Showing papers on "Coherent information published in 2004"
TL;DR: In this paper, it was shown that the contribution of spins greater than 1/2 to the entropy is not negligible, and the value of the Barbero-Immirzi parameter involved in the spectra of all the geometric and physical operators in this theory is different than previously derived.
Abstract: Quantum geometry (the modern loop quantum gravity involving graphs and spin-networks instead of the loops) provides microscopic degrees of freedom that account for black-hole entropy. However, the procedure for state counting used in the literature contains an error and the number of the relevant horizon states is underestimated. In our paper a correct method of counting is presented. Our results lead to a revision of the literature of the subject. It turns out that the contribution of spins greater than 1/2 to the entropy is not negligible. Hence, the value of the Barbero–Immirzi parameter involved in the spectra of all the geometric and physical operators in this theory is different than previously derived. Also, the conjectured relation between quantum geometry and the black-hole quasi-normal modes should be understood again.
440 citations
01 Jan 2004
TL;DR: In this article, the authors propose a model for processing information on p-Adic trees, which is based on the Vaxjo Interpretation of quantum mechanics and Bohmian mechanics for hierarchical information.
Abstract: List of Figures. Introduction. 1: Processing Information on p-Adic Trees. 1.1. Ultrametric Spaces. 1.2. m-adic Geometry. 1.3. Geometry of Information Spaces. 1.4. Dynamical Processing of Information. 1.5. Role of Hierarchical Structure. 1.6. Role of Chance in Processing of Cognitive Information. 1.7. Information Reductionism. 2: Hierarchy of Information. 2.1. Hierarchical Coding of Information. .2.2. Flows of Associations and Ideas. 2.3. How Can the Brain Play Dice? 2.4. Constraints on Information Spaces. 3: p-Adic Dynamical Systems. 3.1. p-Adic Numbers. 3.2. Roots of Unity. 3.3. Dynamical Systems in Non-Archimedian Fields. 3.4. Dynamical Systems in the Field of Complex p-adic Numbers. 3.5. Dynamical Systems in the Fields of p-adic Numbers. 3.6. p-adic Ergodicity. 3.7. Newton's Method (Hensel's Lemma). 3.8. Computer Calculations for Fuzzy Cycles. 4: Random Processing of Information. 4.1. Random Dynamical Systems. 4.2. Long-term Behaviour, Dynamics on the Attractor, Examples. 4.3. Consequences for Cognitive Sciences. 5: Information Quantum Mechanics. 5.1. Quantum-Like Formalism for a One-Layer Brain. 5.2. Motivation Observable. 5.3. Neuron Activation Observable. 5.4. Complex Cognitive Systems: Evolution. 6: Bohmian Mechanics on Information Spaces. 6.1. Newton Laws for Information Processes. 6.2. Bohmian Mechanics for Hierarchical Information. 6.3. Interactions between Information Systems. 6.4. Hamiltonian Equations and Active Information. 6.5. Information Mass. 6.6. Wave Functions Taking Values in p-adic Fields. 6.7. Information Waves on p-adic Trees. 6.8. p-adic Bohmian Mechanics and Waves of Brain Activation. 6.9. Conservation Laws. 6.10. Mechanics of a System of Information Transformers, Constraints on Information Spaces. 6.11. Social and Anomalous Phenomena. 7: Abstract Ultrametric Information Spaces. 7.1. Abstract Ultrametric Spaces. 7.2. Hierarchy of Associations. 7.3. Topology and Materialism. 7.4. Existence of Universal Mental Space. 7.5. Towers of Associations. 7.6. Infinite Information Towers. 8: Pathway Representation of Cognitive Information. 8.1. Model: Thinking on a Cognitive Tree. 8.2. Dynamics in the Information Space. 8.3. Diffusion Model for Dynamics of a Mental State. 8.4. Information Phase Space. 8.5. Mental State as the Distribution of a p-adic Random Walk. 8.6. Discussion of the Neural Pathways Thinking Model. 9: Contextual Approach to Quantum Theory. 9.1. The Vaxjo Interpretation of Quantum Mechanics. 9.2. Contextual Viewpoint of Quantum Stochastics. 9.3. Law of Statistical Balance in Nature. 9.4. Experiments on Quantum-Like Behaviour of the Mind. 9.5. Experimental Confirmation. 10: Frequency Analysis of Foundations of Quantum Mechanics. 10.1. Classification of Transforms of Probability. 10.2. Classical, Quantum and
228 citations
TL;DR: This work defines coherent communication in terms of a simple primitive, shows it is equivalent to the ability to send a classical message with a unitary or isometric operation, and uses it to relate other resources in quantum information theory.
