Quantum channel games reveal new limits on testing quantum processes
Minimax games for quantum channel discrimination
Information Theory
Summary
Figuring out how to tell different quantum processes apart is very important for checking how quantum computers and devices work. The authors look at this problem as a game where two players pick different types of inputs to test or confuse the quantum process. They analyze twelve ways these games can be played depending on what kind of inputs and information each player has. They found exact math formulas that describe how well players can do in each scenario, including long-run limits. Their work also solves an open question from earlier research and strengthens some recent findings.
What this means in practice
- •For quantum hardware testers: Improve strategies for verifying quantum devices by understanding limits of detecting differences between quantum operations under adversarial conditions.
- •For cryptography engineers: Design robust quantum communication protocols that withstand interference by modeling adversaries with entangled or independent input strategies.
A theory result. No direct application yet.
Authors
Kun Fang, Michael X. Cao, Hao-Chung Cheng, Li Gao, Masahito Hayashi
Abstract
Quantum channel discrimination is a primitive task for identifying, verifying, and benchmarking quantum dynamics. Previous studies have primarily considered either the best-case tester-input setting or the worst-case jammer-input setting. Here, we introduce a game-theoretic framework in which both the tester and jammer control separate inputs. Combining three input structures, characterized by whether the tester and jammer use entangled inputs or IID inputs across channel uses, with four information patterns, determined by the visibility of the jammer's strategy and its knowledge of the true hypothesis, yields twelve game models. We provide exact finite blocklength hypothesis testing characterizations of all twelve models in terms of nine minimax hypothesis testing divergences and derive their asymptotic Stein exponents. Notably, for entangled jammers, neither the visibility of the jammer's strategy nor its knowledge of the true hypothesis affects the asymptotic Stein exponent, whereas the information pattern remains consequential for IID jammers. As an example, we study the discrimination of a general channel from a replacer channel and show that all asymptotic Stein exponents coincide with the same additive, single letter quantity. We further develop a general argument that upgrades achievability results to strong converse results, thereby establishing strong converse properties for several game models, resolving an open problem in composite hypothesis testing posed by Berta et al. [Commun. Math. Phys. 385, 55 (2021)], and strengthening several recent results of Lami [arXiv:2510.06340]. The framework and techniques developed here may support future studies of quantum information tasks involving competing roles.