Showing papers on "Coherent information published in 2002"
TL;DR: In this article, the authors show how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission, and show that quantum computers can achieve enhanced speed over their classical counterparts using information-theoretic arguments.
Abstract: Quantum mechanics and information theory are among the most important scientific discoveries of the last century. Although these two areas initially developed separately, it has emerged that they are in fact intimately related. In this review the author shows how quantum information theory extends traditional information theory by exploring the limits imposed by quantum, rather than classical, mechanics on information storage and transmission. The derivation of many key results differentiates this review from the usual presentation in that they are shown to follow logically from one crucial property of relative entropy. Within the review, optimal bounds on the enhanced speed that quantum computers can achieve over their classical counterparts are outlined using information-theoretic arguments. In addition, important implications of quantum information theory for thermodynamics and quantum measurement are intermittently discussed. A number of simple examples and derivations, including quantum superdense coding, quantum teleportation, and Deutsch's and Grover's algorithms, are also included.
976 citations
TL;DR: The amount of work which can be extracted from a heat bath using a bipartite state shared by two parties is considered and the work deficit is derived and provides a new paradigm for understanding quantum nonlocality.
Abstract: We consider the amount of work which can be extracted from a heat bath using a bipartite state $\ensuremath{\rho}$ shared by two parties In general it is less then the amount of work extractable when one party is in possession of the entire state We derive bounds for this ``work deficit'' and calculate it explicitly for a number of different cases In particuar, for pure states the work deficit is exactly equal to the distillable entanglement of the state A form of complementarity exists between physical work which can be extracted and distillable entanglement The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum nonlocality
458 citations
TL;DR: In this paper, the authors give a self-contained introduction to the conceptional and mathematical foundations of quantum information theory, including entanglement measures, channel capacities, relations between both, additivity and continuity properties and asymptotic rates of quantum operations.
325 citations
TL;DR: Only in the case of zero transfer entropy in one direction the authors can reliably infer an asymmetry of the information exchange, and it is shown that finite length scale estimates converge from below and can be used to reject the assumption that the observed processes are independent.
324 citations
TL;DR: In this article, it was shown that the observables and state space of a physical theory are quantum-mechanical, and the implications of alternative answers to a remaining open question about nonlocality and bit commitment.
Abstract: We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.
293 citations
TL;DR: In this article, it was shown that the Holevo bound is the classical information capacity of unital qubit channels, and an explicit formula for this capacity was given for product channels.
Abstract: Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is a unital qubit channel, with the other completely arbitrary. As a byproduct this proves that the Holevo bound is the classical information capacity of such qubit channels, and provides an explicit formula for this classical capacity. Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions. The proof relies on a new bound for the p-norm of an output state from the half-noisy phase-damping channel.
201 citations
TL;DR: In this paper, it was shown that if the loss of coherent information of the input state is small, then approximate quantum error correction is possible, but only if the channel does not decrease the coherent information.
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 quantum error correction is possible.
PACS: 03.67.H, 03.65.U
130 citations
TL;DR: Amos Golan Department of Economics, American University, Roper 200, 4400 Massachusetts Ave., NW, Washington, DC 20016, USA as mentioned in this paper has published a paper on the Golan Decision Process.
116 citations
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TL;DR: A direct proof of the relation between the one-shot classical capacity and the minimal output entropy for covariant quantum channels is suggested.
Abstract: A direct proof of the relation between the one-shot classical capacity and the minimal output entropy for covariant quantum channels is suggested. The structure of covariant channels is described in some detail. A simple proof of a general inequality for entanglement-assisted classical capacity is given.
83 citations
TL;DR: In this article, the authors consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many, and investigate the consequences of storing information in classical or quantum ways.
Abstract: We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.
46 citations
TL;DR: In this article, a nonadditive information theory with the Tsallis entropy indexed by qg1 was introduced and then translated into quantum theory, and the authors examined if this theory has points superior to the ordinary additive information theory, with the von Neumann entropy corresponding to the limit of the Werner-Popescu states of the n-partite N-level system.
