Universal random codes: Capacity regions of the compound quantum multiple-access channel with one classical and one quantum sender

TL;DR

This paper establishes universal coding strategies for a compound quantum multiple-access channel where one sender transmits classical messages and the other transmits quantum information, providing an optimal capacity region characterization.

Contribution

It introduces universal codes for a two-sender quantum communication scenario and characterizes the capacity region for the compound QMAC with mixed classical and quantum transmission.

Findings

Universal codes are constructed for the two-sender quantum communication model.

The achievable rate region with these codes is proven to be optimal.

A multi-letter capacity region characterization is provided for the compound QMAC.

Abstract

We consider the compound memoryless quantum multiple-access channel (QMAC) with two sending terminals. In this model, the transmission is governed by the memoryless extensions of a completely positive and trace preserving map which can be any element of a prescribed set of possible maps. We study a communication scenario, where one of the senders aims for transmission of classical messages while the other sender sends quantum information. Combining powerful universal random coding results for classical and quantum information transmission over point-to-point channels, we establish universal codes for the mentioned two-sender task. Conversely, we prove that the two-dimensional rate region achievable with these codes is optimal. In consequence, we obtain a multi-letter characterization of the capacity region of each compound QMAC for the considered transmission task.