Showing papers on "Coherent information published in 1998"
TL;DR: In this article, the capacity of a classical-quantum channel with arbitrary (possibly mixed) states was shown to be the maximum of the entropy bound with respect to all a priori distributions.
Abstract: It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland, and Wootters (1996), who proved the equality for the pure state channel.
1,032 citations
TL;DR: In this article, it is shown that in high temperature ensemble quantum computation, it is possible to perform interesting physics simulations that have no known efficient classical algorithms, even though the model is less powerful than standard quantum computation in the presence of oracles.
Abstract: In standard quantum computation, the initial state is pure and the answer is determined by making a measurement of some of the bits in the computational basis. What can be accomplished if the initial state is a highly mixed state and the answer is determined by measuring the expectation of ${\ensuremath{\sigma}}_{z}$ on the first bit with bounded sensitivity? This is the situation in high temperature ensemble quantum computation. We show that in this model it is possible to perform interesting physics simulations that have no known efficient classical algorithms, even though the model is less powerful than standard quantum computation in the presence of oracles.
779 citations
TL;DR: It is shown that different applications may result in different channel capacities, and upper bounds on several of these capacities are proved based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory.
Abstract: Noisy quantum channels may be used in many information-carrying applications. We show that different applications may result in different channel capacities. Upper bounds on several of these capacities are proved. These bounds are based on the coherent information, which plays a role in quantum information theory analogous to that played by the mutual information in classical information theory. Many new properties of the coherent information and entanglement fidelity are proved. Two nonclassical features of the coherent information are demonstrated: the failure of subadditivity, and the failure of the pipelining inequality. Both properties arise as a consequence of quantum entanglement, and give quantum information new features not found in classical information theory. The problem of a noisy quantum channel with a classical observer measuring the environment is introduced, and bounds on the corresponding channel capacity proved. These bounds are always greater than for the unobserved channel. We conclude with a summary of open problems.
409 citations
TL;DR: This was significantly extended from the previous article quant-ph/9705043,especially in an information theoretic aspect, by adding new results.
Abstract: We consider a channel coding for sending classical information through a quantum channel with a given ensemble of quantum states (letter states). As is well known, it is generically possible in a quantum channel that the transmittable information in block coding of length $n$ can exceed $n$ times the maximum amount that can be sent without any coding scheme. This so-called superadditivity in classical capacity of a quantum channel is a distinct feature that cannot be found in a classical memoryless channel. In this paper, a practical model of channel coding that shows this property is presented. It consists of a simple code-word selection and the optimum decoding of the code words minimizing the average error probability. At first, optimization of decoding strategy is discussed. Then the channel coding that shows the superadditivity in classical capacity is demonstrated.
124 citations
TL;DR: A brief history of this interaction between information theory and entropy, together with a more detailed look at three areas of connection, namely, recurrence theory, blowing-up bounds, and direct sample-path methods.
Abstract: Information theorists frequently use the ergodic theorem; likewise entropy concepts are often used in information theory. Recently, the two subjects have become partially intertwined as deeper results from each discipline find use in the other. A brief history of this interaction is presented in this paper, together with a more detailed look at three areas of connection, namely, recurrence theory, blowing-up bounds, and direct sample-path methods.
77 citations
TL;DR: It is shown that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information, and the coherent information maximized over all sources and block sizes, but not encodings, is used to bound the quantum capacity.
Abstract: We show that no source encoding is needed in the definition of the capacity of a quantum channel for carrying quantum information. This allows us to use the coherent information maximized over all sources and block sizes, but not encodings, to bound the quantum capacity. We perform an explicit calculation of this maximum coherent information for the quantum erasure channel and apply the bound in order find the erasure channel's capacity without relying on an unproven assumption as in an earlier paper.
28 citations
TL;DR: This work introduces a natural and compelling fourth assumption: if there is no reason to prefer one region of the configuration space over another, then they should be “weighted” equally, the last ingredient necessary to introduce a unique inner product in the linear space of wave functions.
