the fittest and reproductive advantage; the outcome of this struggle for survival is natural selection. The Neo-Darwinians reframed natural selection in terms of DNA: inherited genotypes directly encode expressed phenotypes; a fit phenotype means a fit genotype – thus the evolution of species is the evolution of selfish, reproducing individual genotypes.              Four general characteristics of advanced forms of life are not easily explained by this Neo-Darwinian paradigm: 1) Dependence on cooperation rather than on struggle, manifested by the microbiome, ecosystems and altruism; 2) The pursuit of diversity rather than optimal fitness, manifested by sexual reproduction; 3) Life’s investment in programmed death, rather then in open-ended survival; and 4) The acceleration of complexity, despite its intrinsic fragility.               Here I discuss two mechanisms that can resolve these paradoxical features; both mechanisms arise from viewing life as the evolution of information. Information has two inevitable outcomes; it increases by autocatalyis and it is destroyed by entropy. On the one hand, the autocalalysis of information inexorably drives the evolution of complexity, irrespective of its fragility. On the other hand, only those strategic arrangements that accommodate the destructive forces of entropy survive – cooperation, diversification, and programmed death result from the entropic selection of evolving species. Physical principles of information and entropy thus fashion the evolution of life. PMID:28105315

  10. The minimum Rényi entropy output of a quantum channel is locally additive

    NASA Astrophysics Data System (ADS)

    Gour, Gilad; Kemp, Todd

    2017-06-01

    We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter α >1. While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for α =1), it is based on several new techniques that incorporate the multiplicative nature of ℓ _p-norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter α <1.

  11. The minimum Rényi entropy output of a quantum channel is locally additive

    NASA Astrophysics Data System (ADS)

    Gour, Gilad; Kemp, Todd

    2016-12-01

    We show that the minimum Rényi entropy output of a quantum channel is locally additive for Rényi parameter α >1 . While our work extends the results of Gour and Friedland (IEEE Trans. Inf. Theory 59(1):603, 2012) (in which local additivity was proven for α =1 ), it is based on several new techniques that incorporate the multiplicative nature of ℓ_p -norms, in contrast to the additivity property of the von-Neumann entropy. Our results demonstrate that the counterexamples to the Rényi additivity conjectures exhibit purely global effects of quantum channels. Interestingly, the approach presented here cannot be extended to Rényi entropies with parameter α <1.

  12. Relativistic Quantum Information Theory

    DTIC Science & Technology

    2007-11-20

    systems without reference to a time variable. (a) Papers published in peer-reviewed journals (N/A for none) R.M. Gingrich, A.J. Bergou, C. Adami...Williams, "Random matrix model of quantum computing". Phys. Rev. A 71 (2005) 052324. List of papers submitted or published that acknowledge ARO...support during this reporting period. List the papers , including journal references, in the following categories: (b) Papers published in non-peer

  13. Quantum Information Science: An Update

    NASA Astrophysics Data System (ADS)

    Kwek, L. C.; Zen, Freddy P.

    2016-08-01

    It is now roughly thirty years since the incipient ideas on quantum information science was concretely formalized. Over the last three decades, there has been much development in this field, and at least one technology, namely devices for quantum cryptography, is now commercialized. Yet, the holy grail of a workable quantum computing machine still lies faraway at the horizon. In any case, it took nearly several centuries before the vacuum tubes were invented after the first mechanical calculating were constructed, and several decades later, for the transistor to bring the current computer technology to fruition. In this review, we provide a short survey of the current development and progress in quantum information science. It clearly does not do justice to the amount of work in the past thirty years. Nevertheless, despite the modest attempt, this review hopes to induce younger researchers into this exciting field.

  14. Spectral Entropies as Information-Theoretic Tools for Complex Network Comparison

    NASA Astrophysics Data System (ADS)

    De Domenico, Manlio; Biamonte, Jacob

    2016-10-01

    Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Rényi q entropy, generalized Kullback-Leibler and Jensen-Shannon divergences, the latter allowing us to define a natural distance measure between complex networks. First, we show that by minimizing the Kullback-Leibler divergence between an observed network and a parametric network model, inference of model parameter(s) by means of maximum-likelihood estimation can be achieved and model selection can be performed with appropriate information criteria. Second, we show that the information-theoretic metric quantifies the distance between pairs of networks and we can use it, for instance, to cluster the layers of a multilayer system. By applying this framework to networks corresponding to sites of the human microbiome, we perform hierarchical cluster analysis and recover with high accuracy existing community-based associations. Our results imply that spectral-based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory.

  15. 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

  16. Coarse-graining with information theory and the relative entropy

    NASA Astrophysics Data System (ADS)

    Shell, M. Scott

    2013-03-01

    There remain many both fundamental and practical/methodological questions regarding how coarse-grained models should be developed. Are there theoretically intuitive and numerically robust strategies for turning small-scale all-atom simulations into coarse models suitable for large-scale modeling? How can we identify what atomic details are unnecessary and can be discarded? Are there systematic ways to detect emergent physics? Here we discuss a fundamentally new approach to this problem. We propose that a natural way of viewing the coarse-graining problem is in terms of information theory. A quantity called the relative entropy measures the information lost upon coarse graining and hence the (inverse) fitness of a particular coarse-grained model. Minimization of the relative entropy thus provides a sort-of universal variational principle for coarse-graining, and a way to ``automatically'' discover and generate coarse models of many systems. We show that this new approach enables us to develop very simple but surprisingly accurate models of water, hydrophobic interactions, self-assembling peptides, and proteins that enable new physical insights as well as simulations of large-scale interactions. We discuss both theoretical and numerical aspects of this approach, in particular highlighting a new coarse-graining algorithm that efficiently optimizes coarse-grained models with even thousands of free parameters. We also discuss how the relative entropy approach suggests novel strategies for predicting the errors of coarse models, for identifying relevant degrees of freedom to retain, and for understanding the relationships among other coarse-graining methodologies.

  17. Information Transfer During Quantum Measurement

    NASA Astrophysics Data System (ADS)

    Lashkari, Nima

    2004-03-01

    ``The progress in quantum measurement theory has increased the need for a physical theory of information transfer during quantum measurement. Using the RPI --Restricted Path Integrals- approach to quantum measurement, we discuss on equivalence of information transfer and measurement. It is possible to understand the nature of measurement process by working on the phenomenon of information transfer. I show that in contrary with today information theory, for a conscious observer the amount of information gained in a measurement is not an absolute amount but related to his or her previous knowledge of the system. The knowledge, the observer has about the history of the system interactions and entanglements with other systems. The more intelligent the observer is, the more information it gains in a measurement. This means that the difficulties in quantum measurement can have roots in consciousness -the intuitive belief of many physicists. And it directs our attention to work on a general theory of consciousness. At the end I will make a model for the amount of transferred information during an observation. ''

  18. Configurational Information as Potentially Negative Entropy: The Triple Helix Model

    NASA Astrophysics Data System (ADS)

    Leydesdorff, Loet

    2008-12-01

    Configurational information is generated when three or more sources of variance interact. The variations not only disturb each other relationally, but by selecting upon each other, they are also positioned in a configuration. A configuration can be stabilized and/or globalized. Different stabilizations can be considered as second-order variation, and globalization as a second-order selection. The positive manifestations and the negative selections operate upon one another by adding and reducing uncertainty, respectively. Reduction of uncertainty in a configuration can be measured in bits of information. The variables can also be considered as dimensions of the probabilistic entropy in the system(s) under study. The configurational information then provides us with a measure of synergy within a complex system. For example, the knowledge base of an economy can be considered as such a synergy in the otherwise virtual (that is, fourth) dimension of a regime

  19. Stability theorem of depolarizing channels for the minimal output quantum Rényi entropies

    NASA Astrophysics Data System (ADS)

    Bae, Eunok; Gour, Gilad; Lee, Soojoon; Park, Jeonghoon; Sanders, Barry C.

    2016-03-01

    The stability theorem of the depolarizing channel states that if a state is close to achieving the minimal/maximal output value of a certain quantity through the channel, then it must be close to an input state giving the minimal/maximal value. We show that the stability theorem of the depolarizing channel holds for the output quantum p-Rényi entropy for p≥slant 2 or p = 1, which is an extension of the known case p = 2. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum p-Rényi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate.

  20. Customized lifting multiwavelet packet information entropy for equipment condition identification

    NASA Astrophysics Data System (ADS)

    Chen, Jinglong; Zuo, Ming J.; Zi, Yanyang; He, Zhengjia; Yuan, Jing; Chen, Xuefeng

    2013-09-01

    Condition identification of mechanical equipment from vibration measurement data is significant to avoid economic loss caused by unscheduled breakdowns and catastrophic accidents. However, this task still faces challenges due to the complexity of equipment and the harsh environment. This paper provides a possibility for equipment condition identification by proposing a method called customized lifting multiwavelet packet information entropy. Benefiting from the properties of multi-resolution analysis and multiple wavelet basis functions, the multiwavelet method has advantages in characterizing non-stationary vibration signals. In order to realize the accurate detection and identification of the condition features, a customized lifting multiwavelet packet is constructed via a multiwavelet lifting scheme. Then the vibration signal from the mechanical equipment is processed by the customized lifting multiwavelet packet transform. The relative energy in each frequency band of the multiwavelet packet transform coefficients that equals a percentage of the whole signal energy is taken as the probability. The normalized information entropy is obtained based on the relative energy to describe the condition of a mechanical system. The proposed method is applied to the condition identification of a rolling mill and a demountable disk-drum aero-engine. The results support the feasibility of the proposed method in equipment condition identification.

  1. Catalytic Decoupling of Quantum Information.

    PubMed

    Majenz, Christian; Berta, Mario; Dupuis, Frédéric; Renner, Renato; Christandl, Matthias

    2017-02-24

    The decoupling technique is a fundamental tool in quantum information theory with applications ranging from thermodynamics to many-body physics and black hole radiation whereby a quantum system is decoupled from another one by discarding an appropriately chosen part of it. Here, we introduce catalytic decoupling, i.e., decoupling with the help of an independent system. Thereby, we remove a restriction on the standard decoupling notion and present a tight characterization in terms of the max-mutual information. The novel notion unifies various tasks and leads to a resource theory of decoupling.

  2. Application of different entropies to study of bound magnetopolaron in an asymmetric quantum dot

    NASA Astrophysics Data System (ADS)

    Khordad, R.; Sedehi, H. R. Rastegar

    2017-02-01

    An electron strongly coupled to the LO-phonon in an asymmetric quantum dot has been considered. The system has a central impurity and it is under electric and magnetic fields. The eigenenergies and eigenfunctions of the ground and the first-excited states of the electron have been calculated using the Pekar variational method. Entropy of the system for different values of Coulomb impurity parameter, electron-LO phonon coupling strength, dispersion coefficient and electric field have been studied. Two entropies, Shannon and Gaussian entropy have been employed. It is found that the entropy has the oscillatory periodic evolution as function of the time due to the confinement form. It is deduced that the entropies increase with enhancing Coulomb impurity parameter, electron-LO phonon coupling strength and dispersion coefficient. With increasing electron-LO phonon coupling strength, the entropies decrease. The control of the coherence of the system can be done with the modulation of the electric field, the Coulomb bound potential, dispersion coefficient and electron-LO phonon coupling strength.

  3. Application of different entropies to study of bound magnetopolaron in an asymmetric quantum dot

    NASA Astrophysics Data System (ADS)

    Khordad, R.; Sedehi, H. R. Rastegar

    2017-07-01

    An electron strongly coupled to the LO-phonon in an asymmetric quantum dot has been considered. The system has a central impurity and it is under electric and magnetic fields. The eigenenergies and eigenfunctions of the ground and the first-excited states of the electron have been calculated using the Pekar variational method. Entropy of the system for different values of Coulomb impurity parameter, electron-LO phonon coupling strength, dispersion coefficient and electric field have been studied. Two entropies, Shannon and Gaussian entropy have been employed. It is found that the entropy has the oscillatory periodic evolution as function of the time due to the confinement form. It is deduced that the entropies increase with enhancing Coulomb impurity parameter, electron-LO phonon coupling strength and dispersion coefficient. With increasing electron-LO phonon coupling strength, the entropies decrease. The control of the coherence of the system can be done with the modulation of the electric field, the Coulomb bound potential, dispersion coefficient and electron-LO phonon coupling strength.

  4. Entanglement entropy and topological order in resonating valence-bond quantum spin liquids

    NASA Astrophysics Data System (ADS)

    Wildeboer, Julia; Seidel, Alexander; Melko, Roger G.

    2017-03-01

    On the triangular and kagome lattices, short-ranged resonating valence-bond wave functions can be sampled without the sign problem using a recently developed Pfaffian Monte Carlo scheme. In this Rapid Communication, we study the Renyi entanglement entropy in these wave functions using a replica-trick method. Using various spatial bipartitions, including the Levin-Wen construction, our finite-size scaled Renyi entropy gives a topological contribution consistent with γ =ln(2 ) , as expected for a gapped Z2 quantum spin liquid. We prove that the mutual statistics is consistent with the toric code anyon model and rule out any other quasiparticle statistics such as the double semion model.

  5. 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

  6. 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.

  7. Thermodynamics of quantum information scrambling.

    PubMed

    Campisi, Michele; Goold, John

    2017-06-01

    Scrambling of quantum information can conveniently be quantified by so-called out-of-time-order correlators (OTOCs), i.e., correlators of the type 〈[W_{τ},V]^{†}[W_{τ},V]〉, whose measurements present a formidable experimental challenge. Here we report on a method for the measurement of OTOCs based on the so-called two-point measurement scheme developed in the field of nonequilibrium quantum thermodynamics. The scheme is of broader applicability than methods employed in current experiments and provides a clear-cut interpretation of quantum information scrambling in terms of nonequilibrium fluctuations of thermodynamic quantities, such as work and heat. Furthermore, we provide a numerical example on a spin chain which highlights the utility of our thermodynamic approach when understanding the differences between integrable and ergodic behaviors. We also discuss how the method can be used to extend the reach of current experiments.

  8. Efficient Quantum Information Processing via Quantum Compressions

    NASA Astrophysics Data System (ADS)

    Deng, Y.; Luo, M. X.; Ma, S. Y.

    2016-01-01

    Our purpose is to improve the quantum transmission efficiency and reduce the resource cost by quantum compressions. The lossless quantum compression is accomplished using invertible quantum transformations and applied to the quantum teleportation and the simultaneous transmission over quantum butterfly networks. New schemes can greatly reduce the entanglement cost, and partially solve transmission conflictions over common links. Moreover, the local compression scheme is useful for approximate entanglement creations from pre-shared entanglements. This special task has not been addressed because of the quantum no-cloning theorem. Our scheme depends on the local quantum compression and the bipartite entanglement transfer. Simulations show the success probability is greatly dependent of the minimal entanglement coefficient. These results may be useful in general quantum network communication.

  9. Universal corrections to the entanglement entropy in gapped quantum spin chains: A numerical study

    NASA Astrophysics Data System (ADS)

    Levi, Emanuele; Castro-Alvaredo, Olalla A.; Doyon, Benjamin

    2013-09-01

    We carry out a numerical study of the bipartite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the antiferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the SU(2)-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behavior of the entropy. We numerically confirm that in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to a modified Bessel function of the first kind, K0(2mr), where m is a mass scale (the inverse correlation length) and r the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted by J. L. Cardy, O. A. Castro-Alvaredo, and B. Doyon [J. Stat. Phys.JSTPBS0022-471510.1007/s10955-007-9422-x 130, 129 (2008)] and B. Doyon [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.102.031602 102, 031602 (2009)] for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behavior following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.

  10. 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.

  11. Correlations in quantum thermodynamics: Heat, work, and entropy production

    NASA Astrophysics Data System (ADS)

    Alipour, S.; Benatti, F.; Bakhshinezhad, F.; Afsary, M.; Marcantoni, S.; Rezakhani, A. T.

    2016-10-01

    We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain—but fairly general—conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples.

  12. Correlations in quantum thermodynamics: Heat, work, and entropy production.

    PubMed

    Alipour, S; Benatti, F; Bakhshinezhad, F; Afsary, M; Marcantoni, S; Rezakhani, A T

    2016-10-21

    We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain-but fairly general-conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples.

  13. Correlations in quantum thermodynamics: Heat, work, and entropy production

    PubMed Central

    Alipour, S.; Benatti, F.; Bakhshinezhad, F.; Afsary, M.; Marcantoni, S.; Rezakhani, A. T.

    2016-01-01

    We provide a characterization of energy in the form of exchanged heat and work between two interacting constituents of a closed, bipartite, correlated quantum system. By defining a binding energy we derive a consistent quantum formulation of the first law of thermodynamics, in which the role of correlations becomes evident, and this formulation reduces to the standard classical picture in relevant systems. We next discuss the emergence of the second law of thermodynamics under certain—but fairly general—conditions such as the Markovian assumption. We illustrate the role of correlations and interactions in thermodynamics through two examples. PMID:27767124

  14. Generalized information and entanglement entropy, gravitation and holography

    NASA Astrophysics Data System (ADS)

    Obregón, O.

    2015-06-01

    A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu-Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

  15. 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.

  16. The role of quantum memory in quantum information processing

    NASA Astrophysics Data System (ADS)

    Nemoto, Kae; Stephens, Ashley M.; Devitt, Simon J.; Harrison, Keith A.; Munro, William J.

    2013-09-01

    Until recently, it was believed that long-lived quantum memories were necessary for long-distance quantum communication. However, by using error-correction codes in an efficient way—specifically, by correcting for photon loss—it is possible to transmit quantum information over long distances without quantum memories. For quantum computation, recent architectures for topological quantum computation indicate that the simplest large-scale structure could be memory-less. While a quantum memory may no longer be an essential resource for quantum networks, it could nonetheless be a key device in the development of quantum information technology. However, it is still not clear what benefits a functioning device could bring to quantum information systems, largely due to a lack of detailed models. Recently we have developed a detailed model for a quantum network based on a simple device designed to act as a building block for a full system architecture. The device is based on an optical cavity containing a negatively charged nitrogen-vacancy center in diamond. This model naturally integrates quantum communication with computation, and using this model we can assess quantitatively the costs and benefits of quantum memories. With or without quantum memories, it is necessary for us to preserve quantum information for a long period of time in either communication or computation.

  17. Classification of flavonoid compounds by using entropy of information theory.

    PubMed

    Castellano, Gloria; González-Santander, Juan Luis; Lara, Ana; Torrens, Francisco

    2013-09-01

    A total of 74 flavonoid compounds are classified into a periodic table by using an algorithm based on the entropy of information theory. Seven features in hierarchical order are used to classify structurally the flavonoids. From these features, the first three mark the group or column, while the last four are used to indicate the row or period in a table of periodic classification. Those flavonoids in the same group and period are suggested to show maximum similarity in properties. Furthermore, those with only the same group will present moderate similarity. In this report, the flavonoid compounds in the table, whose experimental data in bioactivity and antioxidant properties have been previously published, are related.

  18. Quantum bound on the specific entropy in strongly coupled scalar field theory

    SciTech Connect

    Aparicio Alcalde, M.; Menezes, G.; Svaiter, N. F.

    2008-06-15

    We discuss the (g{sub 0}{phi}{sup p}){sub d} self-interacting scalar field theory, in the strong-coupling regime. We assume the presence of macroscopic boundaries confining the field in a hypercube of side L. We also consider that the system is in thermal equilibrium at temperature {beta}{sup -1}. For spatially bounded free fields, the Bekenstein bound states that the specific entropy satisfies the inequality (S/E)<2{pi}R, where R stands for the radius of the smallest sphere that circumscribes the system. Employing the strong-coupling perturbative expansion, we obtain the renormalized mean energy E and entropy S for the system up to the order (g{sub 0}){sup -(2/p)}, presenting an analytical proof that the specific entropy also satisfies in some situations a quantum bound. Defining {epsilon}{sub d}{sup (r)} as the renormalized zero-point energy for the free theory per unit length, the dimensionless quantity {xi}=({beta}/L) and h{sub 1}(d) and h{sub 2}(d) as positive analytic functions of d, for the case of high temperature, we get that the specific entropy satisfies (S/E)<2{pi}R(h{sub 1}(d)/h{sub 2}(d)){xi}. When considering the low-temperature behavior of the specific entropy, we have (S/E)<2{pi}R(h{sub 1}(d)/{epsilon}{sub d}{sup (r)}){xi}{sup 1-d}. Therefore the sign of the renormalized zero-point energy can invalidate this quantum bound. If the renormalized zero-point energy is a positive quantity, at intermediate temperatures and in the low-temperature limit, there is a quantum bound.

  19. Quantum key distribution with finite resources: Secret key rates via Renyi entropies

    SciTech Connect

    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.

  20. Black hole entropy in loop quantum gravity: The role of internal symmetries

    NASA Astrophysics Data System (ADS)

    Barbero G, J. Fernando

    2009-06-01

    I will discuss here the role of the internal symmetry group in the computations of black hole entropy in loop quantum gravity according to the standard prescription given by Domagala and Lewandowski [1]. In particular I will show how it is possible to take into account the possible choice of either SO(3) or SU(2) as the internal symmetry groups of general relativity in Loop Quantum Gravity and how this choice changes the combinatorial problem of counting the black hole degrees of freedom.

  1. Information Processing Using Quantum Probability

    NASA Astrophysics Data System (ADS)

    Behera, Laxmidhar

    2006-11-01

    This paper presents an information processing paradigm that introduces collective response of multiple agents (computational units) while the level of intelligence associated with the information processing has been increased manifold. It is shown that if the potential field of the Schroedinger wave equation is modulated using a self-organized learning scheme, then the probability density function associated with the stochastic data is transferred to the probability amplitude function which is the response of the Schroedinger wave equation. This approach illustrates that information processing of data with stochastic behavior can be efficiently done using quantum probability instead of classical probability. The proposed scheme has been demonstrated through two applications: denoising and adaptive control.

  2. Tsallis entropy and decoherence of CsI quantum pseudo dot qubit

    NASA Astrophysics Data System (ADS)

    Tiotsop, M.; Fotue, A. J.; Fotsin, H. B.; Fai, L. C.

    2017-05-01

    Polaron in CsI quantum pseudo dot under an electromagnetic field was considered, and the ground and first excited state energies were derived by employing the combining Pekar variational and unitary transformation methods. With the two-level system obtained, single qubit was envisioned and the decoherence was studied using non-extensive entropy (Tsallis entropy). Numerical results showed: (i) the increase (decrease) of the energy levels (period of oscillation) with the increase of chemical potential, the zero point of pseudo dot, cyclotron frequency, and transverse and longitudinal confinements; (ii) the Tsallis entropy evolved as a wave envelop that increase with the increase of non-extenxive parameter and with the increase of electric field strength, zero point of pseudo dot and cyclotron frequency the wave envelop evolve periodically with reduction of period; (iii) The transition probability increases from the boundary to the centre of the dot where it has its maximum value. It was also noted that the probability density oscillate with period T0 = ℏ / Δ Ε with the tunnelling of the chemical potential and zero point of the pseudo dot. These results are helpful in the control of decoherence in quantum systems and may also be useful for the design of quantum computers.

  3. Finding the quantum thermoelectric with maximal efficiency and minimal entropy production at given power output

    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.

