Showing papers on "Coherent information published in 2001"
TL;DR: In this paper, a general upper bound on the quantum capacity of a one-mode Gaussian channel with attenuation or amplification and classical noise was derived. But the bounds were not explicitly evaluated for the case of a single-mode channel.
Abstract: We show how to compute or at least to estimate various capacity-related quantities for bosonic Gaussian channels. Among these are the coherent information, the entanglement-assisted classical capacity, the one-shot classical capacity, and a quantity involving the transpose operation, shown to be a general upper bound on the quantum capacity, even allowing for finite errors. All bounds are explicitly evaluated for the case of a one-mode channel with attenuation or amplification and classical noise.
476 citations
TL;DR: It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver in the resulting quantum cryptographic information versus disturbance trade-off.
Abstract: A continuous key-distribution scheme is proposed that relies on a pair of conjugate quantum variables. It allows two remote parties to share a secret Gaussian key by encoding it into one of the two quadrature components of a single-mode electromagnetic field. The resulting quantum cryptographic information versus disturbance trade-off is investigated for an individual attack based on the optimal continuous cloning machine. It is shown that the information gained by the eavesdropper then simply equals the information lost by the receiver.
353 citations
TL;DR: In this paper, an entangled two-mode coherent state is studied in the framework of 2-dimensional Hilbert space and an entanglement concentration scheme based on joint Bell-state measurements is worked out.
Abstract: An entangled two-mode coherent state is studied within the framework of 2\ifmmode\times\else\texttimes\fi{}2-dimensional Hilbert space. An entanglement concentration scheme based on joint Bell-state measurements is worked out. When the entangled coherent state is embedded in vacuum environment, its entanglement is degraded but not totally lost. It is found that the larger the initial coherent amplitude, the faster entanglement decreases. We investigate a scheme to teleport a coherent superposition state while considering a mixed quantum channel. We find that the decohered entangled coherent state may be useless for quantum teleportation as it gives the optimal fidelity of teleportation less than the classical limit 2/3.
284 citations
TL;DR: A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory, which is applied to the case of noisy channels, with arbitrary input signal states.
Abstract: We define classical quantum multiway channels for transmission of classical information, after the previous work by Allahverdyan and Saakian (see Quantum Computing and Quantum Communications (Lecture Notes in Computer Science). Berlin, Germany: Springer-Verlag, vol.1509, 1999). Bounds on the capacity region are derived in a uniform way, which are analogous to the classically known ones, simply replacing Shannon (1961) entropy with von Neumann (1955) entropy. For the single receiver case (multiple-access channel) the elect capacity region is determined. These results are applied to the case of noisy channels, with arbitrary input signal states. A second issue of this work is the presentation of a calculus of quantum information quantities, based on the algebraic formulation of quantum theory.
128 citations
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TL;DR: It is shown that, if the loss of coherent information is small, then approximate quantum error correction is possible, and it is proposed that this method can be used to correct quantum channel errors.
Abstract: The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate error correction is possible.
88 citations
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TL;DR: In this article, the authors introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras and give some applications of them to quantum information theory for graduate students or non-experts who are interested in both Geometry and Quantum Information Theory.
Abstract: The purpose of this paper is to introduce several basic theorems of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1), and to give some applications of them to quantum information theory for graduate students or non--experts who are interested in both Geometry and Quantum Information Theory In the first half we make a general review of coherent states and generalized coherent states based on Lie algebras su(2) and su(1,1) from the geometric point of view and, in particular, prove that each resolution of unity can be obtained by the curvature form of some bundle on the parameter space In the latter half we apply a method of generalized coherent states to some important topics in Quantum Information Theory, in particular, swap of coherent states and cloning of coherent ones We construct the swap operator of coherent states by making use of a generalized coherent operator based on su(2) and show an "imperfect cloning" of coherent states, and moreover present some related problems In conclusion we state our dream, namely, a construction of {\bf Geometric Quantum Information Theory}
68 citations
TL;DR: In this paper, the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement was derived and bounded states cannot increase the channel capacity in the classical case.
Abstract: We derive the general formula for the capacity of a noiseless quantum channel assisted by an arbitrary amount of noisy entanglement. In this capacity formula, the ratio of the quantum mutual information and the von Neumann entropy of the sender's share of the noisy entanglement plays the role of mutual information in the completely classical case. A consequence of our results is that bound entangled states cannot increase the capacity of a noiseless quantum channel.
63 citations
TL;DR: In this article, the authors studied the entropy squeezing of a two-level atom in a Kerr-like medium and presented a definition of squeezing for this system, based on information theory.
