Showing papers on "Coherent information published in 2000"
TL;DR: An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time and is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
Abstract: An information theoretic measure is derived that quantifies the statistical coherence between systems evolving in time. The standard time delayed mutual information fails to distinguish information that is actually exchanged from shared information due to common history and input signals. In our new approach, these influences are excluded by appropriate conditioning of transition probabilities. The resulting transfer entropy is able to distinguish effectively driving and responding elements and to detect asymmetry in the interaction of subsystems.
3,653 citations
Journal Article•
TL;DR: In this paper, a short review of ideas in quantum information theory is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems and a new resource: quantum information.
Abstract: In this thesis I present a short review of ideas in quantum information theory. The first chapter contains introductory material, sketching the central ideas of probability and information theory. Quantum mechanics is presented at the level of advanced undergraduate knowledge, together with some useful tools for quantum mechanics of open systems. In the second chapter I outline how classical information is represented in quantum systems and what this means for agents trying to extract information from these systems. The final chapter presents a new resource: quantum information. This resource has some bewildering applications which have been discovered in the last ten years, and continually presents us with unexpected insights into quantum theory and the universe.
The treatment is pedagogical and suitable for beginning graduates in the field.
635 citations
TL;DR: In this paper, it was shown that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly, even irreversibly, with quantum information.
Abstract: A photon in an arbitrary polarization state cannot be cloned perfectly. But suppose that at our disposal we have several copies of a photon in an unknown state. Is it possible to delete the information content of one or more of these photons by a physical process? Specifically, if two photons are in the same initial polarization state, is there a mechanism that produces one photon in the same initial state and the other in some standard polarization state? If this could be done, then one would create a standard blank state onto which one could copy an unknown state approximately, by deterministic cloning or exactly, by probabilistic cloning. This could in principle be useful in quantum computation, where one could store new information in an already computed state by deleting the old information. Here we show, however, that the linearity of quantum theory does not allow us to delete a copy of an arbitrary quantum state perfectly. Though in a classical computer information can be deleted (reversibly) against a copy, the analogous task cannot be accomplished, even irreversibly, with quantum information.
234 citations
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TL;DR: In this article, it was shown that the classical capacity or maximal purity of outputs cannot be increased by using entangled inputs of the channel, and some new partial results also support the conjecture.
Abstract: A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity", and the "maximal output purity". All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture.
136 citations
TL;DR: This chapter surveys what is known about quantum information theory, including some surprising and intriguing possibilities made possible by quantum communication channels.
Abstract: Classical information theory is mostly concerned with the problem of sending classical information – letters in an alphabet, speech, strings of bits – over communications channels which operate in accordance with the laws of classical physics. How does the picture change if we can build quantum-mechanical communications channels? Can we transmit information more efficiently? Can we make use of quantum mechanics to transmit secret information without being eavesdropped on? These are just two of the questions we may ask when communication channels are allowed to be quantum mechanical. This redefinition of what a channel is causes us to go back and re-examine the fundamental questions motivating classical information theory, in the search for new answers. This chapter surveys what is known about quantum information theory, including some surprising and intriguing possibilities made possible by quantum communication channels. Quantum information theory is motivated by the study of communications channels, but it has a much wider domain of application, and it is a thought-provoking challenge to capture in a verbal nutshell the goals of the field. As described in Section 1.6, we can identify three fundamental goals uniting work on quantum information theory: to identify elementary classes of static resources in quantum mechanics (which we identify as types of ‘information’); to identify elementary classes of dynamical processes in quantum mechanics (identified as types of ‘information processing’); and to quantify resource tradeoffs incurred performing elementary dynamical processes.
103 citations
TL;DR: In this paper, the authors follow the development of probability theory from the beginning of the last century, emphasizing that quantum theory is really a generalization of this theory, and the great achievements of probability theories such as the theory of processes, generalized random fields, estimation theory and information geometry, are reviewed.
Abstract: We follow the development of probability theory from the beginning of the last century, emphasizing that quantum theory is really a generalization of this theory. The great achievements of probability theory, such as the theory of processes, generalized random fields, estimation theory, and information geometry, are reviewed. Their quantum versions are then described.
81 citations
TL;DR: The optimality of Gaussian cloning machines that transform N identical input states into M output states is investigated, and bounds on the fidelity of the process are derived via a connection with quantum estimation theory.