Abstract: We define coherent communication in terms of a simple primitive, show it is equivalent to the ability to send a classical message with a unitary or isometric operation, and use it to relate other resources in quantum information theory. Using coherent communication, we are able to generalize superdense coding to prepare arbitrary quantum states instead of only classical messages. We also derive single-letter formulas for the classical and quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed amount of entanglement per use.
91 citations
TL;DR: It is proved that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory and for a subset of such channels, the optimal signal states are identified.
Abstract: We prove that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory. For a subset of such channels we explicitly identify the optimal signal states. We show analytically that for such a class of channels entangled states are indeed optimal above a given memory threshold.
88 citations
TL;DR: A model for correlated noise channels that includes a channel memory state is derived that shows that the structure of any finite-memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite- memory channel where no information is lost to the environment, achieving the upper bound implies that the channel is asymptonically noiseless.
Abstract: In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite-memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no information is lost to the environment, achieving the upper bound implies that the channel is asymptotically noiseless.
85 citations
TL;DR: In this article, the capacity of a memoryless communication channel cannot be increased by the use of feedback, and it is shown that feedback provides no increase in the entanglement-assisted capacities of the memoryless channel.
Abstract: In Shannon information theory, the capacity of a memoryless communication channel cannot be increased by the use of feedback. In quantum information theory, the no-cloning theorem means that noiseless copying and feedback of quantum information cannot be achieved. In this correspondence, quantum feedback is defined as the unlimited use of a noiseless quantum channel from receiver to sender. Given such quantum feedback, it is shown to provide no increase in the entanglement-assisted capacities of a memoryless quantum channel, in direct analogy to the classical case. It is also shown that in various cases of nonassisted capacities, feedback may increase the capacity of memoryless quantum channels.
56 citations
TL;DR: In this article, it was shown that the Bose-Einstein condensate (BEC) wave function can be modeled as a Gaussian-shaped feature in the BEC wave function.
Abstract: We theoretically explore coherent information transfer between ultraslow light pulses and Bose-Einstein condensates (BEC's) and find that storing light pulses in BEC's allows the coherent condensate dynamics to process optical information. We consider BEC's of alkali atoms with a $\ensuremath{\Lambda}$ energy level configuration. In this configuration, one laser (the coupling field) can cause a pulse of a second pulsed laser (the probe field) to propagate with little attenuation (electromagnetically induced transparency) at a very slow group velocity $(\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s})$ and be spatially compressed to lengths smaller than the BEC. These pulses can be fully stopped and later revived by switching the coupling field off and on. Here we develop a formalism, applicable in both the weak- and strong-probe regimes, to analyze such experiments and establish several results: (1) We show that the switching can be performed on time scales much faster than the adiabatic time scale for electromagnetically induced transparancy even in the strong-probe regime. We also study the behavior of the system changes when this time scale is faster than the excited state lifetime. (2) Stopped light pulses write their phase and amplitude information onto spatially dependent atomic wave functions, resulting in coherent two-component BEC dynamics during long storage times. We investigate examples relevant to $^{87}\mathrm{Rb}$ experimental parameters and see a variety of novel dynamics occur, including interference fringes, gentle breathing excitations, and two-component solitons, depending on the relative scattering lengths of the atomic states used and the probe to coupling intensity ratio. We find that the dynamics when the levels $\ensuremath{\mid}F=1,{M}_{F}=\ensuremath{-}1⟩$ and $\ensuremath{\mid}F=2,{M}_{F}=+1⟩$ are used could be well suited to designing controlled processing of the information input on the probe. (3) Switching the coupling field on after the dynamics writes the evolved BEC wave functions density and phase features onto a revived probe pulse, which then propagates out. We establish equations linking the BEC wave function to the resulting output probe pulses in both the strong- and weak-probe regimes. We then identify sources of deviations from these equations due to absorption and distortion of the pulses. These deviations result in imperfect fidelity of the information transfer from the atoms to the light fields and we calculate this fidelity for Gaussian-shaped features in the BEC wave functions. In the weak-probe case, we find that the fidelity is affected both by absorption of very-small-length-scale features and absorption of features occupying regions near the condensate edge. We discuss how to optimize the fidelity using these considerations. In the strong-probe case, we find that when the oscillator strengths for the two transitions are equal the fidelity is not strongly sensitive to the probe strength, while when they are unequal the fidelity is worse for stronger probes. Applications to distant communication between BEC's, squeezed light generation, and quantum information are anticipated.