Abstract: Generalizing Khinchin's classical axiomatic foundation, a basis is developed for nonadditive information theory with the Tsallis entropy indexed by q. The classical nonadditive conditional entropy is introduced and then translated into quantum theory. To examine if this theory has points superior to the ordinary additive information theory with the von Neumann entropy corresponding to the limit $\stackrel{\ensuremath{\rightarrow}}{q}1,$ separability of a one-parameter family of the Werner-Popescu states of the ${N}^{n}$ system (i.e., the n-partite N-level system) is discussed. The nonadditive information theory with $qg1$ is shown to yield a limitation on separability that is stronger than the one derived from the additive theory. How the strongest limitation can be obtained in the limit $\stackrel{\ensuremath{\rightarrow}}{q}\ensuremath{\infty}$ is also shown.
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TL;DR: The highest information rate at which quantum error-correction schemes work reliably on a channel is called the quantum capacity, which is proven to be lower-bounded by the limit of coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes.
Abstract: The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over the set of input density operators which are proportional to the projections onto the code spaces of symplectic stabilizer codes. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a completely positive linear map on a Hilbert space of finite dimension, and the codes that are proven to have the desired performance are symplectic stabilizer codes. On the depolarizing channel, this work's bound is actually the highest possible rate at which symplectic stabilizer codes work reliably.
TL;DR: It is established that in this scenario optimal rate-distortion codes produce no entropy exchange with the environment of any individual qubit.
Abstract: We formulate quantum rate-distortion theory in the most general setting where classical side information is included in the tradeoff. Using a natural distortion measure based on entanglement fidelity and specializing to the case of an unrestricted classical side channel, we find the exact quantum rate-distortion function for a source of isotropic qubits. An upper bound we believe to be exact is found in the case of biased sources. We establish that in this scenario optimal rate-distortion codes produce no entropy exchange with the environment of any individual qubit.
TL;DR: A ‘‘nit’’ is defined as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for n, is fundamentally irreducible to a binary coding.
Abstract: We define a ``nit'' as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for $ng2,$ is fundamentally irreducible to a binary coding. Properties of this measure for entangled many-particle states are discussed. k particles specify k nits in such a way that k mutually commuting measurements of observables with n possible outcomes are sufficient to determine the information.
TL;DR: All aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.
Abstract: Quantum information is defined by applying the concepts of ordinary (Shannon) information theory to a quantum sample space consisting of a single framework or consistent family. A classical analogy for a spin-half particle and other arguments show that the infinite amount of information needed to specify a precise vector in its Hilbert space is not a measure of the information carried by a quantum entity with a d-dimensional Hilbert space; the latter is, instead, bounded by ${\mathrm{log}}_{2}d$ bits (one bit per qubit). The two bits of information transmitted in dense coding are located not in one but in the correlation between two qubits, consistent with this bound. A quantum channel can be thought of as a structure or collection of frameworks, and the physical location of the information in the individual frameworks can be used to identify the location of the channel. Analysis of a quantum circuit used as a model of teleportation shows that the location of the channel depends upon which structure is employed; for ordinary teleportation it is not (contrary to Deutsch and Hayden) present in the two bits resulting from the Bell-basis measurement, but in correlations of these with a distant qubit. In neither teleportation nor dense coding does information travel backwards in time, nor is it transmitted by nonlocal (superluminal) influences. It is (tentatively) proposed that all aspects of quantum information can in principle be understood in terms of the (basically classical) behavior of information in a particular framework, along with the framework dependence of this information.
TL;DR: In this paper, the authors calculate the rate at which information can be recovered from the black-hole spectral lines and conclude that the information that was suspected to be lost may gradually leak back, encoded into the black hole spectral lines.
30 Jun 2002
TL;DR: A general formula of the channel capacity for any (classical-) quantum channel is derived and can be regarded as a quantum version of Verdu and Han's result.