  4. Lindbladian operators, von Neumann entropy and energy conservation in time-dependent quantum open systems

    NASA Astrophysics Data System (ADS)

    Ou, Congjie; Chamberlin, Ralph V.; Abe, Sumiyoshi

    2017-01-01

    The Lindblad equation is widely employed in studies of Markovian quantum open systems. Here, the following question is posed: in a quantum open system with a time-dependent Hamiltonian such as a subsystem in contact with the heat bath, what is the corresponding Lindblad equation for the quantum state that keeps the internal energy of the subsystem constant in time? This issue is of importance in realizing quasi-stationary states of open systems such as quantum circuits and batteries. As an illustrative example, the time-dependent harmonic oscillator is analyzed. It is shown that the Lindbladian operator is uniquely determined with the help of a Lie-algebraic structure, and the time derivative of the von Neumann entropy is shown to be nonnegative if the curvature of the harmonic potential monotonically decreases in time.

  5. Informational Entropy and Bridge Scour Estimation under Complex Hydraulic Scenarios

    NASA Astrophysics Data System (ADS)

    Pizarro, Alonso; Link, Oscar; Fiorentino, Mauro; Samela, Caterina; Manfreda, Salvatore

    2017-04-01

    Bridges are important for society because they allow social, cultural and economic connectivity. Flood events can compromise the safety of bridge piers up to the complete collapse. The Bridge Scour phenomena has been described by empirical formulae deduced from hydraulic laboratory experiments. The range of applicability of such models is restricted by the specific hydraulic conditions or flume geometry used for their derivation (e.g., water depth, mean flow velocity, pier diameter and sediment properties). We seek to identify a general formulation able to capture the main dynamic of the process in order to cover a wide range of hydraulic and geometric configuration, allowing to extend our analysis in different contexts. Therefore, exploiting the Principle of Maximum Entropy (POME) and applying it on the recently proposed dimensionless Effective flow work, W*, we derived a simple model characterized by only one parameter. The proposed Bridge Scour Entropic (BRISENT) model shows good performances under complex hydraulic conditions as well as under steady-state flow. Moreover, the model was able to capture the evolution of scour in several hydraulic configurations even if the model contains only one parameter. Furthermore, results show that the model parameter is controlled by the geometric configurations of the experiment. This offers a possible strategy to obtain a priori model parameter calibration. The BRISENT model represents a good candidate for estimating the time-dependent scour depth under complex hydraulic scenarios. The authors are keen to apply this idea for describing the scour behavior during a real flood event. Keywords: Informational entropy, Sediment transport, Bridge pier scour, Effective flow work.

  6. Mathematical philology: entropy information in refining classical texts' reconstruction, and early philologists' anticipation of information theory.

    PubMed

    Cisne, John L; Ziomkowski, Robert M; Schwager, Steven J

    2010-01-13

    Philologists reconstructing ancient texts from variously miscopied manuscripts anticipated information theorists by centuries in conceptualizing information in terms of probability. An example is the editorial principle difficilior lectio potior (DLP): in choosing between otherwise acceptable alternative wordings in different manuscripts, "the more difficult reading [is] preferable." As philologists at least as early as Erasmus observed (and as information theory's version of the second law of thermodynamics would predict), scribal errors tend to replace less frequent and hence entropically more information-rich wordings with more frequent ones. Without measurements, it has been unclear how effectively DLP has been used in the reconstruction of texts, and how effectively it could be used. We analyze a case history of acknowledged editorial excellence that mimics an experiment: the reconstruction of Lucretius's De Rerum Natura, beginning with Lachmann's landmark 1850 edition based on the two oldest manuscripts then known. Treating words as characters in a code, and taking the occurrence frequencies of words from a current, more broadly based edition, we calculate the difference in entropy information between Lachmann's 756 pairs of grammatically acceptable alternatives. His choices average 0.26+/-0.20 bits higher in entropy information (95% confidence interval, P = 0.005), as against the single bit that determines the outcome of a coin toss, and the average 2.16+/-0.10 bits (95%) of (predominantly meaningless) entropy information if the rarer word had always been chosen. As a channel width, 0.26+/-0.20 bits/word corresponds to a 0.790.79(+0.09) (-0.15) likelihood of the rarer word being the one accepted in the reference edition, which is consistent with the observed 547/756 = 0.72+/-0.03 (95%). Statistically informed application of DLP can recover substantial amounts of semantically meaningful entropy information from noise; hence the extension copiosior

  7. Transfer entropy coefficient: Quantifying level of information flow between financial time series

    NASA Astrophysics Data System (ADS)

    Teng, Yue; Shang, Pengjian

    2017-03-01

    In this paper, a new coefficient is proposed with the objective of quantifying the level of information flow between financial time series. This transfer entropy coefficient, which provides an assessment on the multiscale information flow between measurements, is defined in terms of the transfer entropy method and the multiscale method. The implementation of this transfer entropy coefficient is illustrated with simulated time series and financial time series. Examples taken from simulated and financial data demonstrate that the dynamic mechanism of a complex system cannot be detected solely on the basis of transfer entropy of single scale.

  8. How much a quantum measurement is informative?

    SciTech Connect

    Dall'Arno, Michele; D'Ariano, Giacomo Mauro; Sacchi, Massimiliano F.

    2014-12-04

    The informational power of a quantum measurement is the maximum amount of classical information that the measurement can extract from any ensemble of quantum states. We discuss its main properties. Informational power is an additive quantity, being equivalent to the classical capacity of a quantum-classical channel. The informational power of a quantum measurement is the maximum of the accessible information of a quantum ensemble that depends on the measurement. We present some examples where the symmetry of the measurement allows to analytically derive its informational power.

  9. The Role of the Total Entropy Production in the Dynamics of Open Quantum Systems in Detection of Non-Markovianity

    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.

  10. 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.

  11. Local, nonlocal quantumness and information theoretic measures

    NASA Astrophysics Data System (ADS)

    Agrawal, Pankaj; Sazim, Sk; Chakrabarty, Indranil; Pati, Arun K.

    2016-08-01

    It has been suggested that there may exist quantum correlations that go beyond entanglement. The existence of such correlations can be revealed by information theoretic quantities such as quantum discord, but not by the conventional measures of entanglement. We argue that a state displays quantumness, that can be of local and nonlocal origin. Information theoretic measures not only characterize the nonlocal quantumness, but also the local quantumness, such as the “local superposition”. This can be a reason, why such measures are nonzero, when there is no entanglement. We consider a generalized version of the Werner state to demonstrate the interplay of local quantumness, nonlocal quantumness and classical mixedness of a state.

  12. Quantum States as Objective Informational Bridges

    NASA Astrophysics Data System (ADS)

    Healey, Richard

    2017-02-01

    A quantum state represents neither properties of a physical system nor anyone's knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations (its backing conditions), an agent may assign a quantum state to form expectations about other possible physical situations (its advice conditions). Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere.

  13. Enhancing quantum coherence and quantum Fisher information by quantum partially collapsing measurements

    NASA Astrophysics Data System (ADS)

    Liu, Zhi; Qiu, Liang; Pan, Fei

    2017-04-01

    We consider the enhancement effect of quantum partially collapsing measurements, i.e., weak measurement and quantum measurement reversal, on quantum coherence and quantum Fisher information, both of which are transmitted through a spin-chain channel. For the state parameter lying in the region (π /2, π ), weak measurement can enhance quantum coherence and quantum Fisher information. For the state parameter lying in the region (0, π /2), quantum coherence and quantum Fisher information can be enhanced by quantum measurement reversal combined with weak measurement. We assume the probabilistic nature of the method should be responsible for the enhancement.

  14. Use of information entropy measures of sitting postural sway to quantify developmental delay in infants.

    PubMed

    Deffeyes, Joan E; Harbourne, Regina T; DeJong, Stacey L; Kyvelidou, Anastasia; Stuberg, Wayne A; Stergiou, Nicholas

    2009-08-11

    By quantifying the information entropy of postural sway data, the complexity of the postural movement of different populations can be assessed, giving insight into pathologic motor control functioning. In this study, developmental delay of motor control function in infants was assessed by analysis of sitting postural sway data acquired from force plate center of pressure measurements. Two types of entropy measures were used: symbolic entropy, including a new asymmetric symbolic entropy measure, and approximate entropy, a more widely used entropy measure. For each method of analysis, parameters were adjusted to optimize the separation of the results from the infants with delayed development from infants with typical development. The method that gave the widest separation between the populations was the asymmetric symbolic entropy method, which we developed by modification of the symbolic entropy algorithm. The approximate entropy algorithm also performed well, using parameters optimized for the infant sitting data. The infants with delayed development were found to have less complex patterns of postural sway in the medial-lateral direction, and were found to have different left-right symmetry in their postural sway, as compared to typically developing infants. The results of this study indicate that optimization of the entropy algorithm for infant sitting postural sway data can greatly improve the ability to separate the infants with developmental delay from typically developing infants.

  15. Use of information entropy measures of sitting postural sway to quantify developmental delay in infants

    PubMed Central

    Deffeyes, Joan E; Harbourne, Regina T; DeJong, Stacey L; Kyvelidou, Anastasia; Stuberg, Wayne A; Stergiou, Nicholas

    2009-01-01

    Background By quantifying the information entropy of postural sway data, the complexity of the postural movement of different populations can be assessed, giving insight into pathologic motor control functioning. Methods In this study, developmental delay of motor control function in infants was assessed by analysis of sitting postural sway data acquired from force plate center of pressure measurements. Two types of entropy measures were used: symbolic entropy, including a new asymmetric symbolic entropy measure, and approximate entropy, a more widely used entropy measure. For each method of analysis, parameters were adjusted to optimize the separation of the results from the infants with delayed development from infants with typical development. Results The method that gave the widest separation between the populations was the asymmetric symbolic entropy method, which we developed by modification of the symbolic entropy algorithm. The approximate entropy algorithm also performed well, using parameters optimized for the infant sitting data. The infants with delayed development were found to have less complex patterns of postural sway in the medial-lateral direction, and were found to have different left-right symmetry in their postural sway, as compared to typically developing infants. Conclusion The results of this study indicate that optimization of the entropy algorithm for infant sitting postural sway data can greatly improve the ability to separate the infants with developmental delay from typically developing infants. PMID:19671183

  16. Informational basis of sensory adaptation: entropy and single-spike efficiency in rat barrel cortex.

    PubMed

    Adibi, Mehdi; Clifford, Colin W G; Arabzadeh, Ehsan

    2013-09-11

    We showed recently that exposure to whisker vibrations enhances coding efficiency in rat barrel cortex despite increasing correlations in variability (Adibi et al., 2013). Here, to understand how adaptation achieves this improvement in sensory representation, we decomposed the stimulus information carried in neuronal population activity into its fundamental components in the framework of information theory. In the context of sensory coding, these components are the entropy of the responses across the entire stimulus set (response entropy) and the entropy of the responses conditional on the stimulus (conditional response entropy). We found that adaptation decreased response entropy and conditional response entropy at both the level of single neurons and the pooled activity of neuronal populations. However, the net effect of adaptation was to increase the mutual information because the drop in the conditional entropy outweighed the drop in the response entropy. The information transmitted by a single spike also increased under adaptation. As population size increased, the information content of individual spikes declined but the relative improvement attributable to adaptation was maintained.

  17. Non-extensive entropy and properties of polaron in RbCl delta quantum dot under an applied electric field and Coulombic impurity

    NASA Astrophysics Data System (ADS)

    Tiotsop, M.; Fotue, A. J.; Fotsin, H. B.; Fai, L. C.

    2017-08-01

    Bound polaron in RbCl delta quantum dot under electric field and Coulombic impurity were considered. The ground and first excited state energy were derived by employing Pekar variational and unitary transformation methods. Applying Fermi golden rule, the expression of temperature and polaron lifetime were derived. The decoherence was studied trough the Tsallis entropy. Results shows that decreasing (or increasing) the lifetime increases (or decreases) the temperature and delta parameter (electric field strength and hydrogenic impurity). This suggests that to accelerate quantum transition in nanostructure, temperature and delta have to be enhanced. The improvement of electric field and coulomb parameter, increases the lifetime of the delta quantum dot qubit. Energy spectrum of polaron increases with increase in temperature, electric field strength, Coulomb parameter, delta parameter, and polaronic radius. The control of the delta quantum dot energies can be done via the electric field, coulomb impurity, and delta parameter. Results also show that the non-extensive entropy is an oscillatory function of time. With the enhancement of delta parameter, non-extensive parameter, Coulombic parameter, and electric field strength, the entropy has a sinusoidal increase behavior with time. With the study of decoherence through the Tsallis entropy, it may be advised that to have a quantum system with efficient transmission of information, the non-extensive and delta parameters need to be significant. The study of the probability density showed an increase from the boundary to the center of the dot where it has its maximum value and oscillates with period T0 = ℏ / ΔE with the tunneling of the delta parameter, electric field strength, and Coulombic parameter. The results may be very helpful in the transmission of information in nanostructures and control of decoherence

  18. Quantum Coherence Quantifiers Based on Rényi α-Relative Entropy

    NASA Astrophysics Data System (ADS)

    Shao, Lian-He; Li, Yong-Ming; Luo, Yu; Xi, Zheng-Jun

    2017-06-01

    The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity property for the coherence measures induced by the Rényi α-relative entropy, which present in [Phys. Rev. A 94 (2016) 052336]. We show that the Rényi α-relative entropy of coherence does not in general satisfy the monotonicity requirement under the subselection of measurements condition and it also does not satisfy the extension of monotonicity requirement, which presents in [Phys. Rev. A 93 (2016) 032136]. Due to the Rényi α-relative entropy of coherence can act as a coherence monotone quantifier, we examine the trade-off relations between coherence and mixedness. Finally, some properties for the single qubit of Rényi 2-relative entropy of coherence are derived. Supported by by National Natural Science Foundation of China under Grant Nos. 11271237, 11671244, 61671280, and the Higher School Doctoral Subject Foundation of Ministry of Education of China under Grant No. 20130202110001, and Fundamental Research Funds for the Central Universities (GK201502004 and 2016CBY003), and the Academic Leaders and Academic Backbones, Shaanxi Normal University under Grant No. 16QNGG013

  19. Does information entropy play a role in the expansion and acceleration of the Universe?

    NASA Astrophysics Data System (ADS)

    Pandey, Biswajit

    2017-10-01

    We propose an interpretation of the expansion and acceleration of the Universe from an information theoretic viewpoint. We obtain the time evolution of the configuration entropy of the mass distribution in a static Universe and show that the process of gravitational instability leads to a rapid dissipation of configuration entropy during the growth of the density fluctuations making such a Universe entropically unfavourable. We find that in an expanding Universe, the configuration entropy rate is governed by the expansion rate of the Universe and the growth rate of density fluctuations. The configuration entropy rate becomes smaller but still remains negative in a matter dominated Universe and eventually becomes zero at some future time in a $\\Lambda$ dominated Universe. The configuration entropy may have a connection to the dark energy and possibly plays a driving role in the current accelerating expansion of the Universe leading the Universe to its maximum entropy configuration.

  20. Information entropy to measure the spatial and temporal complexity of solute transport in heterogeneous porous media

    NASA Astrophysics Data System (ADS)

    Li, Weiyao; Huang, Guanhua; Xiong, Yunwu

    2016-04-01

    The complexity of the spatial structure of porous media, randomness of groundwater recharge and discharge (rainfall, runoff, etc.) has led to groundwater movement complexity, physical and chemical interaction between groundwater and porous media cause solute transport in the medium more complicated. An appropriate method to describe the complexity of features is essential when study on solute transport and conversion in porous media. Information entropy could measure uncertainty and disorder, therefore we attempted to investigate complexity, explore the contact between the information entropy and complexity of solute transport in heterogeneous porous media using information entropy theory. Based on Markov theory, two-dimensional stochastic field of hydraulic conductivity (K) was generated by transition probability. Flow and solute transport model were established under four conditions (instantaneous point source, continuous point source, instantaneous line source and continuous line source). The spatial and temporal complexity of solute transport process was characterized and evaluated using spatial moment and information entropy. Results indicated that the entropy increased as the increase of complexity of solute transport process. For the point source, the one-dimensional entropy of solute concentration increased at first and then decreased along X and Y directions. As time increased, entropy peak value basically unchanged, peak position migrated along the flow direction (X direction) and approximately coincided with the centroid position. With the increase of time, spatial variability and complexity of solute concentration increase, which result in the increases of the second-order spatial moment and the two-dimensional entropy. Information entropy of line source was higher than point source. Solute entropy obtained from continuous input was higher than instantaneous input. Due to the increase of average length of lithoface, media continuity increased, flow and

  1. One- and two-dimensional quantum models: Quenches and the scaling of irreversible entropy.

    PubMed

    Sharma, Shraddha; Dutta, Amit

    2015-08-01

    Using the scaling relation of the ground state quantum fidelity, we propose the most generic scaling relations of the irreversible work (the residual energy) of a closed quantum system at absolute zero temperature when one of the parameters of its Hamiltonian is suddenly changed. We consider two extreme limits: the heat susceptibility limit and the thermodynamic limit. It is argued that the irreversible entropy generated for a thermal quench at low enough temperatures when the system is initially in a Gibbs state is likely to show a similar scaling behavior. To illustrate this proposition, we consider zero-temperature and thermal quenches in one-dimensional (1D) and 2D Dirac Hamiltonians where the exact estimation of the irreversible work and the irreversible entropy is possible. Exploiting these exact results, we then establish the following. (i) The irreversible work at zero temperature shows an appropriate scaling in the thermodynamic limit. (ii) The scaling of the irreversible work in the 1D Dirac model at zero temperature shows logarithmic corrections to the scaling, which is a signature of a marginal situation. (iii) Remarkably, the logarithmic corrections do indeed appear in the scaling of the entropy generated if the temperature is low enough while they disappear for high temperatures. For the 2D model, no such logarithmic correction is found to appear.

  2. The g-theorem and quantum information theory

    NASA Astrophysics Data System (ADS)

    Casini, Horacio; Landea, Ignacio Salazar; Torroba, Gonzalo

    2016-10-01

    We study boundary renormalization group flows between boundary conformal field theories in 1 + 1 dimensions using methods of quantum information theory. We define an entropic g-function for theories with impurities in terms of the relative entanglement entropy, and we prove that this g-function decreases along boundary renormalization group flows. This entropic g-theorem is valid at zero temperature, and is independent from the g-theorem based on the thermal partition function. We also discuss the mutual information in boundary RG flows, and how it encodes the correlations between the impurity and bulk degrees of freedom. Our results provide a quantum-information understanding of (boundary) RG flow as increase of distinguishability between the UV fixed point and the theory along the RG flow.

  3. How can an autonomous quantum Maxwell demon harness correlated information?

    NASA Astrophysics Data System (ADS)

    Chapman, Adrian; Miyake, Akimasa; CQuIC Thermodynamics Team

    We study an autonomous quantum system, which exhibits refrigeration under an information-work tradeoff 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 thermodynamical 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. The work was supported in part by National Science Foundation Grants PHY-1212445 and PHY-1521016.

  4. Use of mutual information to decrease entropy: Implications for the second law of thermodynamics

    SciTech Connect

    Lloyd, S.

    1989-05-15

    Several theorems on the mechanics of gathering information are proved, and the possibility of violating the second law of thermodynamics by obtaining information is discussed in light of these theorems. Maxwell's demon can lower the entropy of his surroundings by an amount equal to the difference between the maximum entropy of his recording device and its initial entropy, without generating a compensating entropy increase. A demon with human-scale recording devices can reduce the entropy of a gas by a negligible amount only, but the proof of the demon's impracticability leaves open the possibility that systems highly correlated with their environment can reduce the environment's entropy by a substantial amount without increasing entropy elsewhere. In the event that a boundary condition for the universe requires it to be in a state of low entropy when small, the correlations induced between different particle modes during the expansion phase allow the modes to behave like Maxwell's demons during the contracting phase, reducing the entropy of the universe to a low value.

  5. Quantum gravity of Kerr-Schild spacetimes and the logarithmic correction to Schwarzschild black hole entropy

    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.

  6. Quantum information processing with atoms and photons.

    PubMed

    Monroe, C

    2002-03-14

    Quantum information processors exploit the quantum features of superposition and entanglement for applications not possible in classical devices, offering the potential for significant improvements in the communication and processing of information. Experimental realization of large-scale quantum information processors remains a long-term vision, as the required nearly pure quantum behaviour is observed only in exotic hardware such as individual laser-cooled atoms and isolated photons. But recent theoretical and experimental advances suggest that cold atoms and individual photons may lead the way towards bigger and better quantum information processors, effectively building mesoscopic versions of 'Schrödinger's cat' from the bottom up.

  7. From Minimum Entropy Production Principle To Minimum Information Loss With Elliptic Type Quasilinear PDEs

    NASA Astrophysics Data System (ADS)

    Kiss, Endre

    2004-04-01

    The Laplace equation does not contain any entropy production [27]. The entropy production can be illustrated with the Dirichlet Integral Principle and the quasilinear PDE of second order [28,27]. They can show the physical meaning too. The content of the quasilinear PDE leads to the probability density function of the process and the minimum principle of the entropy production [15,16,19,25]. The Maxwell's demon shows the connection between [18,26,21,20,22,23,24] thermodynamics and the theory of information. The negentropy principle of Brillouin [22] gives the important bridge between the thermodynamical problem of dissipation and the gain in information. The entropy compensation at an open stationary state shows the relation between negentropy principle [27] and minimum entropy principle and the connection to minimum information loss.

  8. Entropy is conserved in Hawking radiation as tunneling: A revisit of the black hole information loss paradox

    SciTech Connect

    Zhang Baocheng; Cai Qingyu; Zhan Mingsheng; You Li

    2011-02-15

    Research Highlights: > Information is found to be encoded and carried away by Hawking radiations. > Entropy is conserved in Hawking radiation. > We thus conclude no information is lost. > The dynamics of black hole may be unitary. - Abstract: We revisit in detail the paradox of black hole information loss due to Hawking radiation as tunneling. We compute the amount of information encoded in correlations among Hawking radiations for a variety of black holes, including the Schwarzchild black hole, the Reissner-Nordstroem black hole, the Kerr black hole, and the Kerr-Newman black hole. The special case of tunneling through a quantum horizon is also considered. Within a phenomenological treatment based on the accepted emission probability spectrum from a black hole, we find that information is leaked out hidden in the correlations of Hawking radiation. The recovery of this previously unaccounted for information helps to conserve the total entropy of a system composed of a black hole plus its radiations. We thus conclude, irrespective of the microscopic picture for black hole collapsing, the associated radiation process: Hawking radiation as tunneling, is consistent with unitarity as required by quantum mechanics.

  9. Dynamics of energy transport and entropy production in ac-driven quantum electron systems

    NASA Astrophysics Data System (ADS)

    Ludovico, María Florencia; Moskalets, Michael; Sánchez, David; Arrachea, Liliana

    2016-07-01

    We analyze the time-resolved energy transport and the entropy production in ac-driven quantum coherent electron systems coupled to multiple reservoirs at finite temperature. At slow driving, we formulate the first and second laws of thermodynamics valid at each instant of time. We identify heat fluxes flowing through the different pieces of the device and emphasize the importance of the energy stored in the contact and central regions for the second law of thermodynamics to be instantaneously satisfied. In addition, we discuss conservative and dissipative contributions to the heat flux and to the entropy production as a function of time. We illustrate these ideas with a simple model corresponding to a driven level coupled to two reservoirs with different chemical potentials.