50 citations
TL;DR: In this paper, the authors apply the Kolmogorov complexity (KCC) to the study of dynamical systems by considering the behavior of a 0-entropy dynamical system.
Abstract: We present some new results that relate information to chaotic
dynamics. In our approach the quantity of information is measured by the
Algorithmic Information Content (Kolmogorov complexity) or by a sort of
computable version of it (Computable Information Content) in which the information
is measured by using a suitable universal data compression algorithm.
We apply these notions to the study of dynamical systems by considering the
asymptotic behavior of the quantity of information necessary to describe their
orbits. When a system is ergodic, this method provides an indicator that equals
the Kolmogorov-Sinai entropy almost everywhere. Moreover, if the entropy is
null, our method gives new indicators that measure the unpredictability of the
system and allows various kind of weak chaos to be classified. Actually, this
is the main motivation of this work. The behavior of a 0-entropy dynamical
system is far to be completely predictable except that in particular cases.
In fact there are 0-entropy systems that exhibit a sort of weak chaos, where
the information necessary to describe the orbit behavior increases with time
more than logarithmically (periodic case) even if less than linearly (positive
entropy case). Also, we believe that the above method is useful to classify
0-entropy time series. To support this point of view, we show some theoretical
and experimental results in specific cases.
46 citations
TL;DR: In this paper, the authors give the trade-off curve showing the capacity of a quantum channel as a function of the amount of entanglement used by the sender and receiver for transmitting information.
Abstract: We give the trade-off curve showing the capacity of a quantum channel as a function of the amount of entanglement used by the sender and receiver for transmitting information. The endpoints of this curve are given by the Holevo-Schumacher-Westmoreland capacity formula and the entanglement-assisted capacity, which is the maximum over all input density matrices of the quantum mutual information. The proof we give is based on the Holevo-Schumacher-Westmoreland formula, and also gives a new and simpler proof for the entanglement-assisted capacity formula.
45 citations
TL;DR: This work shows how it introduces artifacts in quantum process tomography and explains how the resulting estimate of the superoperator may not be completely positive, and goes on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of thesuperoperator eigenvalue spectra.
Abstract: Incoherence in the controlled Hamiltonian is an important limitation on the precision of coherent control in quantum information processing. Incoherence can typically be modeled as a distribution of unitary processes arising from slowly varying experimental parameters. We show how it introduces artifacts in quantum process tomography and we explain how the resulting estimate of the superoperator may not be completely positive. We then go on to attack the inverse problem of extracting an effective distribution of unitaries that characterizes the incoherence via a perturbation theory analysis of the superoperator eigenvalue spectra.
45 citations
TL;DR: It is proved that bound information can be activated: three honest parties can distill a common secret key from different distributions having bound information, demonstrating that quantum information theory can provide useful insight for solving open problems in classical information theory.
Abstract: We prove the conjectured existence of bound information, a classical analog of bound entanglement, in the multipartite scenario We give examples of tripartite probability distributions from which it is impossible to extract any kind of secret key, even in the asymptotic regime, although they cannot be created by local operations and public communication Moreover, we show that bound information can be activated: three honest parties can distill a common secret key from different distributions having bound information Our results demonstrate that quantum information theory can provide useful insight for solving open problems in classical information theory
TL;DR: The idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms) leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights as discussed by the authors.
Abstract: Over the past decade, quantum information theory has developed into a vigorous field of research despite the fact that quantum information, as a precise concept, is undefined. Indeed, the very idea of viewing quantum states as carriers of some kind of information (albeit unknowable in classical terms) leads naturally to interesting questions that might otherwise never have been asked, and corresponding new insights. We discuss some illustrative examples, including a strengthening of the well-known no-cloning theorem leading to a property of permanence for quantum information, and considerations arising from information compression that reflect on fundamental issues.
