One-Shot Classical-Quantum Capacity and Hypothesis Testing

TL;DR

This paper establishes a new approach to quantifying the one-shot classical capacity of quantum channels using hypothesis testing, providing simplified proofs and tight formulas for both memoryless and general channels.

Contribution

It introduces a hypothesis testing-based measure for one-shot quantum channel capacity and extends capacity formulas to arbitrary channels, simplifying existing proofs.

Findings

Capacity approximated by a relative-entropy measure

Unified proof of Holevo-Schumacher-Westmoreland theorem

Tight capacity formulas for general channels

Abstract

The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Stein's lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels. More generally, we obtain tight capacity formulas for arbitrary (not necessarily memoryless) channels.