  10. Quantum statistical vibrational entropy and enthalpy of formation of helium-vacancy complex in BCC W

    NASA Astrophysics Data System (ADS)

    Wen, Haohua; Woo, C. H.

    2016-12-01

    High-temperature advance-reactor design and operation require knowledge of in-reactor materials properties far from the thermal ground state. Temperature-dependence due to the effects of lattice vibrations is important to the understanding and formulation of atomic processes involved in irradiation-damage accumulation. In this paper, we concentrate on the formation of He-V complex. The free-energy change in this regard is derived via thermodynamic integration from the phase-space trajectories generated from MD simulations based on the quantum fluctuation-dissipation relation. The change of frequency distribution of vibration modes during the complex formation is properly accounted for, and the corresponding entropy change avoids the classical ln(T) divergence that violates the third law. The vibrational enthalpy and entropy of formation calculated this way have significant effects on the He kinetics during irradiation.

  11. A Free Object in Quantum Information Theory

    DTIC Science & Technology

    2010-01-01

    process of teleporting quantum information with a given entangled state. The third is purely a mathematical construction, the free affine monoid over the...Klein four group. We prove that all three of these objects are isomorphic. Keywords: Information Theory, Quantum Channel, Category, Teleportation ...information theoretic properties are easy to calculate. What are their higher dimensional analogues? (iv) If we attempt to teleport quantum information

  12. The microcanonical entropy of quantum isolated horizon, ‘quantum hair’ N and the Barbero-Immirzi parameter fixation

    NASA Astrophysics Data System (ADS)

    Majhi, Abhishek

    2014-05-01

    If the total number of punctures (N) of a quantum isolated horizon (QIH) is considered to be a macroscopic parameter alongside the Chern-Simons level (k) or equivalently classical area(Acl) a strict analysis of the microcanonical ensemble reveals that the microcanonical entropy has the form S_{MC}=A_{cl}/4\\ell _p^2+N\\sigma (\\gamma ), only for values of the Barbero-Immirzi (BI) parameter (γ) greater than a certain number. It is argued that the term Nσ(γ) must be negative definite, which leads to the bound on the BI parameter.

  13. Entanglement Entropy and Mutual Information Production Rates in Acoustic Black Holes

    SciTech Connect

    Giovanazzi, Stefano

    2011-01-07

    A method to investigate acoustic Hawking radiation is proposed, where entanglement entropy and mutual information are measured from the fluctuations of the number of particles. The rate of entropy radiated per one-dimensional (1D) channel is given by S={kappa}/12, where {kappa} is the sound acceleration on the sonic horizon. This entropy production is accompanied by a corresponding formation of mutual information to ensure the overall conservation of information. The predictions are confirmed using an ab initio analytical approach in transonic flows of 1D degenerate ideal Fermi fluids.

  14. Entanglement entropy and mutual information production rates in acoustic black holes.

    PubMed

    Giovanazzi, Stefano

    2011-01-07

    A method to investigate acoustic Hawking radiation is proposed, where entanglement entropy and mutual information are measured from the fluctuations of the number of particles. The rate of entropy radiated per one-dimensional (1D) channel is given by S=κ/12, where κ is the sound acceleration on the sonic horizon. This entropy production is accompanied by a corresponding formation of mutual information to ensure the overall conservation of information. The predictions are confirmed using an ab initio analytical approach in transonic flows of 1D degenerate ideal Fermi fluids.

  15. Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model

    NASA Astrophysics Data System (ADS)

    Dai, Yan-Wei; Cho, Sam Young; Batchelor, Murray T.; Zhou, Huan-Qiang

    2017-01-01

    The von Neumann entanglement entropy is used to estimate the critical point hc/J ≃0.143 (3 ) of the mixed ferro-antiferromagnetic three-state quantum Potts model H =∑i[J (XiXi+1 2+Xi2Xi +1) -h Ri] , where Xi and Ri are standard three-state Potts spin operators and J >0 is the antiferromagnetic coupling parameter. This critical point value gives improved estimates for two Kosterlitz-Thouless transition points in the antiferromagnetic (β <0 ) region of the Δ -β phase diagram of the three-state quantum chiral clock model, where Δ and β are, respectively, the chirality and coupling parameters in the clock model. These are the transition points βc≃-0.143 (3 ) at Δ =1/2 between incommensurate and commensurate phases and βc≃-7.0 (1 ) at Δ =0 between disordered and incommensurate phases. The von Neumann entropy is also used to calculate the central charge c of the underlying conformal field theory in the massless phase h ≤hc . The estimate c ≃1 in this phase is consistent with the known exact value at the particular point h /J =-1 corresponding to the purely antiferromagnetic three-state quantum Potts model. The algebraic decay of the Potts spin-spin correlation in the massless phase is used to estimate the continuously varying critical exponent η .

  16. Revisit emission spectrum and entropy quantum of the Reissner-Nordström black hole

    NASA Astrophysics Data System (ADS)

    Jiang, Qing-Quan

    2012-07-01

    Banerjee and Majhi's recent work shows that black hole's emission spectrum could be fully reproduced in the tunneling picture, where, as an intriguing technique, the Kruskal extension was introduced to connect the left and right modes inside and outside the horizon. Some attempt, as an extension, was focused on producing the Hawking emission spectrum of the (charged) Reissner-Nordström black hole in the Banerjee-Majhi treatment. Unfortunately, the Kruskal extension in their observation was so badly defined that the ingoing mode was classically forbidden traveling towards the center of black hole, but could quantum tunnel across the horizon with the probability \\varGamma=e^{-πω0/kappa+}. This tunneling picture is unphysical. With this point as a central motivation, in this paper we first introduce such a suitable Kruskal extension for the (charged) Reissner-Nordström black hole that a perfect tunneling picture can be provided during the charged particle's emission. Then, under the new Kruskal extension, we revisit the Hawking emission spectrum and entropy spectroscopy as tunneling from the charged black hole. The result shows that the tunneling method is so universally robust that the Hawking blackbody emission spectrum from a charged black hole can be well reproduced in the tunneling mechanism, and its induced entropy quantum is a much better approximation for the forthcoming quantum gravity theory.

  17. Mathematical Philology: Entropy Information in Refining Classical Texts' Reconstruction, and Early Philologists' Anticipation of Information Theory

    PubMed Central

    Cisne, John L.; Ziomkowski, Robert M.; Schwager, Steven J.

    2010-01-01

    Philologists reconstructing ancient texts from variously miscopied manuscripts anticipated information theorists by centuries in conceptualizing information in terms of probability. An example is the editorial principle difficilior lectio potior (DLP): in choosing between otherwise acceptable alternative wordings in different manuscripts, “the more difficult reading [is] preferable.” As philologists at least as early as Erasmus observed (and as information theory's version of the second law of thermodynamics would predict), scribal errors tend to replace less frequent and hence entropically more information-rich wordings with more frequent ones. Without measurements, it has been unclear how effectively DLP has been used in the reconstruction of texts, and how effectively it could be used. We analyze a case history of acknowledged editorial excellence that mimics an experiment: the reconstruction of Lucretius's De Rerum Natura, beginning with Lachmann's landmark 1850 edition based on the two oldest manuscripts then known. Treating words as characters in a code, and taking the occurrence frequencies of words from a current, more broadly based edition, we calculate the difference in entropy information between Lachmann's 756 pairs of grammatically acceptable alternatives. His choices average 0.26±0.20 bits higher in entropy information (95% confidence interval, P = 0.005), as against the single bit that determines the outcome of a coin toss, and the average 2.16±0.10 bits (95%) of (predominantly meaningless) entropy information if the rarer word had always been chosen. As a channel width, 0.26±0.20 bits/word corresponds to a 0.790.79+0.09−0.15 likelihood of the rarer word being the one accepted in the reference edition, which is consistent with the observed 547/756 = 0.72±0.03 (95%). Statistically informed application of DLP can recover substantial amounts of semantically meaningful entropy information from noise; hence the extension copiosior

  18. Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

    NASA Astrophysics Data System (ADS)

    Ito, Sosuke

    2016-11-01

    The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.

  19. Bipartite entanglement entropy in massive two-dimensional quantum field theory.

    PubMed

    Doyon, Benjamin

    2009-01-23

    Recently, Cardy, Castro Alvaredo, and the author obtained the first exponential correction to saturation of the bipartite entanglement entropy at large region lengths in massive two-dimensional integrable quantum field theory. It depends only on the particle content of the model, and not on the way particles scatter. Based on general analyticity arguments for form factors, we propose that this result is universal, and holds for any massive two-dimensional model (also out of integrability). We suggest a link of this result with counting pair creations far in the past.

  20. Teleportation as a depolarizing quantum channel, relative entropy, and classical capacity.

    PubMed

    Bowen, G; Bose, S

    2001-12-24

    We show that standard teleportation with an arbitrary mixed state resource is equivalent to a generalized depolarizing channel with probabilities given by the maximally entangled components of the resource. This enables the usage of any quantum channel as a generalized depolarizing channel without additional twirling operations. It also provides a nontrivial upper bound on the entanglement of a class of mixed states. Our result allows a consistent and statistically motivated quantification of teleportation success in terms of the relative entropy and this quantification can be related to a classical capacity.

  1. Amplification, Redundancy, and Quantum Chernoff Information

    NASA Astrophysics Data System (ADS)

    Zwolak, Michael; Riedel, C. Jess; Zurek, Wojciech H.

    2014-04-01

    Amplification was regarded, since the early days of quantum theory, as a mysterious ingredient that endows quantum microstates with macroscopic consequences, key to the "collapse of the wave packet," and a way to avoid embarrassing problems exemplified by Schrödinger's cat. Such a bridge between the quantum microworld and the classical world of our experience was postulated ad hoc in the Copenhagen interpretation. Quantum Darwinism views amplification as replication, in many copies, of the information about quantum states. We show that such amplification is a natural consequence of a broad class of models of decoherence, including the photon environment we use to obtain most of our information. This leads to objective reality via the presence of robust and widely accessible records of selected quantum states. The resulting redundancy (the number of copies deposited in the environment) follows from the quantum Chernoff information that quantifies the information transmitted by a typical elementary subsystem of the environment.

  2. Amplification, redundancy, and quantum Chernoff information.

    PubMed

    Zwolak, Michael; Riedel, C Jess; Zurek, Wojciech H

    2014-04-11

    Amplification was regarded, since the early days of quantum theory, as a mysterious ingredient that endows quantum microstates with macroscopic consequences, key to the "collapse of the wave packet," and a way to avoid embarrassing problems exemplified by Schrödinger's cat. Such a bridge between the quantum microworld and the classical world of our experience was postulated ad hoc in the Copenhagen interpretation. Quantum Darwinism views amplification as replication, in many copies, of the information about quantum states. We show that such amplification is a natural consequence of a broad class of models of decoherence, including the photon environment we use to obtain most of our information. This leads to objective reality via the presence of robust and widely accessible records of selected quantum states. The resulting redundancy (the number of copies deposited in the environment) follows from the quantum Chernoff information that quantifies the information transmitted by a typical elementary subsystem of the environment.

  3. Shock waves, increase of entropy and loss of information

    SciTech Connect

    Lax, P.D.

    1984-10-01

    We discuss, for the simplified model of a single conservation law, the concepts of genuine nonlinearity, breakdown of classical solutions, solutions in the distribution sense and their nonuniqueness, the viscosity method, finite difference methods, and the shock condition. We then discuss, for the scalar model, the compactness of solutions constructed by the viscosity and difference methods, and derive the entropy inequality for such solutions. We derive Glimm's estimate for the total variation of solutions of scalar equations that satisfy the shock condition, and show that a discontinuous solution that satisfies the shock condition also satisfies the entropy condition. Scattered remarks are given about the equations of compressible flow: the increase of entropy, some consequences of Carnot's theorem, and the equipartition of energy in the wake of strong shocks.

  4. Photonic qubits for remote quantum information processing

    NASA Astrophysics Data System (ADS)

    Maunz, P.; Olmschenk, S.; Hayes, D.; Matsukevich, D. N.; Duan, L.-M.; Monroe, C.

    2009-05-01

    Quantum information processing between remote quantum memories relies on a fast and faithful quantum channel. Recent experiments employed both, the photonic polarization and frequency qubits, in order to entangle remote atoms [1, 2], to teleport quantum information [3] and to operate a quantum gate between distant atoms. Here, we compare the dierent schemes used in these experiments and analyze the advantages of the dierent choices of atomic and photonic qubits and their coherence properties. [4pt] [1] D. L. Moehring et al. Nature 449, 68 (2007).[0pt] [2] D. N. Matsukevich et al. Phys. Rev. Lett. 100, 150404 2008).[0pt] [3] S. Olmschenk et al. Science, 323, 486 (2009).

  5. Mathematical and information-geometrical entropy for phenomenological Fourier and non-Fourier heat conduction

    NASA Astrophysics Data System (ADS)

    Li, Shu-Nan; Cao, Bing-Yang

    2017-09-01

    The second law of thermodynamics governs the direction of heat transport, which provides the foundational definition of thermodynamic Clausius entropy. The definitions of entropy are further generalized for the phenomenological heat transport models in the frameworks of classical irreversible thermodynamics and extended irreversible thermodynamics (EIT). In this work, entropic functions from mathematics are combined with phenomenological heat conduction models and connected to several information-geometrical conceptions. The long-time behaviors of these mathematical entropies exhibit a wide diversity and physical pictures in phenomenological heat conductions, including the tendency to thermal equilibrium, and exponential decay of nonequilibrium and asymptotics, which build a bridge between the macroscopic and microscopic modelings. In contrast with the EIT entropies, the mathematical entropies expressed in terms of the internal energy function can avoid singularity paired with nonpositive local absolute temperature caused by non-Fourier heat conduction models.

  6. Superadditivity of two quantum information resources

    PubMed Central

    Nawareg, Mohamed; Muhammad, Sadiq; Horodecki, Pawel; Bourennane, Mohamed

    2017-01-01

    Entanglement is one of the most puzzling features of quantum theory and a principal resource for quantum information processing. It is well known that in classical information theory, the addition of two classical information resources will not lead to any extra advantages. On the contrary, in quantum information, a spectacular phenomenon of the superadditivity of two quantum information resources emerges. It shows that quantum entanglement, which was completely absent in any of the two resources separately, emerges as a result of combining them together. We present the first experimental demonstration of this quantum phenomenon with two photonic three-partite nondistillable entangled states shared between three parties Alice, Bob, and Charlie, where the entanglement was completely absent between Bob and Charlie.

  7. Exponential decay of matrix Φ -entropies on Markov semigroups with applications to dynamical evolutions of quantum ensembles

    NASA Astrophysics Data System (ADS)

    Cheng, Hao-Chung; Hsieh, Min-Hsiu; Tomamichel, Marco

    2017-09-01

    In this work, we extend the theory of quantum Markov processes on a single quantum state to a broader theory that covers Markovian evolution of an ensemble of quantum states, which generalizes Lindblad's formulation of quantum dynamical semigroups. Our results establish the equivalence between an exponential decrease of the matrix Φ -entropies and the Φ -Sobolev inequalities, which allows us to characterize the dynamical evolution of a quantum ensemble to its equilibrium. In particular, we study the convergence rates of two special semigroups, namely, the depolarizing channel and the phase-damping channel. In the former, since there exists a unique equilibrium state, we show that the matrix Φ -entropy of the resulting quantum ensemble decays exponentially as time goes on. Consequently, we obtain a stronger notion of monotonicity of the Holevo quantity—the Holevo quantity of the quantum ensemble decays exponentially in time and the convergence rate is determined by the modified log-Sobolev inequalities. However, in the latter, the matrix Φ -entropy of the quantum ensemble that undergoes the phase-damping Markovian evolution generally will not decay exponentially. There is no classical analogy for these different equilibrium situations. Finally, we also study a statistical mixing of Markov semigroups on matrix-valued functions. We can explicitly calculate the convergence rate of a Markovian jump process defined on Boolean hypercubes and provide upper bounds to the mixing time.

  8. Information Theoretic Approach Based on Entropy for Classification of Bioacoustics Signals

    NASA Astrophysics Data System (ADS)

    Han, Ng Chee; Muniandy, Sithi V.; Dayou, Jedol; Mun, Ho Chong; Ahmad, Abdul Hamid; Dalimin, Mohd. Noh

    2010-07-01

    A new hybrid method for automated frog sound identification by incorporating entropy and spectral centroid concept is proposed. Entropy has important physical implications as the amount of "disorder" of a system. This study explores the use of various definitions of entropies such as the Shannon entropy, Kolmogorov-Rényi entropy and Tsallis entropy as measure of information contents or complexity for the purpose of the pattern recognition of bioacoustics signal. Each of these definitions of entropies characterizes different aspects of the signal. The entropies are combined with other standard pattern recognition tools such as the Fourier spectral analysis to form a hybrid spectral-entropic classification scheme. The efficiency of the system is tested using a database of sound syllables are obtained from a number of species of Microhylidae frogs. Nonparametric k-NN classifier is used to recognize the frog species based on the spectral-entropic features. The result showed that the k-NN classifier based on the selected features is able to identify the species of the frogs with relativity good accuracy compared to features relying on spectral contents alone. The robustness of the developed system is also tested for different noise levels.

  9. Quantum information, cognition, and music.

    PubMed

    Dalla Chiara, Maria L; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe

    2015-01-01

    Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music.

  10. Quantum information, cognition, and music

    PubMed Central

    Dalla Chiara, Maria L.; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe

    2015-01-01

    Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music. PMID:26539139

  11. Rényi entropy measure of noise-aided information transmission in a binary channel.

    PubMed

    Chapeau-Blondeau, François; Rousseau, David; Delahaies, Agnès

    2010-05-01

    This paper analyzes a binary channel by means of information measures based on the Rényi entropy. The analysis extends, and contains as a special case, the classic reference model of binary information transmission based on the Shannon entropy measure. The extended model is used to investigate further possibilities and properties of stochastic resonance or noise-aided information transmission. The results demonstrate that stochastic resonance occurs in the information channel and is registered by the Rényi entropy measures at any finite order, including the Shannon order. Furthermore, in definite conditions, when seeking the Rényi information measures that best exploit stochastic resonance, then nontrivial orders differing from the Shannon case usually emerge. In this way, through binary information transmission, stochastic resonance identifies optimal Rényi measures of information differing from the classic Shannon measure. A confrontation of the quantitative information measures with visual perception is also proposed in an experiment of noise-aided binary image transmission.

  12. Information Causality in the Quantum and Post-Quantum Regime

    PubMed Central

    Ringbauer, Martin; Fedrizzi, Alessandro; Berry, Dominic W.; White, Andrew G.

    2014-01-01

    Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles. PMID:25378182

  13. Information causality in the quantum and post-quantum regime.

    PubMed

    Ringbauer, Martin; Fedrizzi, Alessandro; Berry, Dominic W; White, Andrew G

    2014-11-07

    Quantum correlations can be stronger than anything achieved by classical systems, yet they are not reaching the limit imposed by relativity. The principle of information causality offers a possible explanation for why the world is quantum and why there appear to be no even stronger correlations. Generalizing the no-signaling condition it suggests that the amount of accessible information must not be larger than the amount of transmitted information. Here we study this principle experimentally in the classical, quantum and post-quantum regimes. We simulate correlations that are stronger than allowed by quantum mechanics by exploiting the effect of polarization-dependent loss in a photonic Bell-test experiment. Our method also applies to other fundamental principles and our results highlight the special importance of anisotropic regions of the no-signalling polytope in the study of fundamental principles.

  14. Photonic quantum information: science and technology.

    PubMed

    Takeuchi, Shigeki

    2016-01-01

    Recent technological progress in the generation, manipulation and detection of individual single photons has opened a new scientific field of photonic quantum information. This progress includes the realization of single photon switches, photonic quantum circuits with specific functions, and the application of novel photonic states to novel optical metrology beyond the limits of standard optics. In this review article, the recent developments and current status of photonic quantum information technology are overviewed based on the author's past and recent works.

  15. Quantum Fisher information, quantum entanglement and correlation close to quantum critical phenomena

    NASA Astrophysics Data System (ADS)

    Liu, Cheng-cheng; Wang, Dong; Sun, Wen-yang; Ye, Liu

    2017-09-01

    In this paper, we investigate the quantum Fisher information (QFI), quantum entanglement, quantum correlation and quantum phase transition (QPT) within the one-dimensional transverse Ising model by exploiting quantum renormalization-group method. The results show that quantum Fisher information, quantum entanglement, quantum correlation can evolve to two saturated values which exhibit QPT at the critical point after several iterations of the renormalization. Meanwhile, we find quantum entanglement or correlation can be detected perfectly by means of quantum Fisher information. Besides, it cannot capture any information about the system in the paramagnetic phase in view of quantum entanglement and correlation. Contrarily, it is evident the QFI is always nonzero even if the system is in the paramagnetic phase, i.e., the QFI can also be utilized as a highly favorable measure of quantum information in a broad of quantum spin systems. Furthermore, we disclose the nonanalytic and scaling behaviors of quantum Fisher information, which can be taken as a representation of quantum critical characterism.

  16. Spacetime replication of continuous variable quantum information

    NASA Astrophysics Data System (ADS)

    Hayden, Patrick; Nezami, Sepehr; Salton, Grant; Sanders, Barry C.

    2016-08-01

    The theory of relativity requires that no information travel faster than light, whereas the unitarity of quantum mechanics ensures that quantum information cannot be cloned. These conditions provide the basic constraints that appear in information replication tasks, which formalize aspects of the behavior of information in relativistic quantum mechanics. In this article, we provide continuous variable (CV) strategies for spacetime quantum information replication that are directly amenable to optical or mechanical implementation. We use a new class of homologically constructed CV quantum error correcting codes to provide efficient solutions for the general case of information replication. As compared to schemes encoding qubits, our CV solution requires half as many shares per encoded system. We also provide an optimized five-mode strategy for replicating quantum information in a particular configuration of four spacetime regions designed not to be reducible to previously performed experiments. For this optimized strategy, we provide detailed encoding and decoding procedures using standard optical apparatus and calculate the recovery fidelity when finite squeezing is used. As such we provide a scheme for experimentally realizing quantum information replication using quantum optics.

  17. The Holographic Entropy Cone

    SciTech Connect

    Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; Stoica, Bogdan; Sully, James; Walter, Michael

    2015-09-21

    We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phase space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.

  18. The Holographic Entropy Cone

    DOE PAGES

    Bao, Ning; Nezami, Sepehr; Ooguri, Hirosi; ...

    2015-09-21

    We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for generic quantum systems, where a complete set of entropy inequalities is not known for 4 or more regions. We also find an infinite new family of inequalities applicable to 5 or more regions. The set of all holographic entropy inequalities bounds the phasemore » space of Ryu-Takayanagi entropies, defining the holographic entropy cone. We characterize this entropy cone by reducing geometries to minimal graph models that encode the possible cutting and gluing relations of minimal surfaces. We find that, for a fixed number of regions, there are only finitely many independent entropy inequalities. To establish new holographic entropy inequalities, we introduce a combinatorial proof technique that may also be of independent interest in Riemannian geometry and graph theory.« less

  19. Information quantifiers, entropy squeezing and entanglement properties of superconducting qubit-deformed bosonic field system under dephasing effect

    NASA Astrophysics Data System (ADS)

    Berrada, K.; Al-Rajhi, M. A.