Abstract: We derive a general formula of the channel capacity for any (classical-) quantum channel. It can be regarded as a quantum version of Verdu and Han's result (see IEEE Trans. Inform. Theory, vol.40, p.1147-57, 1994). Our results contain Holevo's (see IEEE Trans. Inform. Theory, vol.44, p.269-73, 1998) and Schumacher and Westmoreland's (see Phys. Rev. A, vol.56, p.131-8, 1997) results as the stationary and memoryless case.
TL;DR: This work generalizes this variable-length and faithful scenario to the general quantum source producing mixed states rho(i) with probability p(i), and finds the optimal compression rate in the limit of large block length differs from the one in the fixed- length and asymptotically faithful scenario.
Abstract: A classical random variable can be faithfully compressed into a sequence of bits with its expected length lying within one bit of Shannon entropy. We generalize this variable-length and faithful scenario to the general quantum source producing mixed states ${\ensuremath{\rho}}_{i}$ with probability ${p}_{i}$. In contrast to the classical case, the optimal compression rate in the limit of large block length differs from the one in the fixed-length and asymptotically faithful scenario. The amount of this gap is interpreted as the genuinely quantum part being incompressible in the former scenario.
TL;DR: In this article, it was shown that for Bernoulli sources, the entanglement-assisted classical capacity is bounded from above by the quantum-dynamical entropy defined in terms of operational partitions of unity.
Abstract: The theories of noncommutative dynamical entropy and quantum symbolic dynamics for quantum-dynamical systems are analyzed from the point of view of quantum information theory. Using a general quantum-dynamical system as a communication channel, one can define different classical capacities depending on the character of resources applied for encoding and decoding procedures and on the type of information sources. It is shown that for Bernoulli sources, the entanglement-assisted classical capacity, which is the largest one, is bounded from above by the quantum-dynamical entropy defined in terms of operational partitions of unity. Stronger results are proved for the particular class of quantum-dynamical systems--quantum Bernoulli shifts. Different classical capacities are exactly computed and the entanglement-assisted one is equal to the dynamical entropy in this case.
TL;DR: In this article, it was shown that unitary depolarizers, which play an important role in quantum information processing, can be constructed in terms of the Pegg-Barnett phase operator.
Abstract: It is shown that unitary depolarizers, which play an important role in quantum information processing, can be constructed in terms of the Pegg-Barnett phase operator. By using the result, the classical information capacity of quantum dense coding with unitary encoding in a finite-dimensional Hilbert space is derived. Furthermore, the relation between the capacity of quantum dense coding and the coherent information of a noisy quantum channel is obtained.
TL;DR: It is shown that in general it is not possible to combine two quantum states of knowledge to obtain the state resulting from the combined information of both observers, but this does not preclude the possibility that a unique, well motivated rule for combining quantumStates of knowledge without reference to a measurement history could be found.
Abstract: In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine independently obtained states of knowledge together to form a new state of knowledge, which is the state which would be possessed by someone having the combined information of both observers. Moreover, this combined state of knowledge can be found without reference to the manner in which the respective observers obtained their information. However, we show that in general this is not possible for quantum states of knowledge; in order to combine two quantum states of knowledge to obtain the state resulting from the combined information of both observers, these observers must also possess information about how their respective states of knowledge were obtained. Nevertheless, we emphasize this does not preclude the possibility that a unique, well motivated rule for combining quantum states of knowledge without reference to a measurement history could be found. We examine both the direct quantum analog of the classical problem, and that of quantum state-estimation, which corresponds to a variant in which the observers share a specific kind of prior information.
PACS: 03.67.-a, 02.50.-r, 03.65.Bz
TL;DR: In this paper, it was shown that the information accessible by simultaneous measurement on both subsystems is not to exceed the part accessible by measurement on one subsystem, which, in turn, is proved to not exceed the von Neumann mutual information.
Abstract: Having the quantum correlations in a general mixed or pure bipartite state in mind, the part of information accessible by simultaneous measurement on both subsystems is shown never to exceed the part accessible by measurement on one subsystem, which, in turn is proved not to exceed the von Neumann mutual information. A particular pair of (opposite-subsystem) observables is shown to be responsible both for the amount of quasiclassical correlations and for that of the purely quantum entanglement in the pure-state case: the former via simultaneous subsystem measurements, and the latter through the entropy of coherence or of incompatibility, which is defined for the general case. The observables at issue are so-called twin observables. A general definition of the latter is given in terms of their detailed properties.