Abstract: The objective of the consistent-amplitude approach to quantum theory has been to justify the mathematical formalism on the basis of three main assumptions: the first defines the subject matter, the second introduces amplitudes as the tools for quantitative reasoning, and the third is an interpretative rule that provides the link to the prediction of experimental outcomes. In this work we introduce a natural and compelling fourth assumption: if there is no reason to prefer one region of the configuration space over another then they should be `weighted' equally. This is the last ingredient necessary to introduce a unique inner product in the linear space of wave functions. Thus, a form of the principle of insufficient reason is implicit in the Hilbert inner product. Armed with the inner product we obtain two results. First, we elaborate on an earlier proof of the Born probability rule. The implicit appeal to insufficient reason shows that quantum probabilities are not more objective than classical probabilities. Previously we had argued that the consistent manipulation of amplitudes leads to a linear time evolution; our second result is that time evolution must also be unitary. The argument is straightforward and hinges on the conservation of entropy. The only subtlety consists of defining the correct entropy; it is the array entropy, not von Neumann's. After unitary evolution has been established we proceed to introduce the useful notion of observables and we explore how von Neumann's entropy can be linked to Shannon's information theory. Finally, we discuss how various connections among the postulates of quantum theory are made explicit within this approach.
28 citations
TL;DR: In this paper, a nonlinear electrical network modeling the generalized Nagumo equation is considered, where the initial load of the lattice consists in the superimposition of a coherent information weakly varying in space and a perturbation of small amplitude.
Abstract: We consider a nonlinear electrical network modeling the generalized Nagumo equation. Focusing on the particular case where the initial load of the lattice consists in the superimposition of a coherent information weakly varying in space and a perturbation of small amplitude, we show that the perturbation can be eliminated quickly, almost without disturbing the information.
21 citations
TL;DR: The recognition activity of biomacromolecules based on quantum non-demolition measurements is regarded as the basis of information processing and Reflective arrows in the set of mappings appearing from quantum measurements correspond to the Gödel numbers created inside a system overcoming its incompleteness.
Abstract: The recognition activity of biomacromolecules based on quantum non-demolition measurements is regarded as the basis of information processing. Reflective arrows in the set of mappings appearing from quantum measurements correspond to the Godel numbers created inside a system overcoming its incompleteness. Temporal evolution is a consequence of contradictory statements about the whole system in which a reflective arrow is both an element of the system and its signification. It results from the solution of a paradox in which the system generates new descriptions non-deducible from its previous states. The active combinatorial process of self modification of information, being an internalized language game, allows a system to create Godel numbers. The whole system is constructed according to percolating coherent events, providing 'vertical' self-assembly that is predetermined by the encoding and internal language games. © 1998 Elsevier Science Ireland Ltd. All rights reserved.
20 citations
TL;DR: An investigation of Einstein's "physical" reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schrodinger-cat paradoxes.
Abstract: An investigation of Einstein's "physical" reality and the concept of quantum reality in terms of information theory suggests a solution to quantum paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schrodinger-cat paradoxes. Quantum reality, the picture based on unitarily evolving wavefunctions, is complete, but appears incomplete from the observer's point of view for fundamental reasons arising from the quantum information theory of measurement. Physical reality, the picture based on classically accessible observables is, in the worst case of EPR experiments, unrelated to the quantum reality it purports to reflect. Thus, quantum information theory implies that only correlations, not the correlata, are physically accessible: the mantra of the Ithaca interpretation of quantum mechanics.
19 citations
TL;DR: The maximum mutual information without coding is investigated for binary quantum-state signals and the truemaximum mutual information is numerically analysed for the binary case.
Abstract: The maximum mutual information without coding is investigated for binary quantum-state signals. The necessary condition for detection operators to represent the information optimal detection is satisfied for M-ary symmetric quantum-state signals by the detection operators derived from the quantum minimax strategy while its purpose is a minimization of the error probability. The true maximum mutual information is numerically analysed for the binary case.
TL;DR: In this paper, the Shannon-Wehrl entropy is used to measure deviation from classicality in quantum systems and the von Neumann entropy plays the same role in open quantum systems.
Abstract: We study information measures in quantum mechanics, with the particular emphasis on providing a quantification of the notion of predictability and classicality. Our primary tool is the Shannon-Wehrl entropy I. We give a precise criterion for phase space classicality of states and argue that in view of this (a) I provides a good measure for the degree of deviation from classicality in closed systems and (b) $I\ensuremath{-}S (S$ the von Neumann entropy) plays the same role in open quantum system. We examine particular examples in nonrelativistic quantum mechanics. Finally we generalize the discussion into the field theory case, and (this being one of our main motivations) we comment on the field classicalization in early universe cosmology.