Abstract: The cloning of conjugate continuous quantum variables is analyzed based on the concept of Gaussian cloning machines, i.e., transformations that yield copies that are Gaussian mixtures centered on the state to be copied. The optimality of Gaussian cloning machines that transform N identical input states into M output states is investigated, and bounds on the fidelity of the process are derived via a connection with quantum estimation theory. In particular, the optimal N-to-$M$ cloning fidelity for coherent states is found to be equal to $MN/(MN+M\ensuremath{-}N).$
79 citations
TL;DR: It is suggested that exchange interaction can also be viewed using ecological ideas related to apparatus-object to help develop the important notion of complementarity in biosystems in relation to the nature and generation of information at the microphysical scale.
Abstract: This paper briefly considers the notion of a biology of quantum information from a number of complementary points of view. We begin with a very brief look at some of the biomolecular systems that are thought to exploit quantum mechanical effects and then turn to the issue of measurement in these systems and the concomitant generation of information. This leads us to look at the internalist stance and the exchange interaction of quantum particles. We suggest that exchange interaction can also be viewed using ecological ideas related to apparatus-object. This can also help develop the important notion of complementarity in biosystems in relation to the nature and generation of information at the microphysical scale.
75 citations
TL;DR: It is shown that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information and if for any bipartite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities.
Abstract: Based on a unified approach to all kinds of quantum capacities we show that the rate of quantum information transmission is bounded by the maximal attainable rate of coherent information Moreover, we show that if for any bipartite state the one-way distillable entanglement is no less than coherent information, then one obtains Shannon-like formulas for all the capacities The inequality also implies that the decrease of distillable entanglement due to the mixing process does not exceed that of the corresponding loss of information about a system
57 citations
TL;DR: This work presents the best encoding procedure when the quantum state is made up of N spins (qubits), and finds that the quality of this optimal procedure depends solely on the dimension of the encoding space.
Abstract: Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of N spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.
48 citations
Journal Article•
TL;DR: It is proved that a quantum state between two parties is entangled if and only if the classical random variables resulting from optimal measurements provide some mutual classical information between the parties.
Abstract: After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In principle, both classical and quantum protocols can be used for this processing. It is a natural question which type of protocols is more powerful. We show that the limits of tolerable noise are identical for classical and quantum protocols in many cases. More specifically, we prove that a quantum state between two parties is entangled if and only if the classical random variables resulting from optimal measurements provide some mutual classical information between the parties. In addition, we present evidence which strongly suggests that the potentials of classical and of quantum protocols are equal in every situation. An important consequence, in the purely classical regime, of such a correspondence would be the existence of a classical counterpart of so-called bound entanglement, namely bound information that cannot be used for generating a secret key by any protocol. This stands in sharp contrast to what was previously believed.
TL;DR: In this paper, it was shown that the thermal conductance of a single channel comprising particles obeying arbitrary fractional statistics is in fact a consequence of a more general universal upper bound involving the averaged entropy and energy currents, involving the single channel connecting heat reservoirs with arbitrary temperatures and chemical potentials.
Abstract: We show that the recently discovered universal upper bound on the thermal conductance of a single channel comprising particles obeying arbitrary fractional statistics is in fact a consequence of a more general universal upper bound, involving the averaged entropy and energy currents of a single channel connecting heat reservoirs with arbitrary temperatures and chemical potentials. The latter upper bound in turn leads, via Holevo's theorem, to a universal (i.e., statistics-independent) upper bound on the optimum capacity for classical information transmission down a single, wideband quantum channel.
Book•
17 Mar 2000Abstract: 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.
TL;DR: I introduce rate-distortion theory for the coding of quantum information and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to store or compress an entangled quantum source with a given maximum level of distortion per source emission.
Abstract: I introduce rate-distortion theory for the coding of quantum information, and derive a lower bound, involving the coherent information, on the rate at which qubits must be used to store or compress an entangled quantum source with a given maximum level of distortion per source emission.
TL;DR: In quantum hypothesis testing, a quantum system is prepared in a member of a known, finite set of states, and the aim is to guess which one with the minimum probability of error as mentioned in this paper.
Abstract: There are fundamental limits to the accuracy with which one can determine the state of a quantum system. I give an overview of the main approaches to quantum state discrimination. Several strategies exist. In quantum hypothesis testing, a quantum system is prepared in a member of a known, finite set of states, and the aim is to guess which one with the minimum probability of error. Error free discrimination is also sometimes possible, if we allow for the possibility of obtaining inconclusive results. If no prior information about the state is provided, then it is impractical to try to determine it exactly, and it must be estimated instead. In addition to reviewing these various strategies, I describe connections between state discrimination, the manipulation of quantum entanglement, and quantum cloning. Recent experimental work is also discussed.