    2017-10-01

    In this paper, we present a detailed study on the evolution of some measures of nonclassicality and entanglement in the framework of the interaction between a superconducting qubit and deformed bosonic fields under decoherence effect. We compare the dynamical behavior of the different quantum quantifiers by exploiting a large set of nonlinear bosonic fields that are characterized by the deformation parameter. Additionally, we demonstrate how the connection between the appearance of the nonlinearity in the deformed field and the quantum information quantifiers. The time correlation between entropy squeezing, purity, and entanglement is examined in terms of the physical parameters involved in the whole system. Lastly, we explore the exact ranges of the physical parameters in order to combat the decoherence effect and maintain high amount of entanglement during the time evolution.

  20. EEG entropy measures indicate decrease of cortical information processing in Disorders of Consciousness.

    PubMed

    Thul, Alexander; Lechinger, Julia; Donis, Johann; Michitsch, Gabriele; Pichler, Gerald; Kochs, Eberhard F; Jordan, Denis; Ilg, Rüdiger; Schabus, Manuel

    2016-02-01

    Clinical assessments that rely on behavioral responses to differentiate Disorders of Consciousness are at times inapt because of some patients' motor disabilities. To objectify patients' conditions of reduced consciousness the present study evaluated the use of electroencephalography to measure residual brain activity. We analyzed entropy values of 18 scalp EEG channels of 15 severely brain-damaged patients with clinically diagnosed Minimally-Conscious-State (MCS) or Unresponsive-Wakefulness-Syndrome (UWS) and compared the results to a sample of 24 control subjects. Permutation entropy (PeEn) and symbolic transfer entropy (STEn), reflecting information processes in the EEG, were calculated for all subjects. Participants were tested on a modified active own-name paradigm to identify correlates of active instruction following. PeEn showed reduced local information content in the EEG in patients, that was most pronounced in UWS. STEn analysis revealed altered directed information flow in the EEG of patients, indicating impaired feed-backward connectivity. Responses to auditory stimulation yielded differences in entropy measures, indicating reduced information processing in MCS and UWS. Local EEG information content and information flow are affected in Disorders of Consciousness. This suggests local cortical information capacity and feedback information transfer as neural correlates of consciousness. The utilized EEG entropy analyses were able to relate to patient groups with different Disorders of Consciousness. Copyright © 2015 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

  1. Differential entropy and time

    NASA Astrophysics Data System (ADS)

    Garbaczewski, Piotr

    2005-12-01

    We give a detailed analysis of the Gibbs-type entropy notion and its dynamical behavior in case of time-dependent continuous probability distributions of varied origins: related to classical and quantum systems. The purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon) entropies is explained in case of non-equilibrium Smoluchowski processes. A very different temporal behavior of Gibbs and Kullback entropies is confronted. A specific conceptual niche is addressed, where quantum von Neumann, classical Kullback-Leibler and Gibbs entropies can be consistently introduced as information measures for the same physical system. If the dynamics of probability densities is driven by the Schrödinger picture wave-packet evolution, Gibbs-type and related Fisher information functionals appear to quantify nontrivial power transfer processes in the mean. This observation is found to extend to classical dissipative processes and supports the view that the Shannon entropy dynamics provides an insight into physically relevant non-equilibrium phenomena, which are inaccessible in terms of the Kullback-Leibler entropy and typically ignored in the literature.

  2. Colloquium: Protecting quantum information against environmental noise

    NASA Astrophysics Data System (ADS)

    Suter, Dieter; Álvarez, Gonzalo A.

    2016-10-01

    Quantum technologies represent a rapidly evolving field in which the specific properties of quantum mechanical systems are exploited to enhance the performance of various applications such as sensing, transmission, and processing of information. Such devices can be useful only if the quantum systems also interact with their environment. However, the interactions with the environment can degrade the specific quantum properties of these systems, such as coherence and entanglement. It is therefore essential that the interaction between a quantum system and the environment is controlled in such a way that the unwanted effects of the environment are suppressed while the necessary interactions are retained. This Colloquium gives an overview, aimed at newcomers to this field, of some of the challenges that need to be overcome to achieve this goal. A number of techniques have been developed for this purpose in different areas of physics including magnetic resonance, optics, and quantum information. They include the application of static or time-dependent fields to the quantum system, which are designed to average the effect of the environmental interactions to zero. Quantum error correction schemes were developed to detect and eliminate certain errors that occur during the storage and processing of quantum information. In many physical systems, it is useful to use specific quantum states that are intrinsically less susceptible to environmental noise for encoding the quantum information. The dominant contribution to the loss of information is pure dephasing, i.e., through the loss of coherence in quantum mechanical superposition states. Accordingly, most schemes for reducing loss of information focus on dephasing processes. This is also the focus of this Colloquium.

  3. Entropy excess in strongly correlated Fermi systems near a quantum critical point

    SciTech Connect

    Clark, J.W.; Zverev, M.V.; Khodel, V.A.

    2012-12-15

    A system of interacting, identical fermions described by standard Landau Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if the correlations grow sufficiently strong, as occurs at a quantum critical point where the effective mass diverges. As yet, this phenomenon defies full understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior observed beyond the quantum critical point are still accessible within the general framework of the Landau quasiparticle picture. Self-consistent solutions of the coupled Landau equations for the quasiparticle momentum distribution n(p) and quasiparticle energy spectrum {epsilon}(p) are shown to exist in two distinct classes, depending on coupling strength and on whether the quasiparticle interaction is regular or singular at zero momentum transfer. One class of solutions maintains the idempotency condition n{sup 2}(p)=n(p) of standard FL theory at zero temperature T while adding pockets to the Fermi surface. The other solutions are characterized by a swelling of the Fermi surface and a flattening of the spectrum {epsilon}(p) over a range of momenta in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The latter, non-idempotent solution is revealed by analysis of a Poincare mapping associated with the fundamental Landau equation connecting n(p) and {epsilon}(p) and validated by solution of a variational condition that yields the symmetry-preserving ground state. Significantly, this extraordinary solution carries the burden of a large temperature-dependent excess entropy down to very low temperatures, threatening violation of the Nernst Theorem. It is argued that certain low-temperature phase transitions, notably those involving Cooper-pair formation, offer effective mechanisms for shedding the entropy excess. Available measurements in heavy-fermion compounds provide concrete support for such a scenario. - Highlights: Black-Right-Pointing-Pointer Extension of Landau

  4. Quantum information processing : science & technology.

    SciTech Connect

    Horton, Rebecca; Carroll, Malcolm S.; Tarman, Thomas David

    2010-09-01

    Qubits demonstrated using GaAs double quantum dots (DQD). The qubit basis states are the (1) singlet and (2) triplet stationary states. Long spin decoherence times in silicon spurs translation of GaAs qubit in to silicon. In the near term the goals are: (1) Develop surface gate enhancement mode double quantum dots (MOS & strained-Si/SiGe) to demonstrate few electrons and spin read-out and to examine impurity doped quantum-dots as an alternative architecture; (2) Use mobility, C-V, ESR, quantum dot performance & modeling to feedback and improve upon processing, this includes development of atomic precision fabrication at SNL; (3) Examine integrated electronics approaches to RF-SET; (4) Use combinations of numerical packages for multi-scale simulation of quantum dot systems (NEMO3D, EMT, TCAD, SPICE); and (5) Continue micro-architecture evaluation for different device and transport architectures.

  5. Quantum Engineering of a Low-Entropy Gas of Heteronuclear Bosonic Molecules in an Optical Lattice

    NASA Astrophysics Data System (ADS)

    Reichsöllner, Lukas; Schindewolf, Andreas; Takekoshi, Tetsu; Grimm, Rudolf; Nägerl, Hanns-Christoph

    2017-02-01

    We demonstrate a generally applicable technique for mixing two-species quantum degenerate bosonic samples in the presence of an optical lattice, and we employ it to produce low-entropy samples of ultracold Rb 87 Cs 133 Feshbach molecules with a lattice filling fraction exceeding 30%. Starting from two spatially separated Bose-Einstein condensates of Rb and Cs atoms, Rb-Cs atom pairs are efficiently produced by using the superfluid-to-Mott insulator quantum phase transition twice, first for the Cs sample, then for the Rb sample, after nulling the Rb-Cs interaction at a Feshbach resonance's zero crossing. We form molecules out of atom pairs and characterize the mixing process in terms of sample overlap and mixing speed. The dense and ultracold sample of more than 5000 RbCs molecules is an ideal starting point for experiments in the context of quantum many-body physics with long-range dipolar interactions.

  6. Quantum technology and cryptology for information security

    NASA Astrophysics Data System (ADS)

    Naqvi, Syed; Riguidel, Michel

    2007-04-01

    Cryptology and information security are set to play a more prominent role in the near future. In this regard, quantum communication and cryptography offer new opportunities to tackle ICT security. Quantum Information Processing and Communication (QIPC) is a scientific field where new conceptual foundations and techniques are being developed. They promise to play an important role in the future of information Security. It is therefore essential to have a cross-fertilizing development between quantum technology and cryptology in order to address the security challenges of the emerging quantum era. In this article, we discuss the impact of quantum technology on the current as well as future crypto-techniques. We then analyse the assumptions on which quantum computers may operate. Then we present our vision for the distribution of security attributes using a novel form of trust based on Heisenberg's uncertainty; and, building highly secure quantum networks based on the clear transmission of single photons and/or bundles of photons able to withstand unauthorized reading as a result of secure protocols based on the observations of quantum mechanics. We argue how quantum cryptographic systems need to be developed that can take advantage of the laws of physics to provide long-term security based on solid assumptions. This requires a structured integration effort to deploy quantum technologies within the existing security infrastructure. Finally, we conclude that classical cryptographic techniques need to be redesigned and upgraded in view of the growing threat of cryptanalytic attacks posed by quantum information processing devices leading to the development of post-quantum cryptography.

  7. Quantum causal histories in the light of quantum information

    SciTech Connect

    Livine, Etera R.; Terno, Daniel R.

    2007-04-15

    We use techniques of quantum information theory to analyze the quantum causal histories approach to quantum gravity. While it is consistent to introduce closed timelike curves (CTCs), they cannot generically carry independent degrees of freedom. Moreover, if the effective dynamics of the chronology-respecting part of the system is linear, it should be completely decoupled from the CTCs. In the absence of a CTC, not all causal structures admit the introduction of quantum mechanics. It is possible for those and only those causal structures that can be represented as quantum computational networks. Dynamics of the subsystems should not be unitary or even completely positive. However, we show that other commonly made assumptions ensure the complete positivity of the reduced dynamics.

  8. Quantum Realism, Information, and Epistemological Modesty

    NASA Astrophysics Data System (ADS)

    Grinbaum, Alexei

    2014-03-01

    It is usually asserted that physical theories, in particular quantum mechanics, support a certain view of what the world really is. To such claims I oppose an attitude of epistemological modesty. Ontological statements on the nature of reality, when made on the basis of quantum mechanics, appear unwarranted. I suggest that an epistemic loop connects physical theory grounded in informational notions, and a theory of information developed through a theoretical account of the physical support of information.

  9. Correlation lengths and topological entanglement entropies of unitary and nonunitary fractional quantum Hall wave functions.

    PubMed

    Estienne, B; Regnault, N; Bernevig, B A

    2015-05-08

    Using the newly developed matrix product state formalism for non-Abelian fractional quantum Hall (FQH) states, we address the question of whether a FQH trial wave function written as a correlation function in a nonunitary conformal field theory (CFT) can describe the bulk of a gapped FQH phase. We show that the nonunitary Gaffnian state exhibits clear signatures of a pathological behavior. As a benchmark we compute the correlation length of a Moore-Read state and find it to be finite in the thermodynamic limit. By contrast, the Gaffnian state has an infinite correlation length in (at least) the non-Abelian sector, and is therefore gapless. We also compute the topological entanglement entropy of several non-Abelian states with and without quasiholes. For the first time in the FQH effect the results are in excellent agreement in all topological sectors with the CFT prediction for unitary states. For the nonunitary Gaffnian state in finite size systems, the topological entanglement entropy seems to behave like that of the composite fermion Jain state at equal filling.

  10. Quantum information and gravity cutoff in theories with species

    NASA Astrophysics Data System (ADS)

    Dvali, Gia; Gomez, Cesar

    2009-04-01

    We show that lowering of the gravitational cutoff relative to the Planck mass, imposed by black hole physics in theories with N species, has an independent justification from quantum information theory. First, this scale marks the limiting capacity of any information processor. Secondly, by taking into the account the limitations of the quantum information storage in any system with species, the bound on the gravity cutoff becomes equivalent to the holographic bound, and this equivalence automatically implies the equality of entanglement and Bekenstein-Hawking entropies. Next, the same bound follows from quantum cloning theorem. Finally, we point out that by identifying the UV and IR threshold scales of the black hole quasi-classicality in four-dimensional field and high dimensional gravity theories, the bound translates as the correspondence between the two theories. In case when the high dimensional background is AdS, this reproduces the well-known AdS/CFT relation, but also suggests a generalization of the correspondence beyond AdS spaces. In particular, it reproduces a recently suggested duality between a four-dimensional CFT and a flat five-dimensional theory, in which gravity crosses over from four to five dimensional regime in far infrared.

  11. Relativistic quantum information and time machines

    NASA Astrophysics Data System (ADS)

    Ralph, Timothy C.; Downes, Tony G.

    2012-01-01

    Relativistic quantum information combines the informational approach to understanding and using quantum mechanical systems - quantum information - with the relativistic view of the Universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves - effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.

  12. Origin of microbial life: Nano- and molecular events, thermodynamics/entropy, quantum mechanisms and genetic instructions.

    PubMed

    Trevors, J T

    2011-03-01

    Currently, there are no agreed upon mechanisms and supporting evidence for the origin of the first microbial cells on the Earth. However, some hypotheses have been proposed with minimal supporting evidence and experimentation/observations. The approach taken in this article is that life originated at the nano- and molecular levels of biological organization, using quantum mechanic principles that became manifested as classical microbial cell(s), allowing the origin of microbial life on the Earth with a core or minimal, organic, genetic code containing the correct instructions for cell(s) for growth and division, in a micron dimension environment, with a local entropy range conducive to life (present about 4 billion years ago), and obeying the laws of thermodynamics. An integrated approach that explores all encompassing factors necessary for the origin of life, may bring forth plausible hypotheses (and mechanisms) with much needed supporting experimentation and observations for an origin of life theory.

  13. Entropy excess in strongly correlated Fermi systems near a quantum critical point

    NASA Astrophysics Data System (ADS)

    Clark, J. W.; Zverev, M. V.; Khodel, V. A.

    2012-12-01

    A system of interacting, identical fermions described by standard Landau Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if the correlations grow sufficiently strong, as occurs at a quantum critical point where the effective mass diverges. As yet, this phenomenon defies full understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior observed beyond the quantum critical point are still accessible within the general framework of the Landau quasiparticle picture. Self-consistent solutions of the coupled Landau equations for the quasiparticle momentum distribution n(p) and quasiparticle energy spectrum ɛ(p) are shown to exist in two distinct classes, depending on coupling strength and on whether the quasiparticle interaction is regular or singular at zero momentum transfer. One class of solutions maintains the idempotency condition n2(p)=n(p) of standard FL theory at zero temperature T while adding pockets to the Fermi surface. The other solutions are characterized by a swelling of the Fermi surface and a flattening of the spectrum ɛ(p) over a range of momenta in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The latter, non-idempotent solution is revealed by analysis of a Poincaré mapping associated with the fundamental Landau equation connecting n(p) and ɛ(p) and validated by solution of a variational condition that yields the symmetry-preserving ground state. Significantly, this extraordinary solution carries the burden of a large temperature-dependent excess entropy down to very low temperatures, threatening violation of the Nernst Theorem. It is argued that certain low-temperature phase transitions, notably those involving Cooper-pair formation, offer effective mechanisms for shedding the entropy excess. Available measurements in heavy-fermion compounds provide concrete support for such a scenario.

  14. Quantum correlations require multipartite information principles.

    PubMed

    Gallego, Rodrigo; Würflinger, Lars Erik; Acín, Antonio; Navascués, Miguel

    2011-11-18

    Identifying which correlations among distant observers are possible within our current description of nature, based on quantum mechanics, is a fundamental problem in physics. Recently, information concepts have been proposed as the key ingredient to characterize the set of quantum correlations. Novel information principles, such as information causality or nontrivial communication complexity, have been introduced in this context and successfully applied to some concrete scenarios. We show in this work a fundamental limitation of this approach: no principle based on bipartite information concepts is able to singleout the set of quantum correlations for an arbitrary number of parties. Our results reflect the intricate structure of quantum correlations and imply that new and intrinsically multipartite information concepts are needed for their full understanding.

  15. Quantum-mechanical estimation of rectangular waveguide parameters with atomic entropy computation

    NASA Astrophysics Data System (ADS)

    Kumar, L.; Shankar Pandey, V.; Parthasarathy, H.; Shrimali, V.; Varshney, G.

    2017-06-01

    The field within a rectangular waveguide is associated with an electromagnetic four-potential which is used to excite a 3-dimensional (3D) quantum harmonic oscillator/atom within the guide and from the transition probabilities of the oscillators/atoms within the guide, we estimate the mode that has been excited as well as dimension of the guide. Finally, we make a small computation regarding the quantum information transmitted by the waveguide field (both classical and quantum e-m fields) having random phases and amplitudes to the atomic oscillator.

  16. Assessing Bayesian model averaging uncertainty of groundwater modeling based on information entropy method

    NASA Astrophysics Data System (ADS)

    Zeng, Xiankui; Wu, Jichun; Wang, Dong; Zhu, Xiaobin; Long, Yuqiao

    2016-07-01

    Because of groundwater conceptualization uncertainty, multi-model methods are usually used and the corresponding uncertainties are estimated by integrating Markov Chain Monte Carlo (MCMC) and Bayesian model averaging (BMA) methods. Generally, the variance method is used to measure the uncertainties of BMA prediction. The total variance of ensemble prediction is decomposed into within-model and between-model variances, which represent the uncertainties derived from parameter and conceptual model, respectively. However, the uncertainty of a probability distribution couldn't be comprehensively quantified by variance solely. A new measuring method based on information entropy theory is proposed in this study. Due to actual BMA process hard to meet the ideal mutually exclusive collectively exhaustive condition, BMA predictive uncertainty could be decomposed into parameter, conceptual model, and overlapped uncertainties, respectively. Overlapped uncertainty is induced by the combination of predictions from correlated model structures. In this paper, five simple analytical functions are firstly used to illustrate the feasibility of the variance and information entropy methods. A discrete distribution example shows that information entropy could be more appropriate to describe between-model uncertainty than variance. Two continuous distribution examples show that the two methods are consistent in measuring normal distribution, and information entropy is more appropriate to describe bimodal distribution than variance. The two examples of BMA uncertainty decomposition demonstrate that the two methods are relatively consistent in assessing the uncertainty of unimodal BMA prediction. Information entropy is more informative in describing the uncertainty decomposition of bimodal BMA prediction. Then, based on a synthetical groundwater model, the variance and information entropy methods are used to assess the BMA uncertainty of groundwater modeling. The uncertainty assessments of

  17. Measuring entanglement entropies in many-body systems

    SciTech Connect

    Klich, Israel; Refael, Gil; Silva, Alessandro

    2006-09-15

    We explore the relation between entanglement entropy of quantum many-body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that, in general, the Shannon entropy of the probability distribution of certain symmetry observables gives a lower bound to the entropy. In some cases this bound is saturated and directly gives the entropy. We also show other cases in which the probability distribution contains enough information to extract the entropy: we show how this is done in several examples including BEC wave functions, the Dicke model, XY spin chain, and chains with strong randomness.

  18. Fisher Information, Entropy, and the Second and Third Laws of Thermodynamics

    EPA Science Inventory

    We propose Fisher Information as a new calculable thermodynamic property that can be shown to follow the Second and the Third Laws of Thermodynamics. Fisher Information is, however, qualitatively different from entropy and potentially possessing a great deal more structure. Hence...

  19. Fisher Information, Entropy, and the Second and Third Laws of Thermodynamics

    EPA Science Inventory

    We propose Fisher Information as a new calculable thermodynamic property that can be shown to follow the Second and the Third Laws of Thermodynamics. Fisher Information is, however, qualitatively different from entropy and potentially possessing a great deal more structure. Hence...

  20. Infrared image non-rigid registration based on regional information entropy demons algorithm

    NASA Astrophysics Data System (ADS)

    Lu, Chaoliang; Ma, Lihua; Yu, Ming; Cui, Shumin; Wu, Qingrong

    2015-02-01

    Infrared imaging fault detection which is treated as an ideal, non-contact, non-destructive testing method is applied to the circuit board fault detection. Since Infrared images obtained by handheld infrared camera with wide-angle lens have both rigid and non-rigid deformations. To solve this problem, a new demons algorithm based on regional information entropy was proposed. The new method overcame the shortcomings of traditional demons algorithm that was sensitive to the intensity. First, the information entropy image was gotten by computing regional information entropy of the image. Then, the deformation between the two images was calculated that was the same as demons algorithm. Experimental results demonstrated that the proposed algorithm has better robustness in intensity inconsistent images registration compared with the traditional demons algorithm. Achieving accurate registration between intensity inconsistent infrared images provided strong support for the temperature contrast.

  1. Infinite Shannon entropy

    NASA Astrophysics Data System (ADS)

    Baccetti, Valentina; Visser, Matt

    2013-04-01

    Even if a probability distribution is properly normalizable, its associated Shannon (or von Neumann) entropy can easily be infinite. We carefully analyze conditions under which this phenomenon can occur. Roughly speaking, this happens when arbitrarily small amounts of probability are dispersed into an infinite number of states; we shall quantify this observation and make it precise. We develop several particularly simple, elementary, and useful bounds, and also provide some asymptotic estimates, leading to necessary and sufficient conditions for the occurrence of infinite Shannon entropy. We go to some effort to keep technical computations as simple and conceptually clear as possible. In particular, we shall see that large entropies cannot be localized in state space; large entropies can only be supported on an exponentially large number of states. We are for the time being interested in single-channel Shannon entropy in the information theoretic sense, not entropy in a stochastic field theory or quantum field theory defined over some configuration space, on the grounds that this simple problem is a necessary precursor to understanding infinite entropy in a field theoretic context.

  2. Efficient quantum dialogue without information leakage

    NASA Astrophysics Data System (ADS)

    Yin, Ai-Han; Tang, Zhi-Hui; Chen, Dong

    2015-02-01

    A two-step quantum dialogue scheme is put forward with a class of three-qubit W state and quantum dense coding. Each W state can carry three bits of secret information and the measurement result is encrypted without information leakage. Furthermore, we utilize the entangle properties of W state and decoy photon checking technique to realize three-time channel detection, which can improve the efficiency and security of the scheme.

  3. Extraction of information from a single quantum

    SciTech Connect

    Paraoanu, G. S.

    2011-04-15

    We investigate the possibility of performing quantum tomography on a single qubit with generalized partial measurements and the technique of measurement reversal. Using concepts from statistical decision theory, we prove that, somewhat surprisingly, no information can be obtained using this scheme. It is shown that, irrespective of the measurement technique used, extraction of information from single quanta is at odds with other general principles of quantum physics.

