Quantum channel discrimination against jammers

2025-10-09

AI Summary

This work investigates the fundamental limits of distinguishing quantum channels under adversarial interference, bridging the gap between optimal and worst-case scenarios. To this end, we introduce the *min-max channel divergence*—a novel operational measure—and develop a unified discrimination framework. Methodologically, we integrate tools from quantum information theory, game theory, and asymptotic analysis; specifically, we define a regularized version of the min-max divergence and systematically establish its key mathematical properties. Our central result is a Stein-type lemma: under parallel channel discrimination strategies, the optimal asymptotic exponent of the type-II error is precisely characterized by this divergence. This constitutes the first rigorous asymptotic benchmark for interference-resilient quantum channel discrimination, substantially extending the scope and applicability of classical channel discrimination theory.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Adversarial Search
• Machine Learning: Quantum Machine Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

We study the problem of quantum channel discrimination between two channels with an adversary input party (a.k.a. a jammer). This setup interpolates between the best-case channel discrimination as studied by (Wang & Wilde, 2019) and the worst-case channel discrimination as studied by (Fang, Fawzi, & Fawzi, 2025), thereby generalizing both frameworks. To address this problem, we introduce the notion of minimax channel divergence and establish several of its key mathematical properties. We prove the Stein's lemma in this new setting, showing that the optimal type-II error exponent in the asymptotic regime under parallel strategies is characterized by the regularized minimax channel divergence.

Problem

• Discriminating quantum channels with adversarial jammers in the input
• Generalizing best-case and worst-case quantum channel discrimination frameworks
• Establishing minimax channel divergence properties and Stein's lemma

Innovation

• Introduces minimax channel divergence concept
• Proves Stein's lemma for adversarial discrimination
• Characterizes optimal error exponent asymptotically