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Classical capacities of quantum channels with environment assistance

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Abstract

A quantum channel physically is a unitary interaction between an information carrying system and an environment, which is initialized in a pure state before the interaction. Conventionally, this state, as also the parameters of the interaction, is assumed to be fixed and known to the sender and receiver. Here, following the model introduced by us earlier [1], we consider a benevolent third party, i.e., a helper, controlling the environment state, and show how the helper’s presence changes the communication game. In particular, we define and study the classical capacity of a unitary interaction with helper, in two variants: one where the helper can only prepare separable states across many channel uses, and one without this restriction. Furthermore, two even more powerful scenarios of pre-shared entanglement between helper and receiver, and of classical communication between sender and helper (making them conferencing encoders) are considered.

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    S. Karumanchi

  2. School of Science and Technology, University of Camerino, Camerino, Italy

    S. Mancini

  3. ICREA and Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, Barcelona, Spain

    A. Winter

  4. Física Teòrica: Informació i Fenòmens Quàntics, Universitat Autònoma de Barcelona, Barcelona, Spain

    D. Yang

  5. Laboratory for Quantum Information, China Jiliang University, Hangzhou, Zhejiang, China

    D. Yang

  6. INFN–Sezione Perugia, Perugia, Italy

    S. Mancini

Authors
  1. S. Karumanchi
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  2. S. Mancini
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  3. A. Winter
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  4. D. Yang
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Corresponding author

Correspondence to S. Karumanchi.

Additional information

Original Russian Text © S. Karumanchi, S. Mancini, A. Winter, D. Yang, 2016, published in Problemy Peredachi Informatsii, 2016, Vol. 52, No. 3, pp. 17–44.

The work was done when the author was with the School of Science and Technology, University of Camerino, Camerino, Italy, and INFN–Sezione Perugia, Perugia, Italy.

Supported by the European Commission, STREP “RAQUEL,” the European Research Council, advanced grant “IRQUAT,” the Spanish MINECO, project no. FIS2013-40627-P, with the support of FEDER funds, as well as by the Generalitat de Catalunya CIRIT, project no. 2014-SGR-966.

Supported by the European Research Council, advanced grant “IRQUAT,” and the NSFC, grant no. 11375165.

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Karumanchi, S., Mancini, S., Winter, A. et al. Classical capacities of quantum channels with environment assistance. Probl Inf Transm 52, 214–238 (2016). https://doi.org/10.1134/S0032946016030029

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  • DOI: https://doi.org/10.1134/S0032946016030029

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