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IEEE Transactions on Information Theory

Private Classical Communication Over Quantum Multiple-Access Channels

Rémi A. Chou

Published Nov 23, 2021• 11 citations
Publisher

Abstract

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.

DOI
10.1109/tit.2021.3130151

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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.
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.
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. Our achievability result decouples the reliability and privacy constraints, which are handled via distributed source coding with quantum side information at the receiver and distributed hashing, respectively. 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.
We study covert classical communication over quantum multiple-access channels (MACs) with general message sets. Specifically, we consider a fully quantum MAC with arbitrary message sets and an arbitrary number of transmitters. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish general one-shot and asymptotic achievable rate regions. For classical-quantum MACs with general message sets, we establish the covert capacity, when the transmitters are restricted to deterministic encoding. Our result recovers, as a special case, known results for classical communication over classical MACs with general message sets, covert communication of a classical message over a classical channel with two transmitters, and classical communication over quantum MACs. We provide three examples of MACs to which our results can be applied, either directly or indirectly, to achieve positive covert rates. Specifically, we first study covert communication over a finite-dimensional MAC with a helper. We then analyze a classical Gaussian MAC with a helper and derive its covert capacity. Finally, we extend the analysis to a single-mode bosonic MAC with a helper and show that positive covert rates can also be achieved in this setting. To the best of our knowledge, this is the first work to achieve positive-rate covert communication over both classical and quantum MACs.
In this paper, the problem of private communication of classical messages over a quantum multiple access channel under one-shot setting is studied. In this regard, we first introduce general quantum multiple access wiretap channel, and then we calculate an achievable secrecy rate region for the main channel. The encoding process follows the combination of the superposition and Wyner wiretap coding schemes, and the decoding technique is based on the simultaneous decoder and convex splitting. At last, we extend the results to the l-user case.
We study covert classical communication over a quantum multiple-access channel (MAC) with a helper. Specifically, we consider three transmitters, where one transmitter helps the other two transmitters communicate covertly with a receiver. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish an achievable rate region. Our result recovers as a special case known results for classical communication over classical MACs with a degraded message set, classical communication over quantum MACs, and classical communication over MACs with a helper. To the best of our knowledge, our result is the first to achieve covert communication with positive rates over both classical and quantum MACs.
We study classical communication over quantum multiple-access channels and their wiretap counterparts with unreliable entanglement assistance. Using a robust superposition coding scheme, we characterize the trade-off between baseline rates that are guaranteed without entanglement and additional rates achievable when entanglement is available. We establish a regularized characterization of the classical capacity region for the quantum multiple-access channel and extend it to regularized secrecy capacity regions under two models: entanglement loss and interception. Specifically, for the class of entanglement-breaking channels, we demonstrate that these regularized regions reduce to computable single-letter formulas.