TL;DR: In this paper, the authors show that the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is taken over all measurements which measure the same ''property'' of the state.
Abstract: How much information about an unknown quantum state can be obtained by a measurement? We propose a model independent answer: the information obtained is equal to the minimum entropy of the outputs of the measurement, where the minimum is taken over all measurements which measure the same ``property'' of the state. This minimization is necessary because the measurement outcomes can be redundant, and this redundancy must be eliminated. We show that this minimum entropy is less or equal than the von Neumann entropy of the unknown states. That is a measurement can extract at most one meaningful bit from every qubit carried by the unknown states.
01 Jan 2000
TL;DR: The discipline of information theory was founded by Claude Shannon in a truly remarkable paper [Sh] which laid down the foundations of the subject.
Abstract: The discipline of information theory was founded by Claude Shannon in a truly remarkable paper [Sh] which laid down the foundations of the subject. We begin with a quote from this paper which is an excellent summary of the main concern of information theory:
The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.
TL;DR: In this paper, a method for representing probabilistic aspects of quantum systems by means of a density function on the space of pure quantum states is introduced, where a maximum entropy argument allows us to obtain a natural density function that only reflects the information provided by the density matrix.
Abstract: A method for representing probabilistic aspects of quantum systems by means of a density function on the space of pure quantum states is introduced. In particular, a maximum entropy argument allows us to obtain a natural density function that only reflects the information provided by the density matrix. This result is applied to derive the Shannon entropy of a quantum state. The information theoretic quantum entropy thereby obtained is shown to have the desired concavity property, and to differ from the conventional von Neumann entropy. This is illustrated explicitly for a two-state system.
TL;DR: In this paper, the coherent information was calculated for information decay in a two-level atom in the presence of an external resonant field, for the information exchange between two coupled twolevel atoms, and for information transfer from a twolevel atom to another atom and to a photon field.
Abstract: The coherent-information concept is used to analyze a variety of simple quantum systems. Coherent information was calculated for the information decay in a two-level atom in the presence of an external resonant field, for the information exchange between two coupled two-level atoms, and for the information transfer from a two-level atom to another atom and to a photon field. The coherent information is shown to be equal to zero for all full-measurement procedures, but it completely retains its original value for quantum duplication. Transmission of information from one open subsystem to another one in the entire closed system is analyzed to learn quantum information about the forbidden atomic transition via a dipole active transition of the same atom. It is argued that coherent information can be used effectively to quantify the information channels in physical systems where quantum coherence plays an important role.
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TL;DR: The essence of the reasoning why Shannon's information is not an adequate choice when defining the information gain in quantum measurements as opposed to classical observations is pointed out.
Abstract: Motivated by Hall's recent comment in quant-ph/0007116 we point out in some detail the essence of our reasoning why we believe that Shannon's information is not an adequate choice when defining the information gain in quantum measurements as opposed to classical observations.
TL;DR: In this paper, it was shown that the binary discretization asymptotically realizes the capacity and the maximum mutual information of the quantum continuous channel, whereas the classical continuous channel does not have such an asymPTotic property.
Abstract: This paper discusses a discretization problem for quantum continuous channels. We show that the binary discretization asymptotically realizes the capacity and the maximum mutual information; the classical continuous channel does not have such an asymptotic property. We further clarify the significance of Gordon's result from the aspect of binary discretization for the maximum mutual information.
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TL;DR: In this paper, the role of product bases in quantum information theory is reviewed and the existence of two sets of bipartite unextendible product bases, in arbitrary dimensions, which are based on a tile construction is proved.
Abstract: We review the role of product bases in quantum information theory. We prove two conjectures which were made in DiVincenzo et al., quant-ph/9908070, namely the existence of two sets of bipartite unextendible product bases, in arbitrary dimensions, which are based on a tile construction. We pose some questions related to complete product bases.
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TL;DR: In this paper, the authors show that the separability of states in quantum mechanics has a close counterpart in classical physics, and that conditional mutual information (a.k.a. conditional information transmission) is a very useful quantity in the study of both quantum and classical separabilities.
Abstract: We show that the separability of states in quantum mechanics has a close counterpart in classical physics, and that conditional mutual information (a.k.a. conditional information transmission) is a very useful quantity in the study of both quantum and classical separabilities. We also show how to define entanglement of formation in terms of conditional mutual information. This paper lays the theoretical foundations for a sequel paper which will present a computer program that can calculate a decomposition of any separable quantum or classical state.
