Universal classical-quantum superposition coding and universal classical-quantum multiple access channel coding

TL;DR

This paper develops universal coding schemes for classical-quantum channels, establishing capacity regions for compound broadcast and multiple access channels using generalized packing lemmas and superposition coding.

Contribution

It introduces universal classical-quantum superposition and multiple access channel codes, providing capacity region formulas for compound channels with degraded message sets.

Findings

Universal superposition coding achieves capacity region corners.

Universal multiple access codes achieve general capacity points.

Single-letter capacity region formula for classical-quantum compound multiple access channels.

Abstract

We derive universal classical-quantum superposition coding and universal classical-quantum multiple access channel code 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. The former universally achieves corner points of the capacity region and the latter universally achieves general points of the capacity region. Combining the latter universal code with the existing result by Quantum Inf Process. 18, 246 (2019), we establish a single-letterized formula for the capacity region of a classical-quantum compound multiple access channel.