TL;DR: A formula of Bures fidelity for displaced squeezed thermal states directly by the displacement and squeezing parameters is given and birefly discuss how the results can apply to quantum information theory.
Abstract: Fidelity plays a key role in quantum information and communication theory. Fidelity can be interpreted as the probability that a decoded message possesses the same information content as the message prior to coding and transmission. In this paper, we give a formula of Bures fidelity for displaced squeezed thermal states directly by the displacement and squeezing parameters and birefly discuss how the results can apply to quantum information theory.
25 Nov 1998
TL;DR: The description problem of searching and decision-making support processes from more fundamental mutual positions of the new information technologies and a modern physics, information physics, are discussed.
Abstract: Principles of quantum soft computing, models of fast quantum searching algorithms and the possibility of its applications for intelligent control of micro-systems are introduced. The description problem of searching and decision-making support processes from more fundamental mutual positions of the new information technologies and a modern physics, information physics, are discussed: (1) in the quantum information theory-the information complexity theory of random symbolic sequences, computation complexity, quantum searching algorithms; and (2) in the modern physics-nonequilibrium thermodynamics and quantum mechanics.
21 Mar 1998
TL;DR: A quantum computer-a new type of machine that exploits the quantum properties of information could perform certain types of calculations far more efficiently than any foreseeable classical computer.
Abstract: Information is something that can be encoded in the state of a physical system, and a computation is a task that can be performed with a physically realizable device. Therefore, since the physical world is fundamentally quantum mechanical, the foundations of information theory and computer science should be sought in quantum physics. In fact, quantum information has weird properties that contrast sharply with the familiar properties of classical information. A quantum computer-a new type of machine that exploits the quantum properties of information-could perform certain types of calculations far more efficiently than any foreseeable classical computer. To build a functional quantum computer will be an enormous technical challenge. New methods for quantum error correction are being developed that can help to prevent a quantum computer from crashing.
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TL;DR: In this paper, a lower bound on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source emission was derived, involving coherent information.
Abstract: I introduce rate-distortion theory for quantum coding, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to encode a quantum source with a given maximum level of distortion per source emission. The convexity of the "information rate-distortion function" which defines this bound is also derived.
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TL;DR: In this article, quantum mutual information, loss, noise and coherent information for a Bosonic attenuation/amplification channel with input Gaussian state was calculated. But the coherent information was shown to be negative for the values of the attenuation coefficient $k < 1/\sqrt{2}$.
Abstract: Quantum information characteristics, such as quantum mutual information, loss, noise and coherent information are explicitly calculated for Bosonic attenuation/amplification channel with input Gaussian state. The coherent information is shown to be negative for the values of the attenuation coefficient $k<1/\sqrt{2}$.
17 Feb 1998
TL;DR: It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities of quantum information theory.
Abstract: The concepts of conditional entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum one is that the entropy and information in quantum systems. The fundamental difference between the classical case and the quantum one is that the entropy and information in quantum systems depend on the choice of measurements performed over the systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities. Specific quantum phenomena such as EPR pairs and "superdense coding" are described and explained in terms of the generalized conditional entropy and information.
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TL;DR: In this article, the introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables, and a preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.
Abstract: Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time regularization that may involve a Wiener measure concentrated on continuous phase space paths. The introduction of constraints is both natural and economical in coherent state path integrals involving only the dynamical and Lagrange multiplier variables. A preliminary indication of how these procedures may possibly be applied to quantum gravity is briefly discussed.
TL;DR: An abstract framework for the local online unsupervised learning of this coherent information using multi-stream neural networks is presented and it is shown that all the rules scale up with the number of streams.
17 Feb 1998
TL;DR: This work investigates physically important case when information is transported by states of an electromagnetic field, and one-way communication by noisy quantum channels is considered.
Abstract: The accessible information in multi-access quantum channels are considered. Classical messages from independent sources, which are represented as some quantum states, are transported by a channel to one address. The messages can interact with each other and with external environment. After statement of problem and proving some general results we investigate physically important case when information is transported by states of an electromagnetic field. One-way communication by noisy quantum channels is also considered.
