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On approximation of infinite-dimensional quantum channels

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Abstract

We develop an approximation approach to infinite-dimensional quantum channels based on a detailed investigation of continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair “channel, input state.” Obtained results are then applied to the problems of continuity of the χ-capacity as a function of a channel, strong additivity of the χ-capacity for infinite-dimensional channels, and approximating representation for the convex closure of the output entropy of an arbitrary quantum channel.

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Authors and Affiliations

  1. Steklov Mathematical Institute, RAS, Moscow, Russia

    M. E. Shirokov & A. S. Holevo

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  1. M. E. Shirokov
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  2. A. S. Holevo
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Correspondence to M. E. Shirokov.

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Original Russian Text © M.E. Shirokov, A.S. Holevo, 2008, published in Problemy Peredachi Informatsii, 2008, Vol. 44, No. 2, pp. 3–22.

Supported in part by the program “Modern Problems of Theoretical Mathematics” of the Russian Academy of Sciences, the Russian Foundation for Basic Research, project no. 06-01-00164-a, and NSH, grant no. 4129.2006.1.

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Shirokov, M.E., Holevo, A.S. On approximation of infinite-dimensional quantum channels. Probl Inf Transm 44, 73–90 (2008). https://doi.org/10.1134/S0032946008020014

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