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Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.


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Book ChapterDOI
13 Aug 2007
TL;DR: In this article, the authors analyzed how measured quantum dynamical systems store and process information, introducing sofic quantum dynamics, and quantified their information storage and processing in terms of entropy rate and excess entropy, giving closed form expressions where possible.
Abstract: We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information storage and processing in terms of entropy rate and excess entropy, giving closed-form expressions where possible. To illustrate the impact of measurement on information storage in quantum processes, we analyze two spin-1 sofic quantum systems that differ only in how they are measured.

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one.
Abstract: We study the one-shot zero-error classical capacity of a quantum channel assisted by quantum no-signalling correlations, and the reverse problem of exact simulation of a prescribed channel by a noiseless classical one. Quantum no-signalling correlations are viewed as two-input and two-output completely positive and trace preserving maps with linear constraints enforcing that the device cannot signal. Both problems lead to simple semidefinite programmes (SDPs) that depend only on the Kraus operator space of the channel. In particular, we show that the zero-error classical simulation cost is precisely the conditional min-entropy of the Choi-Jamiolkowski matrix of the given channel. The zero-error classical capacity is given by a similar-looking but different SDP; the asymptotic zero-error classical capacity is the regularization of this SDP, and in general we do not know of any simple form. Interestingly however, for the class of classical-quantum channels, we show that the asymptotic capacity is given by a much simpler SDP, which coincides with a semidefinite generalization of the fractional packing number suggested earlier by Aram Harrow. This finally results in an operational interpretation of the celebrated Lovasz $\vartheta$ function of a graph as the zero-error classical capacity of the graph assisted by quantum no-signalling correlations, the first information theoretic interpretation of the Lovasz number.

6 citations

Journal ArticleDOI
TL;DR: In this paper, the enigma of entropy on a lattice generated from measurements that define the system is reconsidered from the viewpoint of generalized information theory on a W * algebra (classical and quantum).
Abstract: The enigma of ’’entropy’’ is reconsidered from the viewpoint of generalized information theory on a lattice generated from measurements that define the system. A small (incomplete) set of natural axioms for a global information measure is developed sufficiently to deduce as a special case a generalization of Segal’s entropy on a W*‐algebra (classical and quantum). A simple relationship between monotonicity of entropy and a semigroup on [0,∞] (representing composibility of information) is presented. Various extensions of information‐theoretic results are incidentally proven, including relations between regular composible informations (on an orthocomplemented complete lattice) and measures (on σ—ideals of the lattice).

6 citations

Posted Content
TL;DR: In this paper, a condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained, which shows that a quantum channel preserving the Holevo quantity of at least one (discrete or continuous) ensembles with rank ≥ 0 has the r-partially entanglement-breaking complementary channel.
Abstract: A condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained. This condition shows that a quantum channel preserving the Holevo quantity of at least one (discrete or continuous) ensemble of states with rank $\leq r$ has the r-partially entanglement-breaking complementary channel. Several applications of this result are considered. In particular, it is shown that coincidence of the constrained Holevo capacity and the quantum mutual information of a quantum channel at least at one full rank state implies that this channel is entanglement-breaking.

6 citations

Journal ArticleDOI
TL;DR: In this article, the authors explore the restriction of the coherent information to the positive definite density matrices in the special case where the quantum channels are strictly positive linear maps and show that for any positive integer n, the maximally mixed state is always a critical point for any mixed unitary quantum channels with orthogonal, unitary Kraus operators.
Abstract: This paper will explore the restriction of the coherent information to the positive definite density matrices in the special case where the quantum channels are strictly positive linear maps The space of positive definite density matrices is equipped with an embedded submanifold structure of the real vector space of Hermitian matrices These ensure that the n-shot coherent information is differentiable and allows for the computation of its gradient and Hessian We show that any tensor products of critical points preserve being a critical point of the coherent information Furthermore, we show that for any positive integer n, the maximally mixed state is always a critical point for the class of mixed unitary quantum channels with orthogonal, unitary Kraus operators We determine when the maximally mixed state is a local maximum/minimum or saddle point, including its eigenvectors, for the class of Pauli-erasure channels when n is equal to 1 This class includes the dephrasure channel and Pauli channel and refines potential regions where super-additivity is thought to occur These techniques can be used to study other optimization problems over density matrices and allow the use of manifold optimization algorithms and a better understanding of the quantum capacity problem by utilizing the first and second order geometry

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20234
202211
202122
202017
201923
201818