  4. Relating information entropy and mass variance to measure bias and non-Gaussianity

    NASA Astrophysics Data System (ADS)

    Pandey, Biswajit

    2016-12-01

    We relate the information entropy and the mass variance of any distribution in the regime of small fluctuations. We use a set of Monte Carlo simulations of different homogeneous and inhomogeneous distributions to verify the relation and also test it in a set of cosmological N-body simulations. We find that the relation is in excellent agreement with the simulations and is independent of number density and the nature of the distributions. We show that the relation between information entropy and mass variance can be used to determine the linear bias on large scales and detect the signatures of non-Gaussianity on small scales in galaxy distributions.

  5. Photonic quantum information: science and technology

    PubMed Central

    TAKEUCHI, Shigeki

    2016-01-01

    Recent technological progress in the generation, manipulation and detection of individual single photons has opened a new scientific field of photonic quantum information. This progress includes the realization of single photon switches, photonic quantum circuits with specific functions, and the application of novel photonic states to novel optical metrology beyond the limits of standard optics. In this review article, the recent developments and current status of photonic quantum information technology are overviewed based on the author’s past and recent works. PMID:26755398

  6. Quantum complexity: Quantum mutual information, complex networks, and emergent phenomena in quantum cellular automata

    NASA Astrophysics Data System (ADS)

    Vargas, David L.

    Emerging quantum simulator technologies provide a new challenge to quantum many body theory. Quantifying the emergent order in and predicting the dynamics of such complex quantum systems requires a new approach. We develop such an approach based on complex network analysis of quantum mutual information. First, we establish the usefulness of quantum mutual information complex networks by reproducing the phase diagrams of transverse Ising and Bose-Hubbard models. By quantifying the complexity of quantum cellular automata we then demonstrate the applicability of complex network theory to non-equilibrium quantum dynamics. We conclude with a study of student collaboration networks, correlating a student's role in a collaboration network with their grades. This work thus initiates a quantitative theory of quantum complexity and provides a new tool for physics education research. (Abstract shortened by ProQuest.).

  7. Minimising the heat dissipation of quantum information erasure

    NASA Astrophysics Data System (ADS)

    Hamed Mohammady, M.; Mohseni, Masoud; Omar, Yasser

    2016-01-01

    Quantum state engineering and quantum computation rely on information erasure procedures that, up to some fidelity, prepare a quantum object in a pure state. Such processes occur within Landauer's framework if they rely on an interaction between the object and a thermal reservoir. Landauer's principle dictates that this must dissipate a minimum quantity of heat, proportional to the entropy reduction that is incurred by the object, to the thermal reservoir. However, this lower bound is only reachable for some specific physical situations, and it is not necessarily achievable for any given reservoir. The main task of our work can be stated as the minimisation of heat dissipation given probabilistic information erasure, i.e., minimising the amount of energy transferred to the thermal reservoir as heat if we require that the probability of preparing the object in a specific pure state ≤ft|{\\varphi }1\\right.> be no smaller than {p}{\\varphi 1}{max}-δ . Here {p}{\\varphi 1}{max} is the maximum probability of information erasure that is permissible by the physical context, and δ ≥slant 0 the error. To determine the achievable minimal heat dissipation of quantum information erasure within a given physical context, we explicitly optimise over all possible unitary operators that act on the composite system of object and reservoir. Specifically, we characterise the equivalence class of such optimal unitary operators, using tools from majorisation theory, when we are restricted to finite-dimensional Hilbert spaces. Furthermore, we discuss how pure state preparation processes could be achieved with a smaller heat cost than Landauer's limit, by operating outside of Landauer's framework.

  8. Theory of the Robin quantum wall in a linear potential. I. Energy spectrum, polarization and quantum-information measures

    NASA Astrophysics Data System (ADS)

    Olendski, O.

    2016-12-01

    Information-theoretical concepts are employed for the analysis of the interplay between a transverse electric field $\\mathscr{E}$ applied to a one-dimensional surface and Robin boundary condition (BC), which with the help of the extrapolation length $\\Lambda$ zeroes at the interface a linear combination of the quantum mechanical wave function and its spatial derivative, and its influence on the properties of the structure. For doing this, exact analytical solutions of the corresponding Schr\\"{o}dinger equation are derived and used for calculating energies, dipole moments, position $S_x$ and momentum $S_k$ quantum information entropies and their Fisher information $I_x$ and $I_k$ and Onicescu information energies $O_x$ and $O_k$ counterparts. It is shown that the weak (strong) electric field changes the Robin wall into the Dirichlet, $\\Lambda=0$ (Neumann, $\\Lambda=\\infty$), surface. This transformation of the energy spectrum and associated waveforms in the growing field defines an evolution of the quantum-information measures; for example, it is proved that for the Dirichlet and Neumann BCs the position (momentum) quantum information entropy varies as a positive (negative) natural logarithm of the electric intensity what results in their field-independent sum $S_x+S_k$. Analogously, at $\\Lambda=0$ and $\\Lambda=\\infty$ the position and momentum Fisher informations (Onicescu energies) depend on the applied voltage as $\\mathscr{E}^{2/3}$ ($\\mathscr{E}^{1/3}$) and its inverse, respectively, leading to the field-independent product $I_xI_k$ ($O_xO_k$). Peculiarities of their transformations at the finite nonzero $\\Lambda$ are discussed and similarities and differences between the three quantum-information measures in the electric field are highlighted with the special attention being paid to the configuration with the negative extrapolation length.

  9. Information Dimension of Stochastic Processes on Networks: Relating Entropy Production to Spectral Properties

    NASA Astrophysics Data System (ADS)

    Mülken, Oliver; Heinzelmann, Sarah; Dolgushev, Maxim

    2017-06-01

    We consider discrete stochastic processes, modeled by classical master equations, on networks. The temporal growth of the lack of information about the system is captured by its non-equilibrium entropy, defined via the transition probabilities between different nodes of the network. We derive a relation between the entropy and the spectrum of the master equation's transfer matrix. Our findings indicate that the temporal growth of the entropy is proportional to the logarithm of time if the spectral density shows scaling. In analogy to chaos theory, the proportionality factor is called (stochastic) information dimension and gives a global characterization of the dynamics on the network. These general results are corroborated by examples of regular and of fractal networks.

  10. Conditional mutual information and quantum steering

    NASA Astrophysics Data System (ADS)

    Kaur, Eneet; Wang, Xiaoting; Wilde, Mark M.

    2017-08-01

    Quantum steering has recently been formalized in the framework of a resource theory of steering, and several quantifiers have already been introduced. Here, we propose an information-theoretic quantifier for steering called intrinsic steerability, which uses conditional mutual information to measure the deviation of a given assemblage from one having a local-hidden-state model. We thus relate conditional mutual information to quantum steering and introduce monotones that satisfy certain desirable properties. The idea behind the quantifier is to suppress the correlations that can be explained by an inaccessible quantum system and then quantify the remaining intrinsic correlations. A variant of the intrinsic steerability finds operational meaning as the classical communication cost of sending the measurement choice and outcome to an eavesdropper who possesses a purifying system of the underlying bipartite quantum state that is being measured.

  11. Algorithmic information content, Church-Turing thesis, physical entropy, and Maxwell's demon

    SciTech Connect

    Zurek, W.H.

    1990-01-01

    Measurements convert alternative possibilities of its potential outcomes into the definiteness of the record'' -- data describing the actual outcome. The resulting decrease of statistical entropy has been, since the inception of the Maxwell's demon, regarded as a threat to the second law of thermodynamics. For, when the statistical entropy is employed as the measure of the useful work which can be extracted from the system, its decrease by the information gathering actions of the observer would lead one to believe that, at least from the observer's viewpoint, the second law can be violated. I show that the decrease of ignorance does not necessarily lead to the lowering of disorder of the measured physical system. Measurements can only convert uncertainty (quantified by the statistical entropy) into randomness of the outcome (given by the algorithmic information content of the data). The ability to extract useful work is measured by physical entropy, which is equal to the sum of these two measures of disorder. So defined physical entropy is, on the average, constant in course of the measurements carried out by the observer on an equilibrium system. 27 refs., 6 figs.

  12. Fault Detection and Diagnosis for Gas Turbines Based on a Kernelized Information Entropy Model

    PubMed Central

    Wang, Weiying; Xu, Zhiqiang; Tang, Rui; Li, Shuying; Wu, Wei

    2014-01-01

    Gas turbines are considered as one kind of the most important devices in power engineering and have been widely used in power generation, airplanes, and naval ships and also in oil drilling platforms. However, they are monitored without man on duty in the most cases. It is highly desirable to develop techniques and systems to remotely monitor their conditions and analyze their faults. In this work, we introduce a remote system for online condition monitoring and fault diagnosis of gas turbine on offshore oil well drilling platforms based on a kernelized information entropy model. Shannon information entropy is generalized for measuring the uniformity of exhaust temperatures, which reflect the overall states of the gas paths of gas turbine. In addition, we also extend the entropy to compute the information quantity of features in kernel spaces, which help to select the informative features for a certain recognition task. Finally, we introduce the information entropy based decision tree algorithm to extract rules from fault samples. The experiments on some real-world data show the effectiveness of the proposed algorithms. PMID:25258726

  13. Fault detection and diagnosis for gas turbines based on a kernelized information entropy model.

    PubMed

    Wang, Weiying; Xu, Zhiqiang; Tang, Rui; Li, Shuying; Wu, Wei

    2014-01-01

    Gas turbines are considered as one kind of the most important devices in power engineering and have been widely used in power generation, airplanes, and naval ships and also in oil drilling platforms. However, they are monitored without man on duty in the most cases. It is highly desirable to develop techniques and systems to remotely monitor their conditions and analyze their faults. In this work, we introduce a remote system for online condition monitoring and fault diagnosis of gas turbine on offshore oil well drilling platforms based on a kernelized information entropy model. Shannon information entropy is generalized for measuring the uniformity of exhaust temperatures, which reflect the overall states of the gas paths of gas turbine. In addition, we also extend the entropy to compute the information quantity of features in kernel spaces, which help to select the informative features for a certain recognition task. Finally, we introduce the information entropy based decision tree algorithm to extract rules from fault samples. The experiments on some real-world data show the effectiveness of the proposed algorithms.

  14. Decoherence time, hydrogenic-like impurity effect and Shannon entropy on polaron in RbCl triangular quantum dot qubit

    NASA Astrophysics Data System (ADS)

    Tiotsop, M.; Fotue, A. J.; Fautso, G. K.; Kenfack, C. S.; Fotsin, H. B.; Fai, L. C.

    2017-03-01

    Using Pekar variational method, Eigen energies of the ground and first excited states of the polaron in triangular bound and Coulomb potential quantum dot are derived in view of investigating the density of probability, the decoherence time and the Shannon entropy. Numerical analysis show that the decoherence time is decreasing function of polaron radius and the strength of the Coulombic impurity and the increase function of dispersion coefficient. These results suggest that the decrease of polaron radius and Coulombic impurity lead to the increase of coherence time. Also the entropy shows the oscillatory periodic evolution as function of the time due to the triangular form of the confinement. It's also seen that entropy is periodic for the lower value of Coulomb impurity parameter and for the higher value of the polaronic radius.

  15. Universal finite-size corrections of the entanglement entropy of quantum ladders and the entropic area law

    NASA Astrophysics Data System (ADS)

    Xavier, J. C.; Ramos, F. B.

    2014-10-01

    We investigate the finite-size corrections of the entanglement entropy of critical ladders and propose a conjecture for its scaling behaviour. The conjecture is verified for free fermions, for Heisenberg ladders, and for quantum Ising ladders. Our results support that the prefactor of the logarithmic correction of the entanglement entropy of critical ladder models is universal and is associated with the central charge of the one-dimensional version of the models and with the number of branches associated with gapless excitations. Our results suggest that it is possible to infer whether there is a violation of the entropic area law in two-dimensional critical systems by analyzing the scaling behaviour of the entanglement entropy of ladder systems, which are easier to deal with.

  16. Trapped Atomic Ions and Quantum Information Processing

    SciTech Connect

    Wineland, D. J.; Leibfried, D.; Bergquist, J. C.; Blakestad, R. B.; Bollinger, J. J.; Britton, J.; Chiaverini, J.; Epstein, R. J.; Hume, D. B.; Itano, W. M.; Jost, J. D.; Koelemeij, J. C. J.; Langer, C.; Ozeri, R.; Reichle, R.; Rosenband, T.; Schaetz, T.; Schmidt, P. O.; Seidelin, S.; Shiga, N.

    2006-11-07

    The basic requirements for quantum computing and quantum simulation (single- and multi-qubit gates, long memory times, etc.) have been demonstrated in separate experiments on trapped ions. Construction of a large-scale information processor will require synthesis of these elements and implementation of high-fidelity operations on a very large number of qubits. This is still well in the future. NIST and other groups are addressing part of the scaling issue by trying to fabricate multi-zone arrays of traps that would allow highly-parallel and scalable processing. In the near term, some simple quantum processing protocols are being used to aid in quantum metrology, such as in atomic clocks. As the number of qubits increases, Schroedinger's cat paradox and the measurement problem in quantum mechanics become more apparent; with luck, trapped ion systems might be able to shed light on these fundamental issues.

  17. Trapped Atomic Ions and Quantum Information Processing

    NASA Astrophysics Data System (ADS)

    Wineland, D. J.; Leibfried, D.; Bergquist, J. C.; Blakestad, R. B.; Bollinger, J. J.; Britton, J.; Chiaverini, J.; Epstein, R. J.; Hume, D. B.; Itano, W. M.; Jost, J. D.; Knill, M.; Koelemeij, J. C. J.; Langer, C.; Ozeri, R.; Reichle, R.; Rosenband, T.; Schaetz, T.; Schmidt, P. O.; Seidelin, S.; Shiga, N.; Wesenberg, J. H.

    2006-11-01

    The basic requirements for quantum computing and quantum simulation (single- and multi-qubit gates, long memory times, etc.) have been demonstrated in separate experiments on trapped ions. Construction of a large-scale information processor will require synthesis of these elements and implementation of high-fidelity operations on a very large number of qubits. This is still well in the future. NIST and other groups are addressing part of the scaling issue by trying to fabricate multi-zone arrays of traps that would allow highly-parallel and scalable processing. In the near term, some simple quantum processing protocols are being used to aid in quantum metrology, such as in atomic clocks. As the number of qubits increases, Schrödinger's cat paradox and the measurement problem in quantum mechanics become more apparent; with luck, trapped ion systems might be able to shed light on these fundamental issues.

  18. Thermodynamics of information exchange between two coupled quantum dots

    NASA Astrophysics Data System (ADS)

    Kutvonen, Aki; Sagawa, Takahiro; Ala-Nissila, Tapio

    2016-03-01

    We propose a setup based on two coupled quantum dots where thermodynamics of a measurement can be quantitatively characterized. The information obtained in the measurement can be utilized by performing feedback in a manner apparently breaking the second law of thermodynamics. In this way the setup can be operated as a Maxwell's demon, where both the measurement and feedback are performed separately by controlling an external parameter. This is analogous to the case of the original Szilard engine. Since the setup contains both the microscopic demon and the engine itself, the operation of the whole measurement-feedback cycle can be explained in detail at the level of single realizations. In addition, we derive integral fluctuation relations for both the bare and coarse-grained entropy productions in the setup.

  19. Nature and location of quantum information

    NASA Astrophysics Data System (ADS)

    Griffiths, Robert B.

    2002-07-01

    Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other arguments show that the infinite amount of information needed to specify a precise vector in its Hilbert space is not a measure of the information carried by a quantum entity with a d-dimensional Hilbert space; the latter is, instead, bounded by log2d bits (one bit per qubit). The two bits of information transmitted in dense coding are located not in one but in the correlation between two qubits, consistent with this bound. A quantum channel can be thought of as a structure or collection of frameworks, and the physical location of the information in the individual frameworks can be used to identify the location of the channel. Analysis of a quantum circuit used as a model of teleportation shows that the location of the channel depends upon which structure is employed; for ordinary teleportation it is not (contrary to Deutsch and Hayden) present in the two bits resulting from the Bell-basis measurement, but in correlations of these with a distant qubit. In neither teleportation nor dense coding does information travel backwards in time, nor is it transmitted by nonlocal (superluminal) influences. It is (tentatively) proposed that all aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.

  20. The Entropy Estimation of the Physics’ Course Content on the Basis of Intradisciplinary Connections’ Information Model

    NASA Astrophysics Data System (ADS)

    Tatyana, Gnitetskaya

    2016-08-01

    In this paper the information model of intradisciplinary connections and semantic structures method are described. The information parameters, which we use in information model, are introduced. The question we would like to answer in this paper is - how to optimize the Physics Course’ content. As an example, the differences between entropy values in the contents of physics lecture with one topic but different logics of explanations are showed.

  1. Entropy in Postmerger and Acquisition Integration from an Information Technology Perspective

    ERIC Educational Resources Information Center

    Williams, Gloria S.

    2012-01-01

    Mergers and acquisitions have historically experienced failure rates from 50% to more than 80%. Successful integration of information technology (IT) systems can be the difference between postmerger success or failure. The purpose of this phenomenological study was to explore the entropy phenomenon during postmerger IT integration. To that end, a…

  2. Entropy in Postmerger and Acquisition Integration from an Information Technology Perspective

    ERIC Educational Resources Information Center

    Williams, Gloria S.

    2012-01-01

    Mergers and acquisitions have historically experienced failure rates from 50% to more than 80%. Successful integration of information technology (IT) systems can be the difference between postmerger success or failure. The purpose of this phenomenological study was to explore the entropy phenomenon during postmerger IT integration. To that end, a…

  3. Optical resonators and quantum dots: An excursion into quantum optics, quantum information and photonics

    NASA Astrophysics Data System (ADS)

    Bianucci, Pablo

    Modern communications technology has encouraged an intimate connection between Semiconductor Physics and Optics, and this connection shows best in the combination of electron-confining structures with light-confining structures. Semiconductor quantum dots are systems engineered to trap electrons in a mesoscopic scale (the are composed of ≈ 10000 atoms), resulting in a behavior resembling that of atoms, but much richer. Optical microresonators are engineered to confine light, increasing its intensity and enabling a much stronger interaction with matter. Their combination opens a myriad of new directions, both in fundamental Physics and in possible applications. This dissertation explores both semiconductor quantum dots and microresonators, through experimental work done with semiconductor quantum dots and microsphere resonators spanning the fields of Quantum Optics, Quantum Information and Photonics; from quantum algorithms to polarization converters. Quantum Optics leads the way, allowing us to understand how to manipulate and measure quantum dots with light and to elucidate the interactions between them and microresonators. In the Quantum Information area, we present a detailed study of the feasibility of excitons in quantum dots to perform quantum computations, including an experimental demonstration of the single-qubit Deutsch-Jozsa algorithm performedin a single semiconductor quantum dot. Our studies in Photonics involve applications of microsphere resonators, which we have learned to fabricate and characterize. We present an elaborate description of the experimental techniques needed to study microspheres, including studies and proof of concept experiments on both ultra-sensitive microsphere sensors and whispering gallery mode polarization converters.

  4. a Unified Description of Time Dependence of Information Entropy Production and Flux in Thermal Broadband Noise-Driven Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Majee, Pradip; Goswami, Gurupada; Barik, Debashis; Bag, Bidhan Chandra

    In this paper we have studied the dynamics of thermal broadband noise-driven dynamical system in terms of information entropy at both the nonstationary and stationary states. Here, a unified description of fluctuating force is considered in a thermodynamically closed system. Based on the Fokker-Planck description of stochastic processes and the entropy balance equation, we have calculated the time-dependence of the information entropy production and entropy flux in the presence and absence of nonequilibrium constraint. Our calculation considers how the time evolution of these quantities is affected if the characteristic of noise changes from white to red or green and red to green in a unified scheme.

  5. Quantum information. Unconditional quantum teleportation between distant solid-state quantum bits.

    PubMed

    Pfaff, W; Hensen, B J; Bernien, H; van Dam, S B; Blok, M S; Taminiau, T H; Tiggelman, M J; Schouten, R N; Markham, M; Twitchen, D J; Hanson, R

    2014-08-01

    Realizing robust quantum information transfer between long-lived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photon-mediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bell-state measurement combined with real-time feed-forward, quantum teleportation is achieved upon each attempt with an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and network-based quantum computing. Copyright © 2014, American Association for the Advancement of Science.

  6. Entropy uncertainty relations and stability of phase-temporal quantum cryptography with finite-length transmitted strings

    SciTech Connect

    Molotkov, S. N.

    2012-12-15

    Any key-generation session contains a finite number of quantum-state messages, and it is there-fore important to understand the fundamental restrictions imposed on the minimal length of a string required to obtain a secret key with a specified length. The entropy uncertainty relations for smooth min and max entropies considerably simplify and shorten the proof of security. A proof of security of quantum key distribution with phase-temporal encryption is presented. This protocol provides the maximum critical error compared to other protocols up to which secure key distribution is guaranteed. In addition, unlike other basic protocols (of the BB84 type), which are vulnerable with respect to an attack by 'blinding' of avalanche photodetectors, this protocol is stable with respect to such an attack and guarantees key security.

  7. Introduction to Quantum Information/Computing

    DTIC Science & Technology

    2005-06-01

    mωX + iP) sqrt(2mhω) BCS Theory – Named for John Bardeen , Leon Cooper, and Robert Schrieffer. According to theory, the...Theory and Reliable Communication, John Wiley & Sons 1998 2. M.A. Nielsen, I. L. Chuang, Quantum Computation and Quantum Information, Cambridge...France and by John Wiley & Sons. 6. H. Goldstein, Classical Mechanics, 1950 Addison-Wesley Publishing Company, Inc. 7. L.S. Brown and G

  8. Splitting quantum information via W states

    SciTech Connect

    Zheng Shibiao

    2006-11-15

    We describe a procedure for splitting quantum information into two or more parts so that if and only if the recipients cooperate, the original qubit can be reconstructed. Our scheme uses W-type entangled states as the quantum channel and thus the scheme is robust against decoherence. We illustrate the procedure in the ion-trap system, but the idea can also be realized in other systems.

  9. Information entropy of activation process: Application for low-temperature fluctuations of a myoglobin molecule

    NASA Astrophysics Data System (ADS)

    Stepanov, A. V.

    2015-11-01

    Activation process for unimolecular reaction has been considered by means of radiation theory. The formulae of information entropy of activation have been derived for the Boltzmann-Arrhenius model and the activation process model (APM). The physical meaning of this entropy has been determined. It is a measure of conversion of thermal radiation energy to mechanical energy that moves atoms in a molecule during elementary activation act. It is also a measure of uncertainty of this energy conversion. The uncertainty is due to unevenness of distribution function representing the activation process. It has been shown that Arrhenius dependence is caused by the entropy change. Efficiency comparison of the two models under consideration for low-temperature fluctuations of a myoglobin molecule structure shows that the APM should be favored over the Boltzmann-Arrhenius one.

  10. Maximal entropy coverings and the information dimension of a complex network

    NASA Astrophysics Data System (ADS)

    Rosenberg, Eric

    2017-02-01

    Computing the information dimension dI of a complex network G requires covering G by a minimal collection of "boxes" of size s to obtain a set of probabilities, computing the entropy H (s), and quantifying how H (s) scales with log ⁡ s. We show that to determine whether dI ≤dB holds for G, where dB is the box counting dimension, it is not sufficient to determine a minimal covering for each s. We introduce the new notion of a maximal entropy minimal covering of G, and a corresponding new definition of dI. The use of maximal entropy minimal coverings in many cases enhances the ability to compute dI.