Abstract: In the language of quantum information theory we study the entropy squeezing of a two-level atom in a Kerr-like medium. A definition of squeezing is presented for this system, based on information theory. The utility of the definition is illustrated by examining the entropy squeezing of a two-level atom with a Kerr-like medium. The influence of the non-linear interaction of the Kerr medium, the atomic coherence and the detuning parameter on the properties of the entropy and squeezing of the atomic variables is examined.
45 citations
TL;DR: The nonadditive information content adopted is consistent with the concept of the form invariance structure of the nonextensive entropy and the relation between the nonadditivity q and the codeword length is pointed out.
Abstract: We generalize Shannon's information theory in a nonadditive way by focusing on the source coding theorem. The nonadditive information content we adopted is consistent with the concept of the form invariance structure of the nonextensive entropy. Some general properties of the nonadditive information entropy are studied, in addition, the relation between the nonadditivity q and the codeword length is pointed out.
44 citations
TL;DR: A data processing inequality for quantum communication channels is proved, which states that processing a received quantum state may never increase the mutual information between input and output states.
Abstract: We prove a data processing inequality for quantum communication channels, which states that processing a received quantum state may never increase the mutual information between input and output states.
33 citations
TL;DR: It is shown that if ε can be compressed with arbitrarily high fidelity into A qubits per signal plus any amount of auxiliary classical storage, then A must still be at least as large as the Schumacher limit S of ε, so no part of the quantum information content of δ can be faithfully replaced by classical information.
Abstract: Consider a source ϵ of pure quantum states with von Neumann entropy S . By the quantum source coding theorem, arbitrarily long strings of signals may be encoded asymptotically into S qubits per signal (the Schumacher limit) in such a way that entire strings may be recovered with arbitrarily high fidelity. Suppose that classical storage is free while quantum storage is expensive and suppose that the states of ϵ do not fall into two or more orthogonal subspaces. We show that if ϵ can be compressed with arbitrarily high fidelity into A qubits per signal plus any amount of auxiliary classical storage, then A must still be at least as large as the Schumacher limit S of ϵ. Thus no part of the quantum information content of ϵ can be faithfully replaced by classical information. If the states do fall into orthogonal subspaces, then A may be less than S , but only by an amount not exceeding the amount of classical information specifying the subspace for a signal from the source.
TL;DR: In this paper, the authors show that nonlinear quantum evolution with maximal entropy production has been shown to be a nonlinear process with a maximal entropy, which has escaped scrutiny before the publication of this paper.
Abstract: The author calls attention to previous work with related results, which to his knowledge has escaped scrutiny before the publication of the paper ``Nonlinear quantum evolution with maximal entropy production'' [Phys. Rev. A 63, 022105 (2001)].
TL;DR: The objective of this report is to show a potential of the basic information theoretic methodology for the analysis of various problems of system dynamics, and indicate some challenges and expound the recent results on the maximum information entropy approach to theAnalysis of stochastic dynamical systems.
TL;DR: It is pointed out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes.
Abstract: A concern has been expressed that ``the Jaynes principle can produce fake entanglement'' [R. Horodecki et al., Phys. Rev. A 59, 1799 (1999)]. In this paper we discuss the general problem of distilling maximally entangled states from N copies of a bipartite quantum system about which only partial information is known, for instance, in the form of a given expectation value. We point out that there is indeed a problem with applying the Jaynes principle of maximum entropy to more than one copy of a system, but the nature of this problem is classical and was discussed extensively by Jaynes. Under the additional assumption that the state ${\ensuremath{\rho}}^{(N)}$ of the N copies of the quantum system is exchangeable, one can write down a simple general expression for ${\ensuremath{\rho}}^{(N)}.$ By measuring one or more of the subsystems, one can gain information and update the state estimate for the remaining subsystems with the quantum version of the Bayes rule. Using this rule, we show how to modify two standard entanglement purification protocols, one-way hashing and recurrence, so that they can be applied to exchangeable states. We thus give an explicit algorithm for distilling entanglement from an unknown or partially known quantum state.
24 Jun 2001
TL;DR: In this paper, the authors consider the tradeoff between information gained about a quantum state and disturbance caused by the measurement providing the information and find the way of making it which is least-disturbing, on average, when the initial quantum state is completely unknown.
Abstract: The author considers the tradeoff between information gained about a quantum state and disturbance caused by the measurement providing the information. For every measurement, he finds the way of making it which is least-disturbing, on average, when the initial quantum state is completely unknown.
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TL;DR: A finite-cardinality's set of new ideas concerning algorithmic information issues in Quantum Mechanics is introduced and analyzed.
Abstract: taking aside the review part, a finite-cardinality's set of new ideas concerning algorithmic information issues in Quantum Mechanics is introduced and analyzed
TL;DR: The optimal measurement strategies for maximizing the fidelity given a source that encodes information on the symmetric qubit-states are presented.
