Adversarial quantum channel discrimination

2025-06-03

AI Summary

This work addresses quantum channel discrimination under adversarial conditions: a tester must distinguish between two quantum channels while an adversary has full access to the environment, possesses quantum memory, and may launch adaptive attacks. To tackle this, we introduce the *minimum output channel divergence*, a novel operational measure, and establish the first adversarial extension of the quantum Stein lemma. We prove its strong converse property and generalize the entropy accumulation theorem to divergence analysis over arbitrary channel sequences. Leveraging new chain rules based on measured relative entropy and sandwiched relative entropy, together with constructions of non-adaptive strategies and an efficient algorithm for regularized divergence, we exactly characterize the optimal type-II error exponent in asymmetric hypothesis testing. Remarkably, this exponent is achievable by simple non-adaptive strategies—ensuring computational tractability, universality of the strong converse, and practical feasibility.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

We introduce a new framework for quantum channel discrimination in an adversarial setting, where the tester plays against an adversary who accesses the environmental system and possesses internal quantum memory to perform adaptive strategies. We show that in asymmetric hypothesis testing, the optimal type-II error exponent is precisely characterized by the minimum output channel divergence, a new notion of quantum channel divergence in the worst-case scenario. This serves as a direct analog of the quantum Stein's lemma in the adversarial channel discrimination. Notably, the optimal error exponent can be achieved via simple non-adaptive strategies by the adversary, and its value can be efficiently computed despite its regularization. The strong converse property for quantum channel discrimination also holds in general. This adversarial quantum Stein's lemma is proved by new chain rules for measured and sandwiched relative entropies. Moreover, we derive a generalized version of the entropy accumulation theorem between two arbitrary sequences of quantum channels, extending the existing results from entropy to divergence and providing a solution to the dual formulation of the open problem presented in [IEEE FOCS, pp. 844-850 (2022)].

Problem

• Adversarial quantum channel discrimination framework introduced
• Optimal error exponent characterized by output divergence
• Generalized entropy accumulation theorem for quantum channels

Innovation

• Adversarial quantum channel discrimination framework
• Minimum output channel divergence concept
• Generalized entropy accumulation theorem