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On superactivation of one-shot quantum zero-error capacity and the related property of quantum measurements

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Abstract

We give a detailed description of a low-dimensional quantum channel (input dimension 4, Choi rank 3) demonstrating the symmetric form of superactivation of one-shot quantum zero-error capacity. This property means appearance of a noiseless (perfectly reversible) subchannel in the tensor square of a channel having no noiseless subchannels. Then we describe a quantum channel with an arbitrary given level of symmetric superactivation (including the infinite value). We also show that superactivation of one-shot quantum zero-error capacity of a channel can be reformulated in terms of quantum measurement theory as appearance of an indistinguishable subspace for the tensor product of two observables having no indistinguishable subspaces.

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Authors and Affiliations

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

    M. E. Shirokov

  2. University of Copenhagen, Copenhagen, Denmark

    T. V. Shulman

Authors
  1. M. E. Shirokov
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  2. T. V. Shulman
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Correspondence to M. E. Shirokov.

Additional information

Original Russian Text © M.E. Shirokov, T.V. Shulman, 2014, published in Problemy Peredachi Informatsii, 2014, Vol. 50, No. 3, pp. 35–50.

Supported in part by the Scientific Program “Mathematical Theory of Control and Dynamic Systems” of the Russian Academy of Sciences and by the Russian Foundation for Basic Research, project nos. 2-01-00319-a and 13-01-00295-a).

Supported in part by the Danish Research Council through the Centre for Symmetry and Deformation at the University of Copenhagen.

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Shirokov, M.E., Shulman, T.V. On superactivation of one-shot quantum zero-error capacity and the related property of quantum measurements. Probl Inf Transm 50, 232–246 (2014). https://doi.org/10.1134/S003294601403003X

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  • DOI: https://doi.org/10.1134/S003294601403003X

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