TL;DR: In this article, the authors derived the expression of the maximum Fisher information achievable and its relation with that attainable in pure states and showed that this condition holds even in the more general setting of two-dimensional mixed state systems.
Abstract: We deal with the maximization of classical Fisher information in a quantum system depending on an unknown parameter. This problem has been raised by physicists, who defined [Helstrom (1967) Phys. Lett. A 25 101-102] a quantum counterpart of classical Fisher information, which has been found to constitute an upper bound for classical information itself [Braunstein and Caves (1994) Phys. Rev. Lett. 72 3439-3443]. It has then become of relevant interest among statisticians, who investigated the relations between classical and quantum information and derived a condition for equality in the particular case of two-dimensional pure state systems [Barndorff-Nielsen and Gill (2000) J. Phys. A 33 4481-4490]. In this paper we show that this condition holds even in the more general setting of two-dimensional mixed state systems. We also derive the expression of the maximum Fisher information achievable and its relation with that attainable in pure states.
TL;DR: In this paper, the authors review the experimental achievements made to date in two closely related areas of quantum information science, namely quantum state discrimination and classical information transmission using quantum states, and describe experimental implementations of two optimum discrimination strategies for a pair of nonorthogonal states.
Abstract: The purpose of this chapter is to review the experimental achievements made to date in two closely related areas of quantum information science. These are quantum state discrimination and classical information transmission using quantum states. In all experiments, the states were realised as quantum states of light. We begin by describing experimental implementations of two optimum discrimination strategies for a pair of nonorthogonal states. These are minimum error state discrimination and optimum unambiguous state discrimination. We then consider minimum error discrimination among certain, highly symmetrical sets of three and four states. The measurements involved were closely related to those required to attain the accessible information for such states. These measurements were also implemented. Subsequent accessible information experiments for up to seven quantum states are then described. The final experiment we discuss is an implementation of a novel, non-classical effect in quantum communications known as classical capacity superadditivity.
TL;DR: In this paper, the von Neumann entropy of a finite ensemble of pure quantum states is shown to be monotonically increasing in each of these variables, which suggests a geometrical interpretation of the quantum redundancy involved in the compression process.
Abstract: Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically increasing in each of these variables. Since S is the Schumacher compression limit of E, this monotonicity property suggests a geometrical interpretation of the quantum redundancy involved in the compression process. It provides clarification of previous work in which it was shown that S may be increased while increasing the overlap of each pair of states in the ensemble. As a by-product, our mathematical techniques also provide an interpretation of the subentropy of E.
TL;DR: In this paper, the existence of a natural ultraviolet cutoff at the Planck scale is widely expected and it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication.
Abstract: The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.
TL;DR: In this paper, a Cram\'er-Rao-type inequality is established for the Fisher information as a reciprocal lower bound for the mean-square errors of estimations by locally accessible observables.
Abstract: Quantum estimation theory provides optimal observations for various estimation problems for unknown parameters in the state of the system under investigation. However, the theory has been developed under the assumption that every observable is available for experimenters. Here, we generalize the theory to problems in which the experimenter can use only locally accessible observables. For such problems, we establish a Cram\'er-Rao-type inequality by obtaining an explicit form of the Fisher information as a reciprocal lower bound for the mean-square errors of estimations by locally accessible observables. Furthermore, we explore various local quantum estimation problems for composite systems, where nontrivial combinatorics is needed for obtaining the Fisher information.
TL;DR: In this article, the authors investigated the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver's particles sharing the quantum maximally entangled state.
Abstract: We investigate the dense coding in the case of non-symmetric Hilbert spaces of the sender and receiver's particles sharing the quantum maximally entangled state. The efficiency of gaining classical information is also considered. We conclude that when a more level particle is with the sender, she can obtain a non-symmetric quantum channel from a symmetric one by entanglement transfer. Thus the efficiency of information transmission is improved.
Posted Content•
TL;DR: It is shown that, if the concept of 'active information' in the Bohm interpretation is extended to cover thermal density matrices, then many of the conceptual problems raised by Szilard's paradox appear to be resolved.