TL;DR: In this paper, possible modifications of the Calogero-Vasiliev quantum condition are considered and the problem of constructing coherent states is addressed, and a solution to the problem is given.
Abstract: We consider possible modifications of the Calogero–Vasiliev quantum condition and address the problem of construction of coherent states.
TL;DR: In this article, an orthogonal tetrat basis element made up of two photons can be generated with two optical parametric down-converters and identified with a multiport detection system for coincidences.
Abstract: This work shows that an orthogonal tetrat basis element made up of two photons can be generated with two optical parametric down-converters and identified with a multiport detection system for coincidences. The transmission gain over the usual coding in bits is $g=2.$ The information is assigned to each photon pair using a single conjugate beam of the parametric down-conversion. This system also demonstrates a way to get a pair of disentangled polarized photons by handling just one photon of an entangled pair.
16 Aug 1998
TL;DR: In this paper, the concepts of conditional entropy of a physical system given the state of another system and of information in a physical systems about another one are generalized for quantum systems and it is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities.
Abstract: The concepts of conditional entropy of a physical system given the state of another system and of information in a physical system about another one are generalized for quantum systems. It is shown that some equalities of the classical information theory turn into inequalities for the generalized quantities.
17 Feb 1998
TL;DR: In this article, the authors derive relation between a quantum channel's capacity to convey classical information and its ability to convey quantum information and show that these properties are related to the channel's ability to communicate quantum coherent information.
Abstract: We derive relation between a quantum channel's capacity to convey classical information and its ability to convey quantum information. We also show that these properties of a quantum channel are related to the channel's ability to convey quantum coherent information.
17 Feb 1998
TL;DR: This work has proved strengthened data processing inequality in quantum information theory and applied this results for proving a generalized H-theorem in non equilibrium thermodynamics.
Abstract: Strengthened Lindblad inequality has been proved. We have applied this results for proving a generalized H-theorem in non equilibrium thermodynamics. Information processing also can be considered as some thermodynamically process. From this point of view we have proved strengthened data processing inequality in quantum information theory.
TL;DR: In this paper, the structure of the spaces of propositions and decoherence functions in the consistent-histories approach to generalized quantum theory is outlined, and a definition of information-entropy is described which no need no a priori notion of time.
Abstract: The structure of the spaces of propositions anddecoherence functions in the consistent-historiesapproach to generalized quantum theory is outlined. Itis shown that although the space of decoherencefunctions is convex, there are no pure decoherencefunctions. A definition of information-entropy isdescribed which no needs no a priori notion oftime.
TL;DR: In this article, the notion of diabatic andadiabatic forces exerted by the quantum object on the classical measurement apparatus is discussed, and the relationship between information entropy and thermodynamic entropy is explored.
Abstract: In order to understand the Landau-Lifshitz conjecture on the relationship between quantum measurements and the thermodynamic second law, we discuss the notion of ``diabatic'' and ``adiabatic'' forces exerted by the quantum object on the classical measurement apparatus. The notion of heat and work in measurements is made manifest in this approach, and the relationship between information entropy and thermodynamic entropy is explored.
14 Sep 1998
TL;DR: In this article, the authors analyzed a general quantum channel and described how entanglement changes due to interaction with the environment, and derived the Holevo bound and the number of entangled optical modes transmitted through a quantum channel.
Abstract: Summary form only given. We analyze a general quantum channel, and describe how entanglement changes due to interaction with the environment. We obtain information, entanglement and coherent information. Based on these we relate the two separate uses of the quantum channel and obtain a relationship between the Holevo bound and the amount of entanglement transmitted through a quantum channel. The channel might also represent actions of an eavesdropper so that these results can be used to put bounds on the eavesdropping efficiency. We apply these results to a pair of entangled optical modes when one of them is transmitted through a decoherent channel.
TL;DR: In this paper, a quantum channel is investigated that transmits quantum messages from two independent sources to a unique receiver, and general assertions about the system throughput are proved, and physically important coherent-and squeezed-state transmissions are examined in detail.
Abstract: A quantum channel is investigated that transmits quantum messages from two independent sources to a unique receiver. Several general assertions about the system throughput are proved, and physically important coherent- and squeezed-state transmissions are examined in detail. Some problems of one-source communication in the presence of noise are discussed.