Abstract: We compare and contrast the error probability and fidelity as measures of the quality of the receiver's measurement strategy for a quantum communications system. The error probability is a measure of the ability to retrieve classical information and the fidelity measures the retrieval of quantum information. We present the optimal measurement strategies for maximizing the fidelity given a source that encodes information on the symmetric qubit-states.
TL;DR: In this article, the authors generalized pure quantum entanglement to the case of mixed compound states to include the classical and quantum encodings as particular cases, and characterized true entanglements as transpose-CP but not CP maps.
Abstract: The pure quantum entanglement is generalized to the case of mixed compound states to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized as transpose-CP but not CP maps. The entangled information is introduced as the relative entropy of the mutual and the input state and total information of the entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the supremum of the information over all c-entanglements, and the true quantum entropy, which is achieved at the standard entanglement. The q-capacity, defined as the supremum over all entanglements, doubles the c-capacity in the case of the simple algebra. The conditional q-entropy is positive, and q-information of a quantum channel is additive.
TL;DR: In this article, an analytical expression for the coherent information of the thermal radiation signal transmitted over a thermal radiation noise channel, one of the most essential quantum Gaussian channels, is given.
Abstract: An analytical expression is given to the coherent information of the thermal radiation signal transmitted over the thermal radiation noise channel, one of the most essential quantum Gaussian channels. Focusing on the single normal mode of the thermal radiation signal and noise, we resolve the entangled state density operator, which characterizes quantum information transmission, into a direct product of two parts, with each part being a thermal radiation density operator. The calculation is aided by the technique known as ``integral within ordered product of operators".
TL;DR: In this article, a two-qubit model of a classical channel that is a reduction of a quantum channel is implemented via the correlation of a spin representing information on a channel, with an ancilla spin representing the surrounding world.
Abstract: Nuclear magnetic resonance (NMR) has been used to explore and demonstrate many of the ideas behind quantum information processing (QIP). This work provides an illustrative example of information transfer over both quantum and classical channels using NMR techniques on the two-spin compound 13C-chloroform. A two-qubit model of a classical channel that is a reduction of a quantum channel can be implemented via the correlation of a spin representing information on a channel, with an ancilla spin representing the surrounding world. When information about this correlation is lost or discarded, the channel becomes classical; otherwise, it remains quantum. It is shown that, while classical information can be transmitted over either a quantum or classical channel, quantum information will only survive transmission over a quantum channel. © 2001 John Wiley & Sons, Inc. Concepts Magn Reson 13: 151–158, 2001
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TL;DR: In this article, the von Neumann measurement process underlying interference experiments is considered and it is shown that the uncertainty in the incoming wave, responsible for its interference, translates during measurement into an uncertainty at the measuring apparatus.
Abstract: Consideration of the von Neumann measurement process underlying interference experiments shows that the uncertainty in the incoming wave, responsible for its interference, translates during measurement into an uncertainty at the measuring apparatus. However, subsequent measurement on the apparatus does not reveal any new information about the interfering wave. This observation, in the context of recent advances in quantum information, suggests an argument for an information theoretic interpretation of quantum mechanics.
TL;DR: In this article, the authors investigated the character of the most studied case of the depolarizing channel and other channels and found the maximum of the coherent information to estimate the capacities of the channels.
Abstract: Quantum binary symmetric channels are defined via the invariance of fidelity under unitary transformations of the input density operators. In this definition, they not only include the most studied case of the depolarizing channel but also other channels. We investigate the character of the latter and find the maximum of the coherent information to estimate the capacities of the channels.
14 Aug 2001
TL;DR: A new, mathematically described understanding of physically meaningful information, quantum holography, concerning actual knowledge of the 3 dimensional physical world in natural systems, is proposed, based on demonstrably proven anticipatory quantum mechanical laws and the new awareness in quantum theory.
Abstract: “Can we truly compute, until we understand what information really is?” Gordon Scarrott. A new, mathematically described understanding of physically meaningful information, quantum holography, concerning actual knowledge of the 3 dimensional physical world in natural systems, is proposed. It is based on demonstrably proven anticipatory quantum mechanical laws and the new awareness in quantum theory. This understanding concerns a form of information, which holography shows, almost certainly existed before the origination of living systems and even from the beginning of the cosmos. It produces physically realisable mathematical definitions of the concepts of information, knowledge, learning, intelligence, perception, cognition, etc. Some of its other many advantages are cited. In particular, being quite distinct from bits, which are simply physically realisable mental models for the carriage/transmission of symbolic data (dependent for its meaning on human interpretation) it is not, its mathematical theory indicates, subject to the processing limitations of the combinatorial explosion governing algorithmic complexity, or to the known processing limitations of formal systems, such as the Halting Problem, as they are thought to apply to classical digital computing systems.
