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Inner bounds via simultaneous decoding in quantum network information theory

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Abstract

We prove new inner bounds for several multiterminal channels with classical inputs and quantum outputs. Our inner bounds are all proved in the one-shot setting and are natural analogues of the best classical inner bounds for the respective channels. For some of these channels, similar quantum inner bounds were unknown even in the asymptotic independent and identically distributed setting. We prove our inner bounds by appealing to a new classical–quantum joint typicality lemma established in a companion paper. This lemma allows us to lift to the quantum setting many inner bound proofs for classical multiterminal channels that use intersections and unions of typical sets.

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Notes

  1. Journal version of [9].

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Acknowledgements

I thank Professors Patrick Hayden, David Ding and Hrant Gharibyan for useful discussions, and Dr. Mark Wilde for pointers to important references. I am grateful to the anonymous referees of an earlier version of the paper, whose comments helped greatly in improving the presentation.

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  1. School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, 400005, India

    Pranab Sen

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  1. Pranab Sen
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Sen, P. Inner bounds via simultaneous decoding in quantum network information theory. Sādhanā 46, 18 (2021). https://doi.org/10.1007/s12046-020-01517-9

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