Precise identification of quantum states under noise constraints is essential for quantum information processing. In this study, we generalize the classical best arm identification problem to quantum domains, designing methods for identifying the purest one within $K$ unknown $n$-qubit quantum states using $N$ samples. %, with direct applications in quantum computation and quantum communication. We propose two distinct algorithms: (1) an algorithm employing incoherent measurements, achieving error $\exp\left(- \Omega\left(\frac{N H_1}{\log(K) 2^n }\right) \right)$, and (2) an algorithm utilizing coherent measurements, achieving error $\exp\left(- \Omega\left(\frac{N H_2}{\log(K) }\right) \right)$, highlighting the power of quantum memory. Furthermore, we establish a lower bound by proving that all strategies with fixed two-outcome incoherent POVM must suffer error probability exceeding $ \exp\left( - O\left(\frac{NH_1}{2^n}\right)\right)$. This framework provides concrete design principles for overcoming sampling bottlenecks in quantum technologies.

本研究针对量子信息处理中的噪声约束下的量子态精准识别问题，提出了一种将经典最佳臂识别问题推广至量子领域的创新方法。研究中开发了两种算法，通过不同测量方式来识别未知的$n$-量子位中最纯的量子态，显著降低了识别误差，并提供了克服量子技术中采样瓶颈的具体设计原则。

最纯量子态识别