量子序列参数测试
Quantum sequential parameter testing
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中文总结 AI 辅助
本文提出序列参数测试框架，开发双峰值检验方法，将其应用于量子比特相位和纯度测试，验证其在资源高效认证任务中的优势。
中文摘要 AI 辅助
假设检验中的序列策略采用可变次数的测量轮次，一旦观测数据达到规定的误差容忍度即可做出决策。尽管序列检验在离散假设集上已成熟，但将该框架扩展至连续参数空间面临额外挑战，且在很大程度上尚未被探索。本文引入序列参数测试框架，用于确定未知参数至规定容忍度，通过排除足够远的竞争值以达到目标误差容忍度，明确其与传统参数估计的操作区别，并为连续假设族开发序列检验方法，引入双峰值检验作为序列似然比检验的自然且计算高效的类似方法。将该框架应用于两个典型量子任务：量子比特的相位测试和纯度测试。对于相位测试，数值结果表明，自适应投影测量的平均样本成本与固定副本数的集体协变测量相同；对于纯度测试，局域测量是最优的，序列参数测试相较于固定样本大小协议可显著节省平均样本。我们的结果确立了参数测试为涉及连续参数的资源高效认证任务提供了操作上有意义的框架。
英文摘要
Sequential strategies in hypothesis testing use a variable number of measurement rounds, allowing a decision to be made as soon as the observed data provide a prescribed level of error tolerance. Although sequential testing is well established for a discrete set of hypotheses, extending this framework to a continuous parameter space poses additional challenges and has remained largely unexplored. In this article, we introduce sequential \textit{parameter testing}, a framework for determining an unknown parameter up to a prescribed tolerance by ruling out sufficiently distant competing values with a target error tolerance. We clarify its operational distinction from conventional parameter estimation and develop sequential tests for continuous families of hypotheses, introducing the \textit{twin-peaks test} as a natural and computationally efficient analog of sequential likelihood-ratio testing. We apply the framework to two paradigmatic quantum tasks: testing the phase and the purity of a qubit. For phase testing, we show numerically that adaptive projective measurements achieve the same average sample cost as collective covariant measurements with a fixed number of copies. For purity testing, local measurements are optimal, and sequential parameter testing yields significant average sample savings over fixed sample-size protocols. Our results establish parameter testing as an operationally meaningful framework for resource-efficient certification tasks involving continuous parameters.