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TL;DR: In this article, it was shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.
Abstract: It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle. The coherent state labels, which are essentially instructions for preparing states, make it unnecessary to identify properties with projectors in Hilbert space. This eliminates the so called "eigenvalue-eigenstate" link, and the theory thereby escapes the measurement problem. What the theory allows us to predict is the distribution in the outcomes of tests of relations between coherent states. It is shown that quantum non-determinism can be attributed to a hidden variable (noise) in the space of relations without violating the no-go theorems (e.g. Kochen-Specker). It is shown that the coherent state vacuum is distorted when entangled states are generated. The non-locality of the vacuum permits this distortion to be felt everywhere without the transmission of a signal and thereby accounts for EPR correlations in a manifestly covariant way.
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TL;DR: The channel capacity for the binary symmetric channel is investigated based on the symmetrized definition of the mutual information, which is arising from an attempt of extension of information contentbased on the nonadditivity.
Abstract: The channel capacity for the binary symmetric channel is investigated based on the symmetrized definition of the mutual information, which is arising from an attempt of extension of information content based on the nonadditivity. The negative capacity can emerge as an avoidable consequence for the generalization of the concept of the information entropy when $q >1$.
TL;DR: In this article, it is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum system, resulting in the coherent information and introduced the compatible information measures, respectively.
Abstract: Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum system, resulting in the coherent information and introduced here the compatible information measures, respectively. A sketch of an information optimization of a quantum experimental setup is proposed.
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TL;DR: Quantum information is radically different from classical information in that the quantum formalism (Hilbert space) makes necessary the introduction of irreducible ''nits'' n being an arbitrary natural number (bigger than one), not just bits.
Abstract: Quantum information is radically different from classical information in that the quantum formalism (Hilbert space) makes necessary the introduction of irreducible ``nits,'' n being an arbitrary natural number (bigger than one), not just bits.
01 Jan 2001
TL;DR: This chapter discusses the relationship between entropy information and optics, and the extraction of signal from random noise and distortion and the reconstruction of unknown signals that have been distorted as examples, called signal recovery or restoration.
Abstract: Publisher Summary This chapter discusses the relationship between entropy information and optics. Recent development of optical communication, signal processing, and computing, among other discoveries, the relationship between optics and entropy information has grown more profound. From the viewpoint of mathematic formalism, entropy information is basically a probabilistic concept. In other words, without probability theory there would be no entropy information. Information transmission can be in fact represented by spatial and temporal information. Information channels are described according to the type of input/output ensemble and are considered discrete or continuous. In practice, all communication channels are band limited. An information channel can be a low-pass, bandpass, or discrete bandpass channel. A problem of considerable importance in signal processing is the extraction of signal from random noise and distortion. There are, however, two major approaches to this issue; the extraction of signals that have been lost in random noise as examples, called signal detection, and the reconstruction of unknown signals that have been distorted as examples, called signal recovery or restoration.
13 Jun 2001
TL;DR: In this paper, the authors present the optimal strategies under different assumptions for collective and repeated individual measurements of a system of spin-1/2 particles and show that collective measurements are always better than repeated individual ones.
Abstract: The communication of directions using quantum states is a useful laboratory test for some basic facts of quantum information. For a system of spin-1/2 particles there are different quantum states that can encode directions. This information can later be decoded by means of a generalized measurement. In this talk we present the optimal strategies under different assumptions. c 2008 Optical Society of America OCIS codes: (000.1600) Classical and quantum physics; (200.3050) Information processing Imagine two parties, traditionally called Alice and Bob. Alice wants to communicate a space direction ~ n to Bob, but she only has at her disposal several spin-1/2 particles. She can use them to construct a quantum state that will encode the information about the direction. Upon receiving the state, Bob performs a quantum measurement and tries to retrieve as much of this information as possible. This simple scenario has a long history and it has been invoked to test several hypothesis. The first non trivial question is whether there are differences between collective measurements as compared to repeated individual measurements. In other words, is it better to perform a global measurement on the quantum system as a whole or to measure the spins separately? This was the original motivation of Peres and Wooters (1). Later Massar and Popescu (2) using N parallel spins concluded that collective measurements are always better than individual ones. A turn of events was the work of Gisin and Popescu (3). These authors showed that, in the simple case of N = 2, sending the two spins in an antiparallel state leads to an even greater accuracy. This was the main motivation for our systematic study of the optimal strategies for an arbitrary number of spins. We start by describing the main elements of the scenario.