Private Classical Communication over Quantum Multiple-Access Channels

TL;DR

This paper characterizes the capacity region for private classical communication over quantum multiple-access channels, providing single-letter formulas for degradable channels and demonstrating that multi-user coding can be reduced to point-to-point coding techniques.

Contribution

It derives a regularized capacity region for arbitrary quantum multiple-access channels and establishes a single-letter sum-rate formula for degradable channels, simplifying multi-user coding.

Findings

Single-letter sum-rate formula for degradable channels

Capacity region expression for arbitrary channels

Multi-user coding reduces to point-to-point coding techniques

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.