Towards the ultimate limits of quantum channel discrimination and quantum communication

TL;DR

This paper investigates the fundamental limits of quantum channel discrimination, developing new theoretical tools, establishing key lemmas, and connecting these concepts to quantum communication capacities, thereby advancing the understanding of quantum information processing.

Contribution

It introduces new bounds on quantum divergences, proves a quantum Stein's lemma for channel discrimination, and links channel capacities with discrimination strategies, unifying core quantum information concepts.

Findings

Sharper bounds on quantum hypothesis testing relative entropy

Establishment of a quantum Stein's lemma for memoryless channels

Connections between channel capacities and discrimination strategies

Abstract

Distinguishability is fundamental to information theory and extends naturally to quantum systems. While quantum state discrimination is well understood, quantum channel discrimination remains challenging due to the dynamic nature of channels and the variety of discrimination strategies. This work advances the understanding of quantum channel discrimination and its fundamental limits. We develop new tools for quantum divergences, including sharper bounds on the quantum hypothesis testing relative entropy and additivity results for channel divergences. We establish a quantum Stein's lemma for memoryless channel discrimination, and link the strong converse property to the asymptotic equipartition property and continuity of divergences. Notably, we prove the equivalence of exponentially strong converse properties under coherent and sequential strategies. We further explore the interplay among operational regimes, discrimination strategies, and channel divergences, deriving exponents in various settings and contributing to a unified framework for channel discrimination. Finally, we recast quantum communication tasks as discrimination problems, uncovering deep connections between channel capacities, channel discrimination, and the mathematical structure of channel divergences. These results bridge two core areas of quantum information theory and offer new insights for future exploration.