Adversarial quantum channel discrimination

TL;DR

This paper introduces a new adversarial framework for quantum channel discrimination, providing a complete characterization of the optimal error exponents and linking it to quantum cryptography through entropy accumulation.

Contribution

It defines the minimum output channel divergence, analogous to Stein's lemma, and demonstrates that simple strategies achieve optimal error exponents in adversarial quantum channel discrimination.

Findings

Optimal error exponent characterized by new divergence measure

Simple non-adaptive strategies are sufficient for optimality

Reveals a connection between entropy accumulation and adversarial channel discrimination

Abstract

We introduce a new framework for quantum channel discrimination in an adversarial setting, where the tester plays against an adversary. We show that in asymmetric hypothesis testing, the optimal type-II error exponent is precisely characterized by a new notion of quantum channel divergence (termed the minimum output channel divergence). This serves as a direct analog of the quantum Stein's lemma in this new framework, and complements previous studies on ``best-case'' channel discrimination, thereby providing a complete understanding of the ultimate limits of quantum channel discrimination. Notably, the optimal error exponent can be achieved by simple non-adaptive adversarial strategies, and despite the need for regularization, it remains efficiently computable and satisfies the strong converse property in general. Furthermore, we show that entropy accumulation, a powerful tool in quantum cryptography, can be reframed as an adversarial channel discrimination problem, establishing a new connection between quantum information theory and quantum cryptography.