Abstract: 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.
Posted Content•
TL;DR: In this article, it is shown that the Lieb-thirring inequality can be used to prove this conjecture for one special case, namely when one of the components of the product channel is of the type known as a diagonal channel, which acts on a state by taking the Hadamard product with a positive matrix.
Abstract: Quantum information theory has generated several interesting conjectures involving products of completely positive maps on matrix algebras, also known as quantum channels. In particular it is conjectured that the output state with maximal p-norm from a product channel is always a product state. It is shown here that the Lieb-Thirring inequality can be used to prove this conjecture for one special case, namely when one of the components of the product channel is of the type known as a diagonal channel, which acts on a state by taking the Hadamard product with a positive matrix.
TL;DR: The concept of quantum information isomorphism is proposed, according to which the quantum description of nature is isomorphic to nature itself, which allows the treatment of the wave function of isomorphic images of quantum systems in the laboratory, implying that quantumInformation is indeed carried by these quantum systems.
Abstract: In order to deal most effectively with the unanalyzable quantum whole, the Copenhagen interpretation takes as a "frame of reference" the preparation parameters and outcomes of measurements. It represents a passive, Ptolemaic-like instrumentalism directly related to "what we see in the sky," i.e., to the "surface" of reality. However, the notion of quantum information leads to an active, Copernican-like realism which involves an (intrinsic) ordering principle and the view that the quantum whole is analyzable. It is then possible to consider subsystems as localized in space, controlled individually, and communicated. This makes it natural to treat quantum information (quantum states) not merely as knowledge. Moreover, it involves complementarity between local and nonlocal information. To avoid the dilemma between the Scylla of ontology and the Charybdis of instrumentalism, we propose the concept of quantum information isomorphism, according to which the quantum description of nature is isomorphic to nature itself. By definition it is not just one-to-one mapping, but it preserves the full structure of nature. In particular, it allows the treatment of the wave function of isomorphic images of quantum systems in the laboratory, implying that quantum information is indeed carried by these quantum systems.
Posted Content•
TL;DR: The combinatorics of distributed EPR pairs are characterized for preparing multi-partite entanglement in a real communication network and an idea to combine the features of quantum key distribution and quantum secret sharing is proposed.
Abstract: We investigate the exploitation of various combinatorial properties of graphs and set systems to study several issues in quantum information theory. We characterize the combinatorics of distributed EPR pairs for preparing multi-partite entanglement in a real communication network. This combinatorics helps in the study of various problems in multi-party case by just reducing to the two-party case. Particularly, we use this combinatorics to (1) study various possible and impossible transformations of multi-partite states under LOCC, thus presenting an entirely new approach, not based on entropic criterion, to study such state transformations. (2) present a protocol and proof of its unconditional security for quantum key distribution amongst several trusted parties. (3) propose an idea to combine the features of quantum key distribution and quantum secret sharing. We investigate all the above issues in great detail and finally conclude briefly with some open research directions based on our research.
Journal Article•
TL;DR: It is proved that the rate of the information dissipation is equal to the rateOf information entropy production (or decrease) in the dynamic system, and that information diffusion and information Dissipation happen at the same time.
Abstract: Static statistical information theory is extended to dynamic processes and a dynamical statistical information theory is built up, whose subject is the evolution law of the information entropy and information of dynamical systems. Starting from the state variable evolution equation nonlinear evolution equations of dynamic information entropy density and dynamic information density are derived, that describes respectively the evolution law of information entropy and information. These two equations show that the time rate of change of information entropy density originates together from the drift, diffusion and production in coodinate space and state variable space; and that the time rate of change of information density is caused by the drift, diffusion and dissipation in coodinate space and state variable space. Expressions of drift information flow and diffusion information flow, and concise formulas of information dissipation rate and information entropy production rate are given. It is proved that the rate of the information dissipation (or increase) is equal to the rate of information entropy production (or decrease) in the dynamic system, and that information diffusion and information dissipation happen at the same time. Dynamic mutual information reflecting the dynamic character in the transmission process is presented, which in the limiting case when the proportion of channel length to signal transmission rate approaches zero reduces itself to the present static mutual information. All the above results are derived in a unified fasion from evolution equations of information and information entropy without the addition of any extra assumptions. As exampless of application of the above theoretical formulation, information and information entropy as well as their time rates for three dynamic topics are investigated, viz.: the drift-diffusion transmission of Brownian motion, the kinetics of production of thermal defects, and molecular motors; and the dynamic mutual information of the Gaussian channel are presented.