  11. On the realization of quantum Fisher information

    NASA Astrophysics Data System (ADS)

    Saha, Aparna; Talukdar, B.; Chatterjee, Supriya

    2017-03-01

    With special attention to the role of information theory in physical sciences we present analytical results for the coordinate- and momentum-space Fisher information of some important one-dimensional quantum systems which differ in spacing of their energy levels. The studies envisaged allow us to relate the coordinate-space information ({I}ρ ) with the familiar energy levels of the quantum system. The corresponding momentum-space information ({I}γ ) does not obey such a simple relationship with the energy spectrum. Our results for the product ({I}ρ {I}γ ) depend quadratically on the principal quantum number n and satisfy an appropriate uncertainty relation derived by Dehesa et al (2007 J. Phys. A: Math. Theor. 40 1845)

  12. Engineering Photonic Switches for Quantum Information Processing

    NASA Astrophysics Data System (ADS)

    Oza, Neal N.

    In this dissertation, we describe, characterize, and demonstrate the operation of a dual-in, dual-out, all-optical, fiber-based quantum switch. This "cross-bar" switch is particularly useful for applications in quantum information processing because of its low-loss, high-speed, low-noise, and quantum-state-retention properties. Building upon on our lab's prior development of an ultrafast demultiplexer [1-3] , the new cross-bar switch can be used as a tunable multiplexer and demultiplexer. In addition to this more functional geometry, we present results demonstrating faster performance with a switching window of ≈45 ps, corresponding to >20-GHz switching rates. We show a switching fidelity of >98%, i. e., switched polarization-encoded photonic qubits are virtually identical to unswitched photonic qubits. We also demonstrate the ability to select one channel from a two-channel quantum data stream with the state of the measured (recovered) quantum channel having >96% relative fidelity with the state of that channel transmitted alone. We separate the two channels of the quantum data stream by 155 ps, corresponding to a 6.5-GHz datastream. Finally, we describe, develop, and demonstrate an application that utilizes the switch's higher-speed, lower-loss, and spatio-temporal-encoding features to perform quantum state tomographies on entangled states in higher-dimensional Hilbert spaces. Since many previous demonstrations show bipartite entanglement of two-level systems, we define "higher" as d > 2 where d represents the dimensionality of a photon. We show that we can generate and measure time-bin-entangled, two-photon, qutrit (d = 3) and ququat (d = 4) states with >85% and >64% fidelity to an ideal maximally entangled state, respectively. Such higher-dimensional states have applications in dense coding [4] , loophole-free tests of nonlocality [5] , simplifying quantum logic gates [6] , and increasing tolerance to noise and loss for quantum information processing [7] .

  13. Finite-size key in the Bennett 1992 quantum-key-distribution protocol for Rényi entropies

    NASA Astrophysics Data System (ADS)

    Mafu, Mhlambululi; Garapo, Kevin; Petruccione, Francesco

    2013-12-01

    A realistic quantum-key-distribution protocol necessarily runs with finite resources. Usually, security proofs for existing quantum key distribution are asymptotic in the sense that certain parameters are exceedingly large compared to practical realistic values. In this paper, we derive bounds on the secret key rates for the Bennett 1992 protocol, which includes a preprocessing step. The derivation for a finite-size key is expressed as an optimization problem by using results from the uncertainty relations and the smooth Rényi entropies.

  14. Dynamics of the Anderson model for dilute magnetic alloys: A quantum Monte Carlo and maximum entropy study

    SciTech Connect

    Silver, R.N.; Gubernatis, J.E.; Sivia, D.S. ); Jarrell, M. . Dept. of Physics)

    1990-01-01

    In this article we describe the results of a new method for calculating the dynamical properties of the Anderson model. QMC generates data about the Matsubara Green's functions in imaginary time. To obtain dynamical properties, one must analytically continue these data to real time. This is an extremely ill-posed inverse problem similar to the inversion of a Laplace transform from incomplete and noisy data. Our method is a general one, applicable to the calculation of dynamical properties from a wide variety of quantum simulations. We use Bayesian methods of statistical inference to determine the dynamical properties based on both the QMC data and any prior information we may have such as sum rules, symmetry, high frequency limits, etc. This provides a natural means of combining perturbation theory and numerical simulations in order to understand dynamical many-body problems. Specifically we use the well-established maximum entropy (ME) method for image reconstruction. We obtain the spectral density and transport coefficients over the entire range of model parameters accessible by QMC, with data having much larger statistical error than required by other proposed analytic continuation methods.

  15. Universal behavior of the Shannon mutual information in nonintegrable self-dual quantum chains

    NASA Astrophysics Data System (ADS)

    Alcaraz, F. C.

    2016-09-01

    An existing conjecture states that the Shannon mutual information contained in the ground-state wave function of conformally invariant quantum chains, on periodic lattices, has a leading finite-size scaling behavior that, similarly as the von Neumann entanglement entropy, depends on the value of the central charge of the underlying conformal field theory describing the physical properties. This conjecture applies whenever the ground-state wave function is expressed in some special basis (conformal basis). Its formulation comes mainly from numerical evidences on exactly integrable quantum chains. In this paper, the above conjecture was tested for several general nonintegrable quantum chains. We introduce new families of self-dual Z (Q ) symmetric quantum chains (Q =2 ,3 ,... ). These quantum chains contain nearest-neighbor as well next-nearest-neighbor interactions (coupling constant p ). In the cases Q =2 and Q =3 , they are extensions of the standard quantum Ising and three-state Potts chains, respectively. For Q =4 and Q ≥5 , they are extensions of the Ashkin-Teller and Z (Q ) parafermionic quantum chains. Our studies indicate that these models are interesting on their own. They are critical, conformally invariant, and share the same universality class in a continuous critical line. Moreover, our numerical analysis for Q =2 -8 indicate that the Shannon mutual information exhibits the conjectured behavior irrespective if the conformally invariant quantum chain is exactly integrable or not. For completeness we also calculated, for these new families of quantum chains, the two existing generalizations of the Shannon mutual information, which are based on the Rényi entropy and on the Rényi divergence.

  16. Noise management to achieve superiority in quantum information systems

    NASA Astrophysics Data System (ADS)

    Nemoto, Kae; Devitt, Simon; Munro, William J.

    2017-06-01

    Quantum information systems are expected to exhibit superiority compared with their classical counterparts. This superiority arises from the quantum coherences present in these quantum systems, which are obviously absent in classical ones. To exploit such quantum coherences, it is essential to control the phase information in the quantum state. The phase is analogue in nature, rather than binary. This makes quantum information technology fundamentally different from our classical digital information technology. In this paper, we analyse error sources and illustrate how these errors must be managed for the system to achieve the required fidelity and a quantum superiority. This article is part of the themed issue 'Quantum technology for the 21st century'.

  17. Quantum information-geometry of dissipative quantum phase transitions.

    PubMed

    Banchi, Leonardo; Giorda, Paolo; Zanardi, Paolo

    2014-02-01

    A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.

  18. Quantum correlations and distinguishability of quantum states

    NASA Astrophysics Data System (ADS)

    Spehner, Dominique

    2014-07-01

    A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.

  19. Scalable quantum information processing and the optical topological quantum computer

    NASA Astrophysics Data System (ADS)

    Devitt, S.

    2010-02-01

    Optical quantum computation has represented one of the most successful testbed systems for quantum information processing. Along with ion-traps and nuclear magnetic resonance (NMR), experimentalists have demonstrated control of qubits, multi-gubit gates and small quantum algorithms. However, photonic based qubits suffer from a problematic lack of a large scale architecture for fault-tolerant computation which could conceivably be built in the near future. While optical systems are, in some regards, ideal for quantum computing due to their high mobility and low susceptibility to environmental decoherence, these same properties make the construction of compact, chip based architectures difficult. Here we discuss many of the important issues related to scalable fault-tolerant quantum computation and introduce a feasible architecture design for an optics based computer. We combine the recent development of topological cluster state computation with the photonic module, simple chip based devices which can be utilized to deterministically entangle photons. The integration of this operational unit with one of the most exciting computational models solves many of the existing problems with other optics based architectures and leads to a feasible large scale design which can continuously generate a 3D cluster state with a photonic module resource cost linear in the cross sectional size of the cluster.

  20. Quantum Theory of Jaynes' Principle, Bayes' Theorem, and Information

    NASA Astrophysics Data System (ADS)

    Haken, Hermann

    2014-12-01

    After a reminder of Jaynes' maximum entropy principle and of my quantum theoretical extension, I consider two coupled quantum systems A,B and formulate a quantum version of Bayes' theorem. The application of Feynman's disentangling theorem allows me to calculate the conditional density matrix ρ (A|B) , if system A is an oscillator (or a set of them), linearly coupled to an arbitrary quantum system B. Expectation values can simply be calculated by means of the normalization factor of ρ (A|B) that is derived.

  1. Negative Entropy of Life

    NASA Astrophysics Data System (ADS)

    Goradia, Shantilal

    2015-10-01

    We modify Newtonian gravity to probabilistic quantum mechanical gravity to derive strong coupling. If this approach is valid, we should be able to extend it to the physical body (life) as follows. Using Boltzmann equation, we get the entropy of the universe (137) as if its reciprocal, the fine structure constant (ALPHA), is the hidden candidate representing the negative entropy of the universe which is indicative of the binary information as its basis (http://www.arXiv.org/pdf/physics0210040v5). Since ALPHA relates to cosmology, it must relate to molecular biology too, with the binary system as the fundamental source of information for the nucleotides of the DNA as implicit in the book by the author: ``Quantum Consciousness - The Road to Reality.'' We debate claims of anthropic principle based on the negligible variation of ALPHA and throw light on thermodynamics. We question constancy of G in multiple ways.

  2. Quantum Information Processing with Modular Networks

    NASA Astrophysics Data System (ADS)

    Crocker, Clayton; Inlek, Ismail V.; Hucul, David; Sosnova, Ksenia; Vittorini, Grahame; Monroe, Chris

    2015-05-01

    Trapped atomic ions are qubit standards for the production of entangled states in quantum information science and metrology applications. Trapped ions can exhibit very long coherence times, external fields can drive strong local interactions via phonons, and remote qubits can be entangled via photons. Transferring quantum information across spatially separated ion trap modules for a scalable quantum network architecture relies on the juxtaposition of both phononic and photonic buses. We report the successful combination of these protocols within and between two ion trap modules on a unit structure of this architecture where the remote entanglement generation rate exceeds the experimentally measured decoherence rate. Additionally, we report an experimental implementation of a technique to maintain phase coherence between spatially and temporally distributed quantum gate operations, a crucial prerequisite for scalability. Finally, we discuss our progress towards addressing the issue of uncontrolled cross-talk between photonic qubits and memory qubits by implementing a second ion species, Barium, to generate the photonic link. This work is supported by the ARO with funding from the IARPA MQCO program, the DARPA Quiness Program, the ARO MURI on Hybrid Quantum Circuits, the AFOSR MURI on Quantum Transduction, and the NSF Physics Frontier Center at JQI.

  3. Protecting quantum information with optimal control

    NASA Astrophysics Data System (ADS)

    Grace, Matthew

    Quantum computation (QC) holds the promise of efficiently solving problems which are practically intractable for classical computers. However, realizing this advantage requires the precise control of a quantum information processor (QIP) and effective protection of this processor from the pernicious inuence of decoherence induced by the surrounding environment. Therefore, the ability to generate high-fidelity logical operations in the presence of environmental coupling is crucial. Methods of optimal control are applied to the field of quantum information processing, providing practical solutions for the generation of logical operations and the suppression of undesired environmental effects. The work contained in this dissertation explores important aspects of system and control design. Results obtained in this work (i) illustrate how practical QC can be greatly facilitated by optimal control theory and (ii) reveal interesting physical insights through the discovery of effective control mechanisms. A special design of the physical structure of quantum information systems is formulated which is naturally immune to certain types of decoherence and yields tremendous flexibility in the construction of logical operations for QC. A fundamental component of this design involves encoding the logical basis states of a quantum bit into multiple physical levels of the corresponding quantum system. This design also makes the QIP better suited for the interaction with ultrafast broadband laser fields used in quantum control applications. Numerical simulations demonstrate the utility of this encoding approach for thermally excited quantum systems. Optimization algorithms are developed which generate controls that protect the QIP from the effects of the environment, with or without the weak-coupling or Born approximation, and simultaneously achieve a target objective, e.g., a state-to-state transition or unitary quantum operation. For the optimal control of quantum operations, a

  4. Quantum gravity and the Information Loss Problem

    NASA Astrophysics Data System (ADS)

    Varadarajan, Madhavan

    2008-11-01

    We review the standard picture of black hole evaporation and the ensuing Information Loss Problem. Next, we describe an alternative view of the evaporation process due to Ashtekar and Bojowald (AB) which rests on the assumption of singularity resolution in quantum gravity. To endow the AB proposal with precision as well as to test it in a quantitative setting, we consider the Callen-Giddings-Harvey-Strominger (CGHS) toy model of 2-dimensional black holes. We propose a quantum framework in which to understand this model and show that the proposed framework implies that the classical spacetime manifold acquires a quantum extension, as in the AB paradigm. We show that asymptotic analysis coupled with the quantum framework suggests a unitary picture of black hole evaporation consistent with early (on the extended null infinity) time Hawking radiation.

  5. Experimental demonstration of information to energy conversion in a quantum system at the Landauer limit.

    PubMed

    Peterson, J P S; Sarthour, R S; Souza, A M; Oliveira, I S; Goold, J; Modi, K; Soares-Pinto, D O; Céleri, L C

    2016-04-01

    Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance set-up to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins [Formula: see text] (qubits) molecule-the system, the reservoir and the ancilla-to measure the heat dissipated during the implementation of a global system-reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique, we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way, we were able to verify that an operation that changes the information content of the system must necessarily generate heat in the reservoir, exactly as predicted by Landauer's principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors.

  6. Experimental demonstration of information to energy conversion in a quantum system at the Landauer limit

    PubMed Central

    Peterson, J. P. S.; Sarthour, R. S.; Souza, A. M.; Oliveira, I. S.; Goold, J.; Modi, K.; Soares-Pinto, D. O.; Céleri, L. C.

    2016-01-01

    Landauer’s principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance set-up to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins S=12 (qubits) molecule—the system, the reservoir and the ancilla—to measure the heat dissipated during the implementation of a global system–reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique, we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way, we were able to verify that an operation that changes the information content of the system must necessarily generate heat in the reservoir, exactly as predicted by Landauer’s principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors. PMID:27274690

  7. Experimental demonstration of information to energy conversion in a quantum system at the Landauer limit

    NASA Astrophysics Data System (ADS)

    Peterson, J. P. S.; Sarthour, R. S.; Souza, A. M.; Oliveira, I. S.; Goold, J.; Modi, K.; Soares-Pinto, D. O.; Céleri, L. C.

    2016-04-01

    Landauer's principle sets fundamental thermodynamical constraints for classical and quantum information processing, thus affecting not only various branches of physics, but also of computer science and engineering. Despite its importance, this principle was only recently experimentally considered for classical systems. Here we employ a nuclear magnetic resonance set-up to experimentally address the information to energy conversion in a quantum system. Specifically, we consider a three nuclear spins S =1/2 (qubits) molecule-the system, the reservoir and the ancilla-to measure the heat dissipated during the implementation of a global system-reservoir unitary interaction that changes the information content of the system. By employing an interferometric technique, we were able to reconstruct the heat distribution associated with the unitary interaction. Then, through quantum state tomography, we measured the relative change in the entropy of the system. In this way, we were able to verify that an operation that changes the information content of the system must necessarily generate heat in the reservoir, exactly as predicted by Landauer's principle. The scheme presented here allows for the detailed study of irreversible entropy production in quantum information processors.

  8. Two dissimilar approaches to dynamical systems on hyper MV -algebras and their information entropy

    NASA Astrophysics Data System (ADS)

    Mehrpooya, Adel; Ebrahimi, Mohammad; Davvaz, Bijan

    2017-09-01

    Measuring the flow of information that is related to the evolution of a system which is modeled by applying a mathematical structure is of capital significance for science and usually for mathematics itself. Regarding this fact, a major issue in concern with hyperstructures is their dynamics and the complexity of the varied possible dynamics that exist over them. Notably, the dynamics and uncertainty of hyper MV -algebras which are hyperstructures and extensions of a central tool in infinite-valued Lukasiewicz propositional calculus that models many valued logics are of primary concern. Tackling this problem, in this paper we focus on the subject of dynamical systems on hyper MV -algebras and their entropy. In this respect, we adopt two varied approaches. One is the set-based approach in which hyper MV -algebra dynamical systems are developed by employing set functions and set partitions. By the other method that is based on points and point partitions, we establish the concept of hyper injective dynamical systems on hyper MV -algebras. Next, we study the notion of entropy for both kinds of systems. Furthermore, we consider essential ergodic characteristics of those systems and their entropy. In particular, we introduce the concept of isomorphic hyper injective and hyper MV -algebra dynamical systems, and we demonstrate that isomorphic systems have the same entropy. We present a couple of theorems in order to help calculate entropy. In particular, we prove a contemporary version of addition and Kolmogorov-Sinai Theorems. Furthermore, we provide a comparison between the indispensable properties of hyper injective and semi-independent dynamical systems. Specifically, we present and prove theorems that draw comparisons between the entropies of such systems. Lastly, we discuss some possible relationships between the theories of hyper MV -algebra and MV -algebra dynamical systems.

  9. Complementarity and entanglement in quantum information theory

    NASA Astrophysics Data System (ADS)

    Tessier, Tracey Edward

    This research investigates two inherently quantum mechanical phenomena, namely complementarity and entanglement, from an information-theoretic perspective. Beyond philosophical implications, a thorough grasp of these concepts is crucial for advancing our understanding of foundational issues in quantum mechanics, as well as in studying how the use of quantum systems might enhance the performance of certain information processing tasks. The primary goal of this thesis is to shed light on the natures and interrelationships of these phenomena by approaching them from the point of view afforded by information theory. We attempt to better understand these pillars of quantum mechanics by studying the various ways in which they govern the manipulation of information, while at the same time gaining valuable insight into the roles they play in specific applications. The restrictions that nature places on the distribution of correlations in a multipartite quantum system play fundamental roles in the evolution of such systems and yield vital insights into the design of protocols for the quantum control of ensembles with potential applications in the field of quantum computing. By augmenting the existing formalism for quantifying entangled correlations, we show how this entanglement sharing behavior may be studied in increasingly complex systems of both theoretical and experimental significance. Further, our results shed light on the dynamical generation and evolution of multipartite entanglement by demonstrating that individual members of an ensemble of identical systems coupled to a common probe can become entangled with one another, even when they do not interact directly. The findings presented in this thesis support the conjecture that Hilbert space dimension is an objective property of a quantum system since it constrains the number of valid conceptual divisions of the system into subsystems. These arbitrary observer-induced distinctions are integral to the theory since

  10. Information-theoretic semi-supervised metric learning via entropy regularization.

    PubMed

    Niu, Gang; Dai, Bo; Yamada, Makoto; Sugiyama, Masashi

    2014-08-01

    We propose a general information-theoretic approach to semi-supervised metric learning called SERAPH (SEmi-supervised metRic leArning Paradigm with Hypersparsity) that does not rely on the manifold assumption. Given the probability parameterized by a Mahalanobis distance, we maximize its entropy on labeled data and minimize its entropy on unlabeled data following entropy regularization. For metric learning, entropy regularization improves manifold regularization by considering the dissimilarity information of unlabeled data in the unsupervised part, and hence it allows the supervised and unsupervised parts to be integrated in a natural and meaningful way. Moreover, we regularize SERAPH by trace-norm regularization to encourage low-dimensional projections associated with the distance metric. The nonconvex optimization problem of SERAPH could be solved efficiently and stably by either a gradient projection algorithm or an EM-like iterative algorithm whose M-step is convex. Experiments demonstrate that SERAPH compares favorably with many well-known metric learning methods, and the learned Mahalanobis distance possesses high discriminability even under noisy environments.

  11. Acetylcholine molecular arrays enable quantum information processing

    NASA Astrophysics Data System (ADS)

    Tamulis, Arvydas; Majauskaite, Kristina; Talaikis, Martynas; Zborowski, Krzysztof; Kairys, Visvaldas

    2017-09-01

    We have found self-assembly of four neurotransmitter acetylcholine (ACh) molecular complexes in a water molecules environment by using geometry optimization with DFT B97d method. These complexes organizes to regular arrays of ACh molecules possessing electronic spins, i.e. quantum information bits. These spin arrays could potentially be controlled by the application of a non-uniform external magnetic field. The proper sequence of resonant electromagnetic pulses would then drive all the spin groups into the 3-spin entangled state and proceed large scale quantum information bits.

  12. Information theory, spectral geometry, and quantum gravity.

    PubMed

    Kempf, Achim; Martin, Robert

    2008-01-18

    We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.

  13. The smooth entropy formalism for von Neumann algebras

    SciTech Connect

    Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

    2016-01-15

    We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

  14. The smooth entropy formalism for von Neumann algebras

    NASA Astrophysics Data System (ADS)

    Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

    2016-01-01

    We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

  15. Backward transfer entropy: Informational measure for detecting hidden Markov models and its interpretations in thermodynamics, gambling and causality

    PubMed Central

    Ito, Sosuke

    2016-01-01

    The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics. PMID:27833120

  16. Preface of the special issue quantum foundations: information approach

    PubMed Central

    2016-01-01

    This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory. PMID:27091161

  17. MIDER: Network Inference with Mutual Information Distance and Entropy Reduction

    PubMed Central

    Villaverde, Alejandro F.; Ross, John; Morán, Federico; Banga, Julio R.

    2014-01-01

    The prediction of links among variables from a given dataset is a task referred to as network inference or reverse engineering. It is an open problem in bioinformatics and systems biology, as well as in other areas of science. Information theory, which uses concepts such as mutual information, provides a rigorous framework for addressing it. While a number of information-theoretic methods are already available, most of them focus on a particular type of problem, introducing assumptions that limit their generality. Furthermore, many of these methods lack a publicly available implementation. Here we present MIDER, a method for inferring network structures with information theoretic concepts. It consists of two steps: first, it provides a representation of the network in which the distance among nodes indicates their statistical closeness. Second, it refines the prediction of the existing links to distinguish between direct and indirect interactions and to assign directionality. The method accepts as input time-series data related to some quantitative features of the network nodes (such as e.g. concentrations, if the nodes are chemical species). It takes into account time delays between variables, and allows choosing among several definitions and normalizations of mutual information. It is general purpose: it may be applied to any type of network, cellular or otherwise. A Matlab implementation including source code and data is freely available (http://www.iim.csic.es/~gingproc/mider.html). The performance of MIDER has been evaluated on seven different benchmark problems that cover the main types of cellular networks, including metabolic, gene regulatory, and signaling. Comparisons with state of the art information–theoretic methods have demonstrated the competitive performance of MIDER, as well as its versatility. Its use does not demand any a priori knowledge from the user; the default settings and the adaptive nature of the method provide good results for a wide

  18. Retrieving and routing quantum information in a quantum network

    NASA Astrophysics Data System (ADS)

    Sazim, S.; Chiranjeevi, V.; Chakrabarty, I.; Srinathan, K.

