On Quantum Capacity of Compound Channels

TL;DR

This paper investigates the quantum capacity of compound channels, establishing capacity results for finite cases and informed decoders, and highlighting open problems for more general scenarios.

Contribution

It determines the quantum capacity of finite compound channels and shows that perfect decoder knowledge does not increase capacity, advancing understanding of robust quantum communication.

Findings

Quantum capacity of finite compound channels is characterized.

Perfect decoder knowledge does not increase capacity for finite channels.

Results extend to quantum averaged channels with long-term memory.

Abstract

In this paper we address the issue of universal or robust communication over quantum channels. Specifically, we consider memoryless communication scenario with channel uncertainty which is an analog of compound channel in classical information theory. We determine the quantum capacity of finite compound channels and arbitrary compound channels with informed decoder. Our approach in the finite case is based on the observation that perfect channel knowledge at the decoder does not increase the capacity of finite quantum compound channels. As a consequence we obtain coding theorem for finite quantum averaged channels, the simplest class of channels with long-term memory. The extension of these results to quantum compound channels with uninformed encoder and decoder, and infinitely many constituents remains an open problem.