TL;DR: In this paper, a continuous variables method of quantum key distribution employing strongly polarized coherent states of light is discussed, where the key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures.
Abstract: We discuss a continuous variables method of quantum key distribution employing strongly polarized coherent states of light. The key encoding is performed using the variables known as Stokes parameters, rather than the field quadratures. Their quantum counterpart, the Stokes operators $\hat{S}_i$ (i=1,2,3), constitute a set of non-commuting operators, being the precision of simultaneous measurements of a pair of them limited by an uncertainty-like relation. Alice transmits a conveniently modulated two-mode coherent state, and Bob randomly measures one of the Stokes parameters of the incoming beam. After performing reconciliation and privacy amplification procedures, it is possible to distill a secret common key. We also consider a non-ideal situation, in which coherent states with thermal noise, instead of pure coherent states, are used for encoding.
TL;DR: In this article, the entanglement of pair coherent states in the phase damping channel was investigated and a scheme for teleportation via pair-consistent coherent states was proposed, and the fidelity of the scheme was analyzed.
Abstract: We investigate the entanglement of pair coherent states in the phase damping channel by adopting the relative entropy of entanglement and propose a protocol of teleportation via pair coherent states The fidelity of the protocol is then analyzed and the influence of phase damping on the teleportation fidelity examined
TL;DR: A family of bipartite quantum Gaussian states with three parameters is studied analytically and the upper bound of relative entropy of entanglement and distillableEntanglement of the states with infinitive squeezing is determined.
Abstract: I study a family of bipartite quantum Gaussian states with three parameters, calculate Gaussian entanglement of formation analytically and the upper bound of relative entropy of entanglement, compare them with the coherent information of the states. Based on the numerical observation, I determine the relative entropy of entanglement and distillable entanglement of the states with infinitive squeezing.
TL;DR: In this paper, an information-theoretic description of induced transitions between stationary states in the space of control parameters is given for nonextensive self-organized systems, and the S-and I-theorems on changes in nonadditive entropy and information difference measures are proved in the general form when the effective Hamiltonian function is unknown.
Abstract: An information-theoretic description of induced transitions between stationary states in the space of control parameters is given for nonextensive self-organized systems. The S- and I-theorems on changes in nonadditive entropy and information difference measures are proved in the general form when the effective Hamiltonian function is unknown. The statistical method is used to derive the q-entropy and q-information difference depending on the distribution seminorm.
Posted Content•
01 Dec 2004
TL;DR: In this article, it was shown that the Holevo bound can be further extended to obtain one which is yet again tighter for inefficient measurements, which is a quantum version of the concavity of the mutual information.
Abstract: The Holevo bound is a bound the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland and Wootters [Schumacher, Westmoreland and Wootters, Phys. Rev. Lett. 76, 3452 (1996)] derived a bound which reduces to the Holevo bound for complete measurements, but which is tighter for incomplete measurements. The most general quantum operations may be both incomplete and inefficient. Here we show that the bound derived by SWW can be further extended to obtain one which is yet again tighter for inefficient measurements. This allows us in addition to obtain a generalization of a bound derived by Hall, and to show that the average reduction in the von Neumann entropy during a quantum operation is concave in the initial state, for all quantum operations. This is a quantum version of the concavity of the mutual information. We also show that both this average entropy reduction, and the mutual information for pure state ensembles, are Schur-concave for unitarily covariant measurements; that is, for these measurements, information gain increases with initial uncertainty.
Posted Content•
TL;DR: In this article, the strong relation between information theory and physics is discussed, beginning with the concept of bit and its representation with classical physical systems, and then going to the quantum bit and exposing some differences and similarities.
Abstract: This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, beginning by the concept of bit and its representation with classical physical systems, and then going to the concept of quantum bit (the so-called ``qubit'') and exposing some differences and similarities. This paper is intended to be read by non-specialists and undergraduate students of Computer Science, Mathematics and Physics, with knowledge of Linear Algebra and Quantum Mechanics.