量子信道辨识的极小极大博弈
Minimax games for quantum channel discrimination
- The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
- RWTH Aachen University（亚琛工业大学）
- City University of Hong Kong (Dongguan)（香港城市大学（东莞））
- National Taiwan University（台湾大学）
- National Center for Theoretical Sciences（国家理论科学中心）
- Hon Hai (Foxconn) Quantum Computing Center（鸿海（富士康）量子计算中心）
- Wuhan University（武汉大学）
- Wuhan Institute of Quantum Science and Technology（武汉量子技术研究院）
- International Quantum Academy（国际量子学院）
- Nagoya University（名古屋大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出量子信道辨识的博弈论框架，涵盖十二种博弈模型，给出精确刻画和渐近Stein指数，并解决开放问题。
AI中文摘要：
量子信道辨识是识别、验证和基准测试量子动力学的一项基本任务。以往的研究主要考虑最佳情况的测试者输入设置或最坏情况的干扰者输入设置。在此，我们引入一个博弈论框架，其中测试者和干扰者各自控制独立的输入。结合三种输入结构（由测试者和干扰者在信道使用中是否使用纠缠输入或独立同分布输入来表征）与四种信息模式（由干扰者策略的可见性及其对真实假设的了解程度决定），产生了十二种博弈模型。我们以九个极小极大假设检验散度给出了所有十二种模型的精确有限块长假设检验刻画，并推导了它们的渐近Stein指数。值得注意的是，对于纠缠干扰者，干扰者策略的可见性及其对真实假设的了解程度均不影响渐近Stein指数，而对于独立同分布干扰者，信息模式仍然具有重要影响。作为示例，我们研究了从替换信道中辨识一般信道的问题，并表明所有渐近Stein指数均与相同的加性单字母量一致。我们进一步发展了一个通用论证，将可实现性结果升级为强逆结果，从而为几种博弈模型建立了强逆性质，解决了Berta等人[Commun. Math. Phys. 385, 55 (2021)]提出的复合假设检验中的一个开放问题，并加强了Lami [arXiv:2510.06340]的几个近期结果。这里开发的框架和技术可能支持未来涉及竞争角色的量子信息任务的研究。
英文摘要：
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.