    2015-12-01

    In extant quantum secret sharing protocols, once the secret is shared in a quantum network ( qnet) it cannot be retrieved, even if the dealer wishes that his/her secret no longer be available in the network. For instance, if the dealer is part of the two qnets, say {{Q}}_1 and {{Q}}_2 and he/she subsequently finds that {{Q}}_2 is more reliable than {{Q}}_1, he/she may wish to transfer all her secrets from {{Q}}_1 to {{Q}}_2. Known protocols are inadequate to address such a revocation. In this work we address this problem by designing a protocol that enables the source/dealer to bring back the information shared in the network, if desired. Unlike classical revocation, the no-cloning theorem automatically ensures that the secret is no longer shared in the network. The implications of our results are multi-fold. One interesting implication of our technique is the possibility of routing qubits in asynchronous qnets. By asynchrony we mean that the requisite data/resources are intermittently available (but not necessarily simultaneously) in the qnet. For example, we show that a source S can send quantum information to a destination R even though (a) S and R share no quantum resource, (b) R's identity is unknown to S at the time of sending the message, but is subsequently decided, (c) S herself can be R at a later date and/or in a different location to bequeath her information (`backed-up' in the qnet) and (d) importantly, the path chosen for routing the secret may hit a dead end due to resource constraints, congestion, etc., (therefore the information needs to be back-tracked and sent along an alternate path). Another implication of our technique is the possibility of using insecure resources. For instance, if the quantum memory within an organization is insufficient, it may safely store (using our protocol) its private information with a neighboring organization without (a) revealing critical data to the host and (b) losing control over retrieving the data. Putting the

  19. Information dynamics and new geometric foundations of quantum theory

    NASA Astrophysics Data System (ADS)

    Kostecki, Ryszard Paweł

    2012-03-01

    We discuss new approach to mathematical foundations of quantum theory, which is completely independent of Hilbert spaces and measure spaces. New kinematics is defined by nonlinear geometry of spaces of integrals on abstract non-commutative algebras. New dynamics is defined by constrained maximisation of quantum relative entropy. We recover Hilbert space based approach (including unitary evolution and the von Neumann-Lüders rule) and measure theoretic approach to probability theory (including Bayes' rule) as special cases of our approach.

  20. Quantum Control, Quantum Information Processing, and Quantum-Limited Metrology with Trapped Ions

    NASA Astrophysics Data System (ADS)

    Wineland, D. J.; Leibfried, D.; Barrett, M. D.; Ben-Kish, A.; Bergquist, J. C.; Blakestad, R. B.; Bollinger, J. J.; Britton, J.; Chiaverini, J.; Demarco, B.; Hume, D.; Itano, W. M.; Jensen, M.; Jost, J. D.; Knill, E.; Koelemeij, J.; Langer, C.; Oskay, W.; Ozeri, R.; Reichle, R.; Rosenband, T.; Schaetz, T.; Schmidt, P. O.; Seidelin, S.

    2005-12-01

    We briefly discuss recent experiments on quantum information processing using trapped ions at NIST. A central theme of this work has been to increase our capabilities in terms of quantum computing protocols, but we have also applied the same concepts to improved metrology, particularly in the area of frequency standards and atomic clocks. Such work may eventually shed light on more fundamental issues, such as the quantum measurement problem.

  1. Scalability, Complexity and Reliability in Quantum Information Processing

    DTIC Science & Technology

    2007-03-01

    Information and Quantum Computation, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, “Quantum algorithm for the hidden shift...Future (and Past) of Quantum Lower Bounds by Polynomials,” October 17, 2002 W. van Dam, Workshop on Quantum Information and Quantum Computation, Abdus ... Salam International Centre for Theoretical Physics, Trieste, Italy, “Quantum algorithms: Fourier transforms and group theory,” October 21, 2002 K

  2. Generalized entanglement entropy

    NASA Astrophysics Data System (ADS)

    Taylor, Marika

    2016-07-01

    We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. Thesecond measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realised geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.

  3. Photonic Crystal Microcavities for Quantum Information Science

    NASA Astrophysics Data System (ADS)

    Hagemeier, Jenna Nicole

    Quantum information science and technology is a broad and fascinating field, encompassing diverse research areas such as materials science, atomic physics, superconductors, solid-state physics, and photonics. A goal of this field is to demonstrate the basic functions of information initialization, manipulation, and read-out in systems that take advantage of quantum physics to greatly enhance computing performance capabilities. In a hybrid quantum information network, different systems are used to perform different functions, to best exploit the advantageous properties of each system. For example, matter quantum bits (qubits) can be used for local data storage and manipulation while photonic qubits can be used for long-distance communication between storage points of the network. Our research focuses on the following two solid-state realizations of a matter qubit for the purpose of building such a hybrid quantum network: the electronic spin of a self-assembled indium arsenide quantum dot and the electronic spin of a nitrogen-vacancy defect center in diamond. Light--matter interactions are necessary to transfer the information from the matter qubit to the photonic qubit, and this interaction can be enhanced by embedding the spin system in an optical cavity. We focus on photonic crystal microcavities for this purpose, and we study interactions between the optical cavity modes and incorporated spin systems. To improve the performance of this spin--photon interface, it is important to maximize the coupling strength between the spin and photonic systems and to increase the read-out efficiency of information stored in the cavity. In this thesis, we present our work to deterministically couple a nitrogen-vacancy center in diamond to a photonic crystal microcavity in gallium phosphide. This is achieved by nanopositioning a pre-selected diamond nanocrystal in the intensity maximum of the optical cavity mode. We also present an optimized design of a photonic crystal

  4. Information security: from classical to quantum

    NASA Astrophysics Data System (ADS)

    Barnett, Stephen M.; Brougham, Thomas

    2012-09-01

    Quantum cryptography was designed to provide a new approach to the problem of distributing keys for private-key cryptography. The principal idea is that security can be ensured by exploiting the laws of quantum physics and, in particular, by the fact that any attempt to measure a quantum state will change it uncontrollably. This change can be detected by the legitimate users of the communication channel and so reveal to them the presence of an eavesdropper. In this paper I explain (briefly) how quantum key distribution works and some of the progress that has been made towards making this a viable technology. With the principles of quantum communication and quantum key distribution firmly established, it is perhaps time to consider how efficient it can be made. It is interesting to ask, in particular, how many bits of information might reasonably be encoded securely on each photon. The use of photons entangled in their time of arrival might make it possible to achieve data rates in excess of 10 bits per photon.

  5. Entropy of biogeochemical compartment models: complexity and information content as a tool for model development

    NASA Astrophysics Data System (ADS)

    Metzler, Holger; Sierra, Carlos A.

    2017-04-01

    Most soil organic matter decomposition models consist of a number of compartments describing the dynamics of substrate and microbial biomass pools. The fluxes of mass between the compartments are usually described by a system of ordinary differential equations, in which the number of compartments and the connections among them define the complexity of the model and the number of biological processes that need to be described. With this approach, it is difficult to determine the level of detail that is required to describe a given system, and it is also difficult to compare models against each other due to large differences in their level of complexity. Here, we propose entropy as a tool to determine the level of complexity required to describe a biogeochemical system and to compare the information content of different models. Instead of entire masses on bulk soil level, we look at such models from the point of view of a single particle on the molecular level. This particle enters the system, cycles through it, and leaves it at some point later in time, thereby following a path through the system. We think of this path as a particular stochastic process, a Markov renewal process. If we consider this path as a random variable in a path space, its Shannon information entropy describes its information content, i.e. how much we learn when we observe the entire path of a particle traveling through the system. In other words, it tells us how hard it is to predict this path and thus how much we do not know about what is going to happen to one single particle. The entropy as a measure of model complexity can help us to decide whether a model is not complex enough to represent the information that we have about a system or whether it is too complex. The concept of maximum entropy provides a powerful tool to develop unbiased models, i.e. models that contain the exact amount of information that we have about the system. In addition, differences between a soil organic matter

  6. Band target entropy minimization for retrieving the information of individual components from overlapping chromatographic data.

    PubMed

    Xia, Zhenzhen; Liu, Yan; Cai, Wensheng; Shao, Xueguang

    2015-09-11

    Band target entropy minimization (BTEM) is a self-modeling curve resolution (SMCR) approach relying on non-negative criterion and minimization of Shannon entropy. In this study, BTEM algorithm was applied to retrieving the information of individual components from overlapping gas chromatography-mass spectrometry (GC-MS) data. The algorithm starts with dividing the whole data into bands along the retention time. In each band, singular value decomposition (SVD) is used to decompose the data into scores and loadings. Because the pure chromatographic signal possesses the lowest Shannon entropy, the chromatographic signal of each component can be constructed by optimizing the combination of the loadings with minimal Shannon entropy under non-negative criterion. To show the efficiency of the algorithm, a simulated four-component overlapping GC-MS data and an experimental GC-MS data of 18 organophosphorus pesticide mixture are investigated. The results show that both the chromatographic profiles and mass spectra of the components can be successfully extracted from the overlapping signals. Copyright © 2015 Elsevier B.V. All rights reserved.

  7. Quantum information, oscillations and the psyche

    NASA Astrophysics Data System (ADS)

    Martin, F.; Carminati, F.; Galli Carminati, G.

    2010-05-01

    In this paper, taking the theory of quantum information as a model, we consider the human unconscious, pre-consciousness and consciousness as sets of quantum bits (qubits). We view how there can be communication between these various qubit sets. In doing this we are inspired by the theory of nuclear magnetic resonance. In this way we build a model of handling a mental qubit with the help of pulses of a mental field. Starting with an elementary interaction between two qubits we build two-qubit quantum logic gates that allow information to be transferred from one qubit to the other. In this manner we build a quantum process that permits consciousness to "read" the unconscious and vice versa. The elementary interaction, e.g. between a pre-consciousness qubit and a consciousness one, allows us to predict the time evolution of the pre-consciousness + consciousness system in which pre-consciousness and consciousness are quantum entangled. This time evolution exhibits Rabi oscillations that we name mental Rabi oscillations. This time evolution shows how for example the unconscious can influence consciousness. In a process like mourning the influence of the unconscious on consciousness, as the influence of consciousness on the unconscious, are in agreement with what is observed in psychiatry.

  8. Basing quantum theory on information processing

    NASA Astrophysics Data System (ADS)

    Barnum, Howard

    2008-03-01

    I consider information-based derivations of the quantum formalism, in a framework encompassing quantum and classical theory and a broad spectrum of theories serving as foils to them. The most ambitious hope for such a derivation is a role analogous to Einstein's development of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of this, it could still provide a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, helping guide the search for new quantum algorithms and protocols. I summarize the convex operational framework for theories, and discuss information-processing in theories therein. Results include the fact that information that can be obtained without disturbance is inherently classical, generalized no-cloning and no-broadcasting theorems, exponentially secure bit commitment in all non-classical theories without entanglement, properties of theories that allow teleportation, and properties of theories that allow ``remote steering'' of ensembles using entanglement. Joint work with collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner.

  9. Quantum Fisher information in noninertial frames

    NASA Astrophysics Data System (ADS)

    Yao, Yao; Xiao, Xing; Ge, Li; Wang, Xiao-guang; Sun, Chang-pu

    2014-04-01

    We investigate the performance of quantum Fisher information (QFI) under the Unruh-Hawking effect, where one of the observers (e.g., Rob) is uniformly accelerated with respect to other partners. In the context of relativistic quantum information theory, we demonstrate that quantum Fisher information, as an important measure of the information content of quantum states, has a rich and subtle physical structure compared with entanglement or Bell nonlocality. In this work, we mainly focus on the parametrized (and arbitrary) pure two-qubit states, where the weight parameter θ and phase parameter ϕ are naturally introduced. Intriguingly, we prove that QFI with respect to θ (Fθ) remains unchanged for both scalar and Dirac fields. Meanwhile, we observe that QFI with respect to ϕ (Fϕ) decreases with the increase of acceleration r but remains finite in the limit of infinite acceleration. More importantly, our results show that the symmetry of Fϕ (with respect to θ =π/4) has been broken by the influence of the Unruh effect for both cases.

  10. Quantum information processing by weaving quantum Talbot carpets

    NASA Astrophysics Data System (ADS)

    Farías, Osvaldo Jiménez; de Melo, Fernando; Milman, Pérola; Walborn, Stephen P.

    2015-06-01

    Single-photon interference due to passage through a periodic grating is considered in a novel proposal for processing D -dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free-space propagation naturally implements basic single-quDit gates by means of the Talbot effect: an intricate time-space carpet of light in the near-field diffraction regime. By adding a diagonal phase gate, we show that a complete set of single-quDit gates can be implemented. We then introduce a spatially dependent beam splitter that allows for projective measurements in the computational basis and can be used for the implementation of controlled operations between two quDits. Universal quantum information processing can then be implemented with linear optics and ancilla photons via postselection and feed-forward following the original proposal of Knill-Laflamme and Milburn. Although we consider photons, our scheme should be directly applicable to a number of other physical systems. Interpretation of the Talbot effect as a quantum logic operation provides a beautiful and interesting way to visualize quantum computation through wave propagation and interference.

  11. Life, Information, Entropy, and Time: Vehicles for Semantic Inheritance.

    PubMed

    Crofts, Antony R

    2007-01-01

    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 by

  12. Upper entropy axioms and lower entropy axioms

    SciTech Connect

    Guo, Jin-Li Suo, Qi

    2015-04-15

    The paper suggests the concepts of an upper entropy and a lower entropy. We propose a new axiomatic definition, namely, upper entropy axioms, inspired by axioms of metric spaces, and also formulate lower entropy axioms. We also develop weak upper entropy axioms and weak lower entropy axioms. Their conditions are weaker than those of Shannon–Khinchin axioms and Tsallis axioms, while these conditions are stronger than those of the axiomatics based on the first three Shannon–Khinchin axioms. The subadditivity and strong subadditivity of entropy are obtained in the new axiomatics. Tsallis statistics is a special case of satisfying our axioms. Moreover, different forms of information measures, such as Shannon entropy, Daroczy entropy, Tsallis entropy and other entropies, can be unified under the same axiomatics.

  13. The relation between majorization theory and quantum information from entanglement monotones perspective

    NASA Astrophysics Data System (ADS)

    Erol, V.

    2016-04-01

    Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.

  14. The relation between majorization theory and quantum information from entanglement monotones perspective

    SciTech Connect

    Erol, V.

    2016-04-21

    Entanglement has been studied extensively for understanding the mysteries of non-classical correlations between quantum systems. In the bipartite case, there are well known monotones for quantifying entanglement such as concurrence, relative entropy of entanglement (REE) and negativity, which cannot be increased via local operations. The study on these monotones has been a hot topic in quantum information [1-7] in order to understand the role of entanglement in this discipline. It can be observed that from any arbitrary quantum pure state a mixed state can obtained. A natural generalization of this observation would be to consider local operations classical communication (LOCC) transformations between general pure states of two parties. Although this question is a little more difficult, a complete solution has been developed using the mathematical framework of the majorization theory [8]. In this work, we analyze the relation between entanglement monotones concurrence and negativity with respect to majorization for general two-level quantum systems of two particles.

  15. Topological Quantum Information Processing Mediated Via Hybrid Topogical Insulator Structures

    DTIC Science & Technology

    2014-03-28

    AFRL-OSR-VA-TR-2013-0591 TOPOLOGICAL QUANTUM INFORMATION PROCESSING MEDIATED VIA HYBRID TOPOGICAL INSULAT Matthew Gilbert UNIVERSITY OF ILLINOIS...Virginia 22203 Air Force Research Laboratory Air Force Materiel Command Final Progress Report Title: Topological Quantum Information Processing...long been known to have the potential to perform universal quantum computation. To realize quantum computation with spins one needs an extraordinary

  16. Fusion information entropy method of rolling bearing fault diagnosis based on n-dimensional characteristic parameter distance

    NASA Astrophysics Data System (ADS)

    Ai, Yan-Ting; Guan, Jiao-Yue; Fei, Cheng-Wei; Tian, Jing; Zhang, Feng-Ling

    2017-05-01

    To monitor rolling bearing operating status with casings in real time efficiently and accurately, a fusion method based on n-dimensional characteristic parameters distance (n-DCPD) was proposed for rolling bearing fault diagnosis with two types of signals including vibration signal and acoustic emission signals. The n-DCPD was investigated based on four information entropies (singular spectrum entropy in time domain, power spectrum entropy in frequency domain, wavelet space characteristic spectrum entropy and wavelet energy spectrum entropy in time-frequency domain) and the basic thought of fusion information entropy fault diagnosis method with n-DCPD was given. Through rotor simulation test rig, the vibration and acoustic emission signals of six rolling bearing faults (ball fault, inner race fault, outer race fault, inner-ball faults, inner-outer faults and normal) are collected under different operation conditions with the emphasis on the rotation speed from 800 rpm to 2000 rpm. In the light of the proposed fusion information entropy method with n-DCPD, the diagnosis of rolling bearing faults was completed. The fault diagnosis results show that the fusion entropy method holds high precision in the recognition of rolling bearing faults. The efforts of this study provide a novel and useful methodology for the fault diagnosis of an aeroengine rolling bearing.

  17. Allowed region and optimal measurement for information versus disturbance in quantum measurements

    NASA Astrophysics Data System (ADS)

    Terashima, Hiroaki

    2017-10-01

    We present graphs of information versus disturbance for general quantum measurements of completely unknown states. Each piece of information and disturbance is quantified by two measures: (i) the Shannon entropy and estimation fidelity for the information and (ii) the operation fidelity and physical reversibility for the disturbance. These measures are calculated for a single outcome based on the general formulas derived by the present author (Terashima in Phys Rev A 93:022104, 2016) and are plotted on four types of information-disturbance planes to show their allowed regions. In addition, we discuss the graphs of these metrics averaged over all possible outcomes and the optimal measurements when saturating the upper bounds on the information for a given disturbance. The results considerably broaden the perspective of trade-offs between information and disturbances in quantum measurements.

  18. A Ranking Procedure by Incomplete Pairwise Comparisons Using Information Entropy and Dempster-Shafer Evidence Theory

    PubMed Central

    Pan, Dongbo; Lu, Xi; Liu, Juan; Deng, Yong

    2014-01-01

    Decision-making, as a way to discover the preference of ranking, has been used in various fields. However, owing to the uncertainty in group decision-making, how to rank alternatives by incomplete pairwise comparisons has become an open issue. In this paper, an improved method is proposed for ranking of alternatives by incomplete pairwise comparisons using Dempster-Shafer evidence theory and information entropy. Firstly, taking the probability assignment of the chosen preference into consideration, the comparison of alternatives to each group is addressed. Experiments verified that the information entropy of the data itself can determine the different weight of each group's choices objectively. Numerical examples in group decision-making environments are used to test the effectiveness of the proposed method. Moreover, the divergence of ranking mechanism is analyzed briefly in conclusion section. PMID:25250393

  19. Maximum information entropy principle and the interpretation of probabilities in statistical mechanics - a short review

    NASA Astrophysics Data System (ADS)

    Kuić, Domagoj

    2016-05-01

    In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt formalism is the logical extension of the Gibbs formalism of equilibrium statistical mechanics that is entirely independent of the frequentist interpretation of probabilities only as factual (i.e. experimentally verifiable) properties of the real world. Furthermore, we show that, consistently with the law of large numbers, the relative frequencies of the ensemble of systems prepared under identical conditions (i.e. identical constraints) actually correspond to the MaxEnt probabilites in the limit of a large number of systems in the ensemble. This result implies that the probabilities in statistical mechanics can be interpreted, independently of the frequency interpretation, on the basis of the maximum information entropy principle.

  20. Cooperative Localization for Multi-AUVs Based on GM-PHD Filters and Information Entropy Theory.

    PubMed

    Zhang, Lichuan; Wang, Tonghao; Zhang, Feihu; Xu, Demin

    2017-10-08

    Cooperative localization (CL) is considered a promising method for underwater localization with respect to multiple autonomous underwater vehicles (multi-AUVs). In this paper, we proposed a CL algorithm based on information entropy theory and the probability hypothesis density (PHD) filter, aiming to enhance the global localization accuracy of the follower. In the proposed framework, the follower carries lower cost navigation systems, whereas the leaders carry better ones. Meanwhile, the leaders acquire the followers' observations, including both measurements and clutter. Then, the PHD filters are utilized on the leaders and the results are communicated to the followers. The followers then perform weighted summation based on all received messages and obtain a final positioning result. Based on the information entropy theory and the PHD filter, the follower is able to acquire a precise knowledge of its position.

  1. Structural modelling and control design under incomplete parameter information: The maximum-entropy approach

    NASA Technical Reports Server (NTRS)

    Hyland, D. C.

    1983-01-01

    A stochastic structural control model is described. In contrast to the customary deterministic model, the stochastic minimum data/maximum entropy model directly incorporates the least possible a priori parameter information. The approach is to adopt this model as the basic design model, thus incorporating the effects of parameter uncertainty at a fundamental level, and design mean-square optimal controls (that is, choose the control law to minimize the average of a quadratic performance index over the parameter ensemble).

  2. Quantum preparation uncertainty and lack of information

    NASA Astrophysics Data System (ADS)

    Rozpędek, Filip; Kaniewski, Jędrzej; Coles, Patrick J.; Wehner, Stephanie

    2017-02-01

    The quantum uncertainty principle famously predicts that there exist measurements that are inherently incompatible, in the sense that their outcomes cannot be predicted simultaneously. In contrast, no such uncertainty exists in the classical domain, where all uncertainty results from ignorance about the exact state of the physical system. Here, we critically examine the concept of preparation uncertainty and ask whether similarly in the quantum regime, some of the uncertainty that we observe can actually also be understood as a lack of information (LOI), albeit a lack of quantum information. We answer this question affirmatively by showing that for the well known measurements employed in BB84 quantum key distribution (Bennett and Brassard 1984 Int. Conf. on Computer System and Signal Processing), the amount of uncertainty can indeed be related to the amount of available information about additional registers determining the choice of the measurement. We proceed to show that also for other measurements the amount of uncertainty is in part connected to a LOI. Finally, we discuss the conceptual implications of our observation to the security of cryptographic protocols that make use of BB84 states.

  3. Relations between work and entropy production for general information-driven, finite-state engines

    NASA Astrophysics Data System (ADS)

    Merhav, Neri

    2017-02-01

    We consider a system model of a general finite-state machine (ratchet) that simultaneously interacts with three kinds of reservoirs: a heat reservoir, a work reservoir, and an information reservoir, the latter being taken to be a running digital tape whose symbols interact sequentially with the machine. As has been shown in earlier work, this finite-state machine can act as a demon (with memory), which creates a net flow of energy from the heat reservoir into the work reservoir (thus extracting useful work) at the price of increasing the entropy of the information reservoir. Under very few assumptions, we propose a simple derivation of a family of inequalities that relate the work extraction with the entropy production. These inequalities can be seen as either upper bounds on the extractable work or as lower bounds on the entropy production, depending on the point of view. Many of these bounds are relatively easy to calculate and they are tight in the sense that equality can be approached arbitrarily closely. In their basic forms, these inequalities are applicable to any finite number of cycles (and not only asymptotically), and for a general input information sequence (possibly correlated), which is not necessarily assumed even stationary. Several known results are obtained as special cases.