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TL;DR: In this article, a quantum theory of mind is proposed, which is based on a relativistic version of von Neumann's quantum theory, and the effects of mental action on brain activity are achieved by a Quantum Zeno Effect.
Abstract: Recent theoretical and experimental papers support the prevailing opinion that large warm systems will rapidly lose quantum coherence, and that classical properties will emerge. This rapid loss of coherence would naturally be expected to block any critical role for quantum theory in explaining the interaction between our conscious experiences and the physical activities of our brains. However, there is a quantum theory of mind in which the efficacy of mental effort is not affected by decoherence effects. In this theory the effects of mental action on brain activity is achieved by a Quantum Zeno Effect that is not weakened by decoherence. The theory is based on a relativistic version of von Neumann's quantum theory. It encompasses all the predictions of Copenhagen quantum theory, which include all the validated predictions of classical physical theory. In addition, it forges two-way dynamical links between the physical and experiential aspects of nature. The theory has significant explanatory power.
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TL;DR: In the information interpretation of quantum mechanics, information is the most fundamental, basic entity and the concept of a many-to-one state reduction is not a fundamental one but results from the practical impossibility to reconstruct the original state after the measurement.
Abstract: In the information interpretation of quantum mechanics, information is the most fundamental, basic entity. Every quantized system is associated with a definite discrete amount of information (cf. Zeilinger). This information content remains constant at all times and is permutated one-to-one throughout the system evolution. What is interpreted as measurement is a particular type of information transfer over a fictitious interface. The concept of a many-to-one state reduction is not a fundamental one but results from the practical impossibility to reconstruct the original state after the measurement.
TL;DR: This work defines an optimal decomposition as a decomposition for which the average preparation information is minimal, and characterizes the system–environment correlations.
Abstract: Consider a joint quantum state of a system and its environment. A measurement on the environment induces a decomposition of the system state. Using algorithmic information theory, we define the preparation information of a pure or mixed state in a given decomposition. We then define an optimal decomposition as a decomposition for which the average preparation information is minimal. The average preparation information for an optimal decomposition characterizes the system-environment correlations. We discuss properties and applications of the concepts introduced above and give several examples.
NEC1
TL;DR: In this paper, the authors describe a key-distribution scheme in which two nearly orthogonal coherent states carry the key, and the superposition of these states (cat states) protects the communication channel from eavesdropping.
Abstract: Quantum-mechanical complementarity ensures the security of the key-distribution scheme reported by Brassard and Bennet in 1984 (BB84), but does not prohibit use of multi-photons as a signal carrier. We describe a novel BB84 scheme in which two nearly orthogonal coherent states carry the key, and the superposition of these states (cat states) protects the communication channel from eavesdropping. Information leakage to eavesdroppers can be determined from the visibility of the interferential fringes in the distribution of the outcome when a certain quadrature component is measured through homodyne detection. The effect of channel loss and detector inefficiency is discussed.
TL;DR: It is verified that the concept of the conventional error correction scheme does not play an important role to demonstrate, at least, the super additiveness of quantum channel, and that rather one can apply them to only selection of code word states with desirable Hamming distance.
Abstract: This paper presents a review and some results on problems of super additiveness in quantum channel for Shannon information. Especially, how to investigate concrete systems showing super additiveness is discussed. It is verified that the concept of the conventional error correction scheme does not play an important role to demonstrate, at least, the super additiveness of quantum channel, and that rather one can apply them to only selection of code word states with desirable Hamming distance. Finally, some properties of quantum reliability function are given, which are useful to discuss the general property of coding with super additiveness.
Journal Article•
TL;DR: An information theory of quantum cryptography is proposed by intruducing the quantum measurement channel and the mutual information is calculated, and a new criteria for checking Eve is estimated.
Abstract: In this paper,we propose an information theory of quantum cryptography by intruducing the quantum measurement channel The mutual information is calculated,and a new criteria for checking Eve is estimated
TL;DR: In this article, it was shown that information about the original state preparation is not entirely lost as a result of the measurement-induced collapse of the quantum state, and that an infinite number of independent observers who have no prior knowledge about the initial state can gain partial information.
Abstract: How much information about the original state preparation can be extracted from a quantum system which has already been measured? That is, how many independent (noncommunicating) observers can measure the quantum system sequentially and give a nontrivial estimation of the original unknown state? We investigate these questions, and show from a simple example that information about the original preparation is not entirely lost as a result of the measurement-induced collapse of the quantum state, and that an infinite number of independent observers who have no prior knowledge about the initial state can gain partial information about the original preparation of the quantum system.