TL;DR: In this paper, a complete description of atomic storage states which may appear in the electromagnetically induced transparency (EIT) is presented, and the spatial coherence has been included in the atomic collective operators and the atomic storage state.
Abstract: We present a complete description of atomic storage states which may appear in the electromagnetically induced transparency (EIT). The result shows that the spatial coherence has been included in the atomic collective operators and the atomic storage states. In some limits, a set of multimode atomic storage states has been established in correspondence with the multimode Fock states of the electromagnetic field. This gives a better understanding of the fact that, in EIT, the optical coherent information can be preserved and recovered.
TL;DR: In this paper, the authors introduce purification for a pair (ρ, Φ), where ρ is a quantum state and Φ is a channel, which allows in particular a natural extension of the properties of related information quantities (mutual and coherent informations) to the channels with arbitrary input and output spaces.
Abstract: In this note we introduce purification for a pair (ρ, Φ), where ρ is a quantum state and Φ is a channel, which allows in particular a natural extension of the properties of related information quantities (mutual and coherent informations) to the channels with arbitrary input and output spaces.
PACS: 03.67.Hk
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TL;DR: This note presents a practical cryptography protocol for transmitting classical and quantum information secretly and directly and describes a simple and efficient way to implement this protocol.
Abstract: This note presents a practical cryptography protocol for transmitting classical and quantum information secretly and directly.
01 Jan 2002
TL;DR: 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.
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 \( k < 1\sqrt 2 \).
TL;DR: In this article, the authors established the limit for the compression of information from such a source and showed that asymptotically it is given by the von Neumann entropy rate.
Abstract: A system of interacting qubits can be viewed as a non-iid quantum information source A possible model of such a source is provided by a quantum spin system, in which spin-1/2 particles located at sites of a lattice interact with each other We establish the limit for the compression of information from such a source and show that asymptotically it is given by the von Neumann entropy rate Our result can be viewed as a quantum ana-logue of Shannon's noiseless coding theorem for a class of non-iid quantum informa-tion sources From the probabilistic point of view it is an analog of the Shannon-McMillan-Breiman theorem considered as a cornerstone of modern Information Theory
PACS: 0367-a; 0367Lx
TL;DR: This work identifies economic value as the reduction of entropy mathematically and explores the relation between physical entropy and economic value and shows how the detailed investigation of information theory, thermodynamic theory and the theory of evolution resolves the conceptual difficulties that confound us for many years.
Abstract: More than half century ago, Shannon's identification of information as the reduction of entropy greatly clarified the meaning of information and established information theory as a science. Since all human activities represent extraction and transformation of low entropy from the environment, it is natural to relate economic value to low entropy. However, some conceptual difficulties prevented the development of an entropy theory of value. In this work, we identify economic value as the reduction of entropy mathematically and explore the relation between physical entropy and economic value. In the process, we show how the detailed investigation of information theory, thermodynamic theory and the theory of evolution resolves the conceptual difficulties that confound us for many years. The entropy theory of value, by establishing the theory of value on the firm foundation of thermodynamics, greatly clarified many fundamental issues in economic theory and human activities.
TL;DR: In this article, a scheme for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions is presented, which operates essentially by distributing information over two pairs of qubits and through error-prevention procedures.
Abstract: A scheme is presented for protecting one-qubit quantum information against decoherence due to a general environment and local exchange interactions. The scheme operates essentially by distributing information over two pairs of qubits and through error-prevention procedures. In the scheme, quantum information is encoded through a decoherence-free subspace for collective phase errors and exchange errors affecting the qubits in pairs; leakage out of the encoding space due to amplitude damping is reduced by quantum Zeno effect. In addition, how to construct decoherence-free states for n-qubit information against phase and exchange errors is discussed.