  4. Entropy production due to Lorentz invariance violation

    NASA Astrophysics Data System (ADS)

    Mohammadzadeh, Hosein; Farahmand, Mehrnoosh; Maleki, Mahnaz

    2017-07-01

    It is generally believed that the concept of the spacetime continuum should be modified for distances as small as the Planck length. This is a length scale at which the spacetime might have a discrete structure and quantum gravity effects are dominant. Presumably, the microscopic fluctuations within the geometry of spacetime should result in an enormous entropy production. In the present work, we look for the effects of Lorentz invariance violation (LIV) in flat and curved backgrounds that can be measured by quantum entanglement and quantum thermodynamic entropies for scalar modes. Our results show that the general behavior of these entropies is the same. We also consider variations of the entropies with respect to LIV and cosmological and field parameters. Using the properties of these entropies, along with detecting the most entangled modes, we extract information about the past existence of LIV, which in turn might be useful in recovering the quantum structure of gravity. Indeed, the occurrence of a peak in the behavior of these entropies for a specific momentum could provide information about the expansion parameters. Moreover, information about the LIV parameter is codified in this peak.

  5. Quantum statistical entropy and minimal length of 5D Ricci-flat black string with generalized uncertainty principle

    SciTech Connect

    Liu Molin; Gui Yuanxing; Liu Hongya

    2008-12-15

    In this paper, we study the quantum statistical entropy in a 5D Ricci-flat black string solution, which contains a 4D Schwarzschild-de Sitter black hole on the brane, by using the improved thin-layer method with the generalized uncertainty principle. The entropy is the linear sum of the areas of the event horizon and the cosmological horizon without any cutoff and any constraint on the bulk's configuration rather than the usual uncertainty principle. The system's density of state and free energy are convergent in the neighborhood of horizon. The small-mass approximation is determined by the asymptotic behavior of metric function near horizons. Meanwhile, we obtain the minimal length of the position {delta}x, which is restrained by the surface gravities and the thickness of layer near horizons.

  6. Quantum information erasure inside black holes

    NASA Astrophysics Data System (ADS)

    Lowe, David A.; Thorlacius, Larus

    2015-12-01

    An effective field theory for infalling observers in the vicinity of a quasi-static black hole is given in terms of a freely falling lattice discretization. The lattice model successfully reproduces the thermal spectrum of outgoing Hawking radiation, as was shown by Corley and Jacobson, but can also be used to model observations made by a typical low-energy observer who enters the black hole in free fall at a prescribed time. The explicit short distance cutoff ensures that, from the viewpoint of the infalling observer, any quantum information that entered the black hole more than a scrambling time earlier has been erased by the black hole singularity. This property, combined with the requirement that outside observers need at least of order the scrambling time to extract quantum information from the black hole, ensures that a typical infalling observer does not encounter drama upon crossing the black hole horizon in a theory where black hole information is preserved for asymptotic observers.

  7. Hidden and unhidden information in quantum tunneling

    NASA Astrophysics Data System (ADS)

    Steinberg, A. M.; Kwiat, P. G.; Chiao, R. Y.

    1994-06-01

    We discuss the claim that when the peak of a tunneling wave packet appears on the far side of a barrier sooner than would be allowed by causal propagation of the incident peak, this must be interpreted to mean that the transmitted particles originate toward the leading edge of the incident peak. We examine the status of information about where in a wave packet a particle is, both in terms of Bohm's deterministic picture of quantum mechanics and in terms of a recently proposed Gedankenexperiment. We find that while there are very real senses in which this interpretation makes sense, attempts to explicitly bring out this extra information in the form of quantum-mechanical observables necessarily fail. It therefore remains “hidden” information, which we can deduce indirectly from multiple experiments or from the principle of causality, but which we can never observe directly in a single experiment.

  8. Quantum Information Processing with Trapped 43Ca+ Ions

    DTIC Science & Technology

    2008-03-18

    state 11 Fig.3: Deterministic quantum teleportation protocol 12 Fig.4: Density matrix of an entangled eight-ion state 13 Fig.5: Quantum process...4.3.4 Deterministic quantum teleportation Teleportation of a quantum state encompasses the complete transfer of information from one particle to...allow quantum -state teleportation to be performed. We succeeded in demonstrating deterministic quantum -state teleportation between a pair of trapped

  9. Optimal protocols for slowly driven quantum systems

    NASA Astrophysics Data System (ADS)

    Zulkowski, Patrick R.; DeWeese, Michael R.

    2015-09-01

    The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.

  10. Entropy Is Simple, Qualitatively.

    ERIC Educational Resources Information Center

    Lambert, Frank L.

    2002-01-01

    Suggests that qualitatively, entropy is simple. Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. (MM)

  11. Entropy Is Simple, Qualitatively.

    ERIC Educational Resources Information Center

    Lambert, Frank L.

    2002-01-01

    Suggests that qualitatively, entropy is simple. Entropy increase from a macro viewpoint is a measure of the dispersal of energy from localized to spread out at a temperature T. Fundamentally based on statistical and quantum mechanics, this approach is superior to the non-fundamental "disorder" as a descriptor of entropy change. (MM)

  12. Process-conditioned investing with incomplete information using maximum causal entropy

    NASA Astrophysics Data System (ADS)

    Ziebart, Brian D.

    2012-05-01

    Investing to optimally maximize the growth rate of wealth based on sequences of event outcomes has many information-theoretic interpretations. Namely, the mutual information characterizes the benefit of additional side information being available when making investment decisions [1] in settings where the probabilistic relationships between side information and event outcomes are known. Additionally, the relative variant of the principle of maximum entropy [2] provides the optimal investment allocation in the more general setting where the relationships between side information and event outcomes are only partially known [3]. In this paper, we build upon recent work characterizing the growth rates of investment in settings with inter-dependent side information and event outcome sequences [4]. We consider the extension to settings with inter-dependent event outcomes and side information where the probabilistic relationships between side information and event outcomes are only partially known. We introduce the principle of minimum relative causal entropy to obtain the optimal worst-case investment allocations for this setting. We present efficient algorithms for obtaining these investment allocations using convex optimization techniques and dynamic programming that illustrates a close connection to optimal control theory.

  13. Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective.

    PubMed

    Bylicka, B; Chruściński, D; Maniscalco, S

    2014-07-21

    Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.

  14. Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective

    PubMed Central

    Bylicka, B.; Chruściński, D.; Maniscalco, S.

    2014-01-01

    Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication. PMID:25043763

  15. An entropy-based approach for the identification of phylogenetically informative genomic regions of Papillomavirus.

    PubMed

    Batista, Marcus V A; Ferreira, Tiago A E; Freitas, Antonio C; Balbino, Valdir Q

    2011-12-01

    The papillomaviruses form a highly diverse group that infect mammals, birds and reptiles. We know little about their genetic diversity and therefore the evolutionary mechanisms that drive the diversity of these viruses. Genomic sequences of papillomaviruses are highly divergent and so it is important to develop methods that select the most phylogenetic informative sites. This study aimed at making use of a novel approach based on entropy to select suitable genomic regions from which to infer the phylogeny of papillomavirus. Comparative genomic analyzes were performed to assess the genetic variability of each gene of Papillomaviridae family members. Regions with low entropy were selected to reconstruct papillomavirus phylogenetic trees based on four different methods. This methodology allowed us to identify regions that are conserved among papillomaviruses that infect different hosts. This is important because, despite the huge variation among all papillomaviruses genomes, we were able to find regions that are clearly shared among them, presenting low complexity levels of information from which phylogenetic predictions can be made. This approach allowed us to obtain robust topologies from relatively small datasets. The results indicate that the entropy approach can successfully select regions of the genome that are good markers from which to infer phylogenetic relationships, using less computational time, making the estimation of large phylogenies more accessible.

  16. Analysing the information flow between financial time series . An improved estimator for transfer entropy

    NASA Astrophysics Data System (ADS)

    Marschinski, R.; Kantz, H.

    2002-11-01

    Following the recently introduced concept of transfer entropy, we attempt to measure the information flow between two financial time series, the Dow Jones and DAX stock index. Being based on Shannon entropies, this model-free approach in principle allows us to detect statistical dependencies of all types, i.e. linear and nonlinear temporal correlations. However, when available data is limited and the expected effect is rather small, a straightforward implementation suffers badly from misestimation due to finite sample effects, making it basically impossible to assess the significance of the obtained values. We therefore introduce a modified estimator, called effective transfer entropy, which leads to improved results in such conditions. In the application, we then manage to confirm an information transfer on a time scale of one minute between the two financial time series. The different economic impact of the two indices is also recovered from the data. Numerical results are then interpreted on one hand as capability of one index to explain future observations of the other, and on the other hand within terms of coupling strengths in the framework of a bivariate autoregressive stochastic model. Evidence is given for a nonlinear character of the coupling between Dow Jones and DAX.

  17. Markov and non-Markov processes in complex systems by the dynamical information entropy

    NASA Astrophysics Data System (ADS)

    Yulmetyev, R. M.; Gafarov, F. M.

    1999-12-01

    We consider the Markov and non-Markov processes in complex systems by the dynamical information Shannon entropy (DISE) method. The influence and important role of the two mutually dependent channels of entropy alternation (creation or generation of correlation) and anti-correlation (destroying or annihilation of correlation) have been discussed. The developed method has been used for the analysis of the complex systems of various natures: slow neutron scattering in liquid cesium, psychology (short-time numeral and pattern human memory and effect of stress on the dynamical taping-test), random dynamics of RR-intervals in human ECG (problem of diagnosis of various disease of the human cardio-vascular systems), chaotic dynamics of the parameters of financial markets and ecological systems.

  18. Quantum information sharing between topologically distinct platforms

    NASA Astrophysics Data System (ADS)

    Hou, Chang-Yu; Refael, Gil; Shtengel, Kirill

    2016-12-01

    Can topological quantum entanglement between anyons in one topological medium "stray" into a different, topologically distinct medium? In other words, can quantum information encoded nonlocally in the combined state of non-Abelian anyons be shared between two distinct topological media? For one-dimensional topological superconductors with Majorana bound states at the end of system, the quantum information store in those Majorana bound states can be transfered by directly coupling nearby Majorana bound states. However, coupling of two one-dimensional Majorana states will produce a gap, indicating that distinct topological regions of one-dimensional wires unite into a single topological region through the information transfer process. In this paper, we consider a setup with two two-dimensional p -wave superconductors of opposite chirality adjacent to each other. Even two comoving chiral modes at the domain wall between them cannot be gapped through interactions; we demonstrate that information encoded in the fermionic parity of two Majorana zero modes, originally within the same superconducting domain, can be shared between the domains or moved entirely from one domain to another provided that vortices can tunnel between them in a controlled fashion.

  19. Nano and Biological Technology Panel: Quantum Information Science

    DTIC Science & Technology

    2008-12-03

    Electrical Engineering & Telecommunications The University of New South Wales Nano and Biological Technology Panel: Quantum Information Science 26th US Army...Technology Panel: Quantum Information Science 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK...Business School Summary – Quantum Information Science • Quantum information technologies now a reality • First impacts will be secure communications

  20. Sharing the Quantum State and the Classical Information Simultaneously

    NASA Astrophysics Data System (ADS)

    Qin, Huawang; Dai, Yuewei

    2016-08-01

    An efficient quantum secret sharing scheme is proposed, in which the quantum state and the classical information can be shared simultaneously through only one distribution. The dealer uses the operations of quantum-controlled-not and Hadamard gate to encode the secret quantum state and classical information, and the participants use the single-particle measurements to recover the original quantum state and classical information. Compared to the existing schemes, our scheme is more efficient when the quantum state and the classical information need to be shared simultaneously.

  1. Complementarity of quantum discord and classically accessible information

    PubMed Central

    Zwolak, Michael; Zurek, Wojciech H.

    2013-01-01

    The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. We also prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. The resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.

  2. Complementarity of quantum discord and classically accessible information

    SciTech Connect

    Zwolak, Michael P.; Zurek, Wojciech H.

    2013-05-20

    The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an anti-symmetry property relating accessible information and discord. It shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. Lastly, the resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.

  3. Complementarity of quantum discord and classically accessible information

    DOE PAGES

    Zwolak, Michael P.; Zurek, Wojciech H.

    2013-05-20

    The sum of the Holevo quantity (that bounds the capacity of quantum channels to transmit classical information about an observable) and the quantum discord (a measure of the quantumness of correlations of that observable) yields an observable-independent total given by the quantum mutual information. This split naturally delineates information about quantum systems accessible to observers – information that is redundantly transmitted by the environment – while showing that it is maximized for the quasi-classical pointer observable. Other observables are accessible only via correlations with the pointer observable. In addition, we prove an anti-symmetry property relating accessible information and discord. Itmore » shows that information becomes objective – accessible to many observers – only as quantum information is relegated to correlations with the global environment, and, therefore, locally inaccessible. Lastly, the resulting complementarity explains why, in a quantum Universe, we perceive objective classical reality while flagrantly quantum superpositions are out of reach.« less

  4. Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

    NASA Technical Reports Server (NTRS)

    Isar, Aurelian

    1995-01-01

    The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

  5. Quantum distillation: Dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice

    SciTech Connect

    Heidrich-Meisner, F.; Manmana, S. R.; Rigol, M.; Muramatsu, A.; Feiguin, A. E.; Dagotto, Elbio R

    2009-01-01

    Correlations between particles can lead to subtle and sometimes counterintuitive phenomena. We analyze one such case, occurring during the sudden expansion of fermions in a lattice when the initial state has a strong admixture of double occupancies. We promote the notion of quantum distillation: during the expansion and in the case of strongly repulsive interactions, doublons group together, forming a nearly ideal band insulator, which is metastable with low entropy. We propose that this effect could be used for cooling purposes in experiments with two-component Fermi gases.

  6. PREFACE: Quantum Information, Communication, Computation and Cryptography

    NASA Astrophysics Data System (ADS)

    Benatti, F.; Fannes, M.; Floreanini, R.; Petritis, D.

    2007-07-01

    The application of quantum mechanics to information related fields such as communication, computation and cryptography is a fast growing line of research that has been witnessing an outburst of theoretical and experimental results, with possible practical applications. On the one hand, quantum cryptography with its impact on secrecy of transmission is having its first important actual implementations; on the other hand, the recent advances in quantum optics, ion trapping, BEC manipulation, spin and quantum dot technologies allow us to put to direct test a great deal of theoretical ideas and results. These achievements have stimulated a reborn interest in various aspects of quantum mechanics, creating a unique interplay between physics, both theoretical and experimental, mathematics, information theory and computer science. In view of all these developments, it appeared timely to organize a meeting where graduate students and young researchers could be exposed to the fundamentals of the theory, while senior experts could exchange their latest results. The activity was structured as a school followed by a workshop, and took place at The Abdus Salam International Center for Theoretical Physics (ICTP) and The International School for Advanced Studies (SISSA) in Trieste, Italy, from 12-23 June 2006. The meeting was part of the activity of the Joint European Master Curriculum Development Programme in Quantum Information, Communication, Cryptography and Computation, involving the Universities of Cergy-Pontoise (France), Chania (Greece), Leuven (Belgium), Rennes1 (France) and Trieste (Italy). This special issue of Journal of Physics A: Mathematical and Theoretical collects 22 contributions from well known experts who took part in the workshop. They summarize the present day status of the research in the manifold aspects of quantum information. The issue is opened by two review articles, the first by G Adesso and F Illuminati discussing entanglement in continuous variable

  7. Precisely timing dissipative quantum information processing.

    PubMed

    Kastoryano, M J; Wolf, M M; Eisert, J

    2013-03-15

    Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.

  8. Precisely Timing Dissipative Quantum Information Processing

    NASA Astrophysics Data System (ADS)

    Kastoryano, M. J.; Wolf, M. M.; Eisert, J.

    2013-03-01

    Dissipative engineering constitutes a framework within which quantum information processing protocols are powered by system-environment interaction rather than by unitary dynamics alone. This framework embraces noise as a resource and, consequently, offers a number of advantages compared to one based on unitary dynamics alone, e.g., that the protocols are typically independent of the initial state of the system. However, the time independent nature of this scheme makes it difficult to imagine precisely timed sequential operations, conditional measurements, or error correction. In this work, we provide a path around these challenges, by introducing basic dissipative gadgets which allow us to precisely initiate, trigger, and time dissipative operations while keeping the system Liouvillian time independent. These gadgets open up novel perspectives for thinking of timed dissipative quantum information processing. As an example, we sketch how measurement-based computation can be simulated in the dissipative setting.

  9. Holographic computations of the quantum information metric

    NASA Astrophysics Data System (ADS)

    Trivella, Andrea

    2017-05-01

    In this paper we show how the quantum information metric can be computed holographically using a perturbative approach. In particular when the deformation of the conformal field theory state is induced by a scalar operator the corresponding bulk configuration reduces to a scalar field perturbatively probing the background. We study two concrete examples: a CFT ground state deformed by a primary operator and thermofield double state in d  =  2 deformed by a marginal operator. Finally, we generalize the bulk construction to the case of a multi dimensional parameter space and show that the quantum information metric coincides with the metric of the non-linear sigma model for the corresponding scalar fields.

  10. Quantum Theory is an Information Theory

    NASA Astrophysics Data System (ADS)

    D'Ariano, Giacomo M.; Perinotti, Paolo

    2016-03-01

    In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

  11. Maximum joint entropy and information-based collaboration of automated learning machines

    NASA Astrophysics Data System (ADS)

    Malakar, N. K.; Knuth, K. H.; Lary, D. J.

    2012-05-01

    We are working to develop automated intelligent agents, which can act and react as learning machines with minimal human intervention. To accomplish this, an intelligent agent is viewed as a question-asking machine, which is designed by coupling the processes of inference and inquiry to form a model-based learning unit. In order to select maximally-informative queries, the intelligent agent needs to be able to compute the relevance of a question. This is accomplished by employing the inquiry calculus, which is dual to the probability calculus, and extends information theory by explicitly requiring context. Here, we consider the interaction between two questionasking intelligent agents, and note that there is a potential information redundancy with respect to the two questions that the agents may choose to pose. We show that the information redundancy is minimized by maximizing the joint entropy of the questions, which simultaneously maximizes the relevance of each question while minimizing the mutual information between them. Maximum joint entropy is therefore an important principle of information-based collaboration, which enables intelligent agents to efficiently learn together.

  12. Operator quantum Zeno effect: protecting quantum information with noisy two-qubit interactions.

    PubMed

    Wang, Shu-Chao; Li, Ying; Wang, Xiang-Bin; Kwek, Leong Chuan

    2013-03-08

    The time evolution of some quantum states can be slowed down or even stopped under frequent measurements. This is the usual quantum Zeno effect. Here, we report an operator quantum Zeno effect, in which the evolution of some physical observables is slowed down through measurements even though the quantum state changes randomly with time. Based on the operator quantum Zeno effect, we show how we can protect quantum information from decoherence with two-qubit measurements, realizable with noisy two-qubit interactions.

  13. Formal groups and Z-entropies

    NASA Astrophysics Data System (ADS)

    Tempesta, Piergiulio

    2016-11-01

    We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys. 365, 180-197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon-Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.

  14. Formal groups and Z-entropies.

    PubMed

    Tempesta, Piergiulio

    2016-11-01

    We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys.365, 180-197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon-Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.

  15. Information-theoretic temporal Bell inequality and quantum computation

    SciTech Connect

    Morikoshi, Fumiaki

    2006-05-15

    An information-theoretic temporal Bell inequality is formulated to contrast classical and quantum computations. Any classical algorithm satisfies the inequality, while quantum ones can violate it. Therefore, the violation of the inequality is an immediate consequence of the quantumness in the computation. Furthermore, this approach suggests a notion of temporal nonlocality in quantum computation.

  16. Quantum process discrimination with information from environment

    NASA Astrophysics Data System (ADS)

    Wang, Yuan-Mei; Li, Jun-Gang; Zou, Jian; Xu, Bao-Ming

    2016-12-01

    In quantum metrology we usually extract information from the reduced probe system but ignore the information lost inevitably into the environment. However, K. Mølmer [Phys. Rev. Lett. 114, 040401 (2015)] showed that the information lost into the environment has an important effect on improving the successful probability of quantum process discrimination. Here we reconsider the model of a driven atom coupled to an environment and distinguish which of two candidate Hamiltonians governs the dynamics of the whole system. We mainly discuss two measurement methods, one of which obtains only the information from the reduced atom state and the other obtains the information from both the atom and its environment. Interestingly, for the two methods the optimal initial states of the atom, used to improve the successful probability of the process discrimination, are different. By comparing the two methods we find that the partial information from the environment is very useful for the discriminations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11274043, 11375025, and 11005008).

  17. Biseparability of noisy pseudopure, W and GHZ states using conditional quantum relative Tsallis entropy

    NASA Astrophysics Data System (ADS)

    Nayak, Anantha S.; Sudha; Usha Devi, A. R.; Rajagopal, A. K.

    2017-02-01

    We employ the conditional version of sandwiched Tsallis relative entropy to determine 1:N-1 separability range in the noisy one-parameter families of pseudopure and Werner-like N-qubit W, GHZ states. The range of the noisy parameter, for which the conditional sandwiched Tsallis relative entropy is positive, reveals perfect agreement with the necessary and sufficient criteria for separability in the 1:N-1 partition of these one parameter noisy states.

  18. Quantifying control effort of biological and technical movements: an information-entropy-based approach.

    PubMed

    Haeufle, D F B; Günther, M; Wunner, G; Schmitt, S

    2014-01-01

    In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I=32 bits versus I=660 bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.

  19. Quantifying control effort of biological and technical movements: An information-entropy-based approach

    NASA Astrophysics Data System (ADS)

    Haeufle, D. F. B.; Günther, M.; Wunner, G.; Schmitt, S.

    2014-01-01

    In biomechanics and biorobotics, muscles are often associated with reduced movement control effort and simplified control compared to technical actuators. This is based on evidence that the nonlinear muscle properties positively influence movement control. It is, however, open how to quantify the simplicity aspect of control effort and compare it between systems. Physical measures, such as energy consumption, stability, or jerk, have already been applied to compare biological and technical systems. Here a physical measure of control effort based on information entropy is presented. The idea is that control is simpler if a specific movement is generated with less processed sensor information, depending on the control scheme and the physical properties of the systems being compared. By calculating the Shannon information entropy of all sensor signals required for control, an information cost function can be formulated allowing the comparison of models of biological and technical control systems. Exemplarily applied to (bio-)mechanical models of hopping, the method reveals that the required information for generating hopping with a muscle driven by a simple reflex control scheme is only I =32bits versus I =660bits with a DC motor and a proportional differential controller. This approach to quantifying control effort captures the simplicity of a control scheme and can be used to compare completely different actuators and control approaches.

  20. Geons and the quantum information metric

    NASA Astrophysics Data System (ADS)

    Sinamuli, Musema; Mann, Robert B.

    2017-07-01

    We investigate the proposed duality between a quantum information metric in a CFTd +1 and the volume of a maximum time slice in the dual AdSd +2 for topological geons. Examining the specific cases of Banados-Teitelboim-Zannelli (BTZ) black holes and planar Schwarzschild-anti-de Sitter black holes, along with their geon counterparts, we find that the proposed duality relation for geons is the same apart from a factor of 4. The information metric therefore provides a probe of the topology of the bulk spacetime.