Adversarial quantum 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.

Contains the sections "Application 2: adversarial quantum channel discrimination" and "Application 3: a relative entropy accumulation theorem" from arXiv:2411.04035v2. v2: close to published version