Classical Capacities of Averaged and Compound Quantum Channels

TL;DR

This paper establishes the capacity formulas for averaged and compound classical-quantum channels, demonstrating the existence of reliable universal codes under limited channel knowledge using universal approximation techniques.

Contribution

It provides the first capacity formulas for compound and averaged classical-quantum channels, extending classical results to the quantum setting with universal coding strategies.

Findings

Capacity formulas for compound channels derived

Universal classical-quantum codes proven to exist

Capacity results align with classical analogs

Abstract

We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on the universal classical approximation of the quantum relative entropy which in turn relies on the universal hypothesis testing results.