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arXiv:2011.00410 · IEEE Transactions on Information Theory

Universal Classical-Quantum Superposition Coding and Universal Classical-Quantum Multiple Access Channel Coding

Masahito Hayashi, Ning Cai

Published Nov 30, 2021• 6 citations
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Abstract

We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel coding by using generalized packing lemmas for the type method. Using our classical-quantum universal superposition code, we establish the capacity region of a classical-quantum compound broadcast channel with degraded message sets. Our universal classical-quantum multiple access channel codes have two types of codes. One is a code with joint decoding and the other is a code with separate decoding. It is not so easy to construct a former code that universally achieves general points of the capacity region beyond corner points. First, we construct the latter code that universally achieves general points of the capacity region. Then, converting the latter code to the former coder, we construct the above desired code with the former type.

DOI
10.1109/tit.2021.3131575

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We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. In our achievability result, we decouple the reliability and privacy constraints, which are handled via source coding with quantum side information and universal hashing, respectively. Hence, we also establish that the multi-user coding problem under consideration can be handled solely via point-to-point coding techniques. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.
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