标题： 量子序贯通用假设检验 显示英文标题

标题： Quantum Sequential Universal Hypothesis Testing

摘要： 量子假设检验（QHT）涉及未知量子态的统计推断。 在复合假设的一般情况下，QHT的目标是根据对状态的多个副本进行测量，来确定未知量子态属于两个状态类中的哪一个。 先前关于具有复合假设的QHT的研究集中在固定副本的两步协议上，先进行状态估计，然后进行优化的联合测量。 然而，这种固定副本的方法可能效率不高，因为它无论测试任务的内在难度如何，都使用相同数量的副本。 为了解决这些限制，我们引入了量子序贯通用检验（QSUT），这是一种用于复合假设一般情况下的序贯QHT的新框架。 QSUT基于通用推理，并在旨在探索假设空间的自适应局部测量和为最大区分而优化的联合测量之间交替进行。 QSUT被证明在对假设结构做出最少假设的情况下，可以严格控制第一类错误。 我们提出了QSUT的两个实际实例，一个基于Helstrom-Holevo检验，另一个利用浅层变分量子电路。 在一系列复合QHT任务中的实证结果表明，与最先进的固定副本策略相比，QSUT始终能降低副本复杂度。 显示英文摘要

摘要： Quantum hypothesis testing (QHT) concerns the statistical inference of unknown quantum states. In the general setting of composite hypotheses, the goal of QHT is to determine whether an unknown quantum state belongs to one or another of two classes of states based on the measurement of a number of copies of the state. Prior art on QHT with composite hypotheses focused on a fixed-copy two-step protocol, with state estimation followed by an optimized joint measurement. However, this fixed-copy approach may be inefficient, using the same number of copies irrespective of the inherent difficulty of the testing task. To address these limitations, we introduce the quantum sequential universal test (QSUT), a novel framework for sequential QHT in the general case of composite hypotheses. QSUT builds on universal inference, and it alternates between adaptive local measurements aimed at exploring the hypothesis space and joint measurements optimized for maximal discrimination. QSUT is proven to rigorously control the type I error under minimal assumptions about the hypothesis structure. We present two practical instantiations of QSUT, one based on the Helstrom-Holevo test and one leveraging shallow variational quantum circuits. Empirical results across a range of composite QHT tasks demonstrate that QSUT consistently reduces copy complexity relative to state-of-the-art fixed-copy strategies.