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Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel

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Abstract

Several relations between the Holevo capacity and entanglement-assisted classical capacity of a quantum channel are proved; necessary and sufficient conditions for their coincidence are obtained. In particular, it is shown that these capacities coincide if (respectively, only if) the channel (respectively, the χ-essential part of the channel) belongs to the class of classical-quantum channels (the χ-essential part is a restriction of a channel obtained by discarding all states that are useless for transmission of classical information). The obtained conditions and their corollaries are generalized to channels with linear constraints. By using these conditions it is shown that the question of coincidence of the Holevo capacity and entanglement-assisted classical capacity depends on the form of a constraint. Properties of the difference between quantum mutual information and the χ-function of a quantum channel are explored.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    M. E. Shirokov

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  1. M. E. Shirokov
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Correspondence to M. E. Shirokov.

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Original Russian Text © M.E. Shirokov, 2012, published in Problemy Peredachi Informatsii, 2012, Vol. 48, No. 2, pp. 3–20.

Supported in part by the Scientific Program “Mathematical Control Theory and Dynamic Systems” of the Russian Academy of Sciences and the Russian Foundation for Basic Research, project nos. 10-01-00139-a and 12-01-00319-a.

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Shirokov, M.E. Conditions for coincidence of the classical capacity and entanglement-assisted capacity of a quantum channel. Probl Inf Transm 48, 85–101 (2012). https://doi.org/10.1134/S0032946012020019

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  • DOI: https://doi.org/10.1134/S0032946012020019

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