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On the structure of optimal sets for a quantum channel

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Abstract

Special sets of states, called optimal, which are related to the Holevo capacity and to the minimal output entropy of a quantum channel, are considered. By methods of convex analysis and operator theory, structural properties of optimal sets and conditions of their coincidence are explored for an arbitrary channel. It is shown that strong additivity of the Holevo capacity for two given channels provides projective relations between optimal sets for the tensor product of these channels and optimal sets for the individual channels.

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    M. E. Shirokov

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  1. M. E. Shirokov
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Original Russian Text © M.E. Shirokov, 2006, published in Problemy Peredachi Informatsii, 2006, Vol. 42, No. 4, pp. 23–40.

Supported in part by the Russian Foundation for Basic Research, project no. 06-01-00164a, and the program “Modern Problems of Theoretical Mathematics” of the Russian Academy of Sciences.

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Shirokov, M.E. On the structure of optimal sets for a quantum channel. Probl Inf Transm 42, 282–297 (2006). https://doi.org/10.1134/S0032946006040028

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  • DOI: https://doi.org/10.1134/S0032946006040028

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