The quantum Cramér–Rao bound (QCRB) provides an ultimate precision limit allowed by quantum mechanics in parameter estimation. Given any quantum state dependent on a single parameter, there is always a positive-operator valued measurement (POVM) saturating the QCRB. However, the QCRB-saturating POVM cannot always be implemented efficiently, especially in multipartite systems. In this paper, we show that the POVM based on local operations and classical communication is QCRB-saturating for arbitrary pure states or rank-two mixed states with varying probability distributions over fixed eigenbasis. Local measurements without classical communication, however, is not QCRB-saturating in general.

中文翻译：

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使用LOCC饱和量子Cramér–Rao界

量子Cramér-Rao界（QCRB）提供了极限力学极限，这是量子力学在参数估计中允许的。给定任何依赖于单个参数的量子态，总是存在一个使QCRB饱和的正算子值测量（POVM）。但是，QCRB饱和POVM不能始终有效地实现，尤其是在多部分系统中。在本文中，我们证明了基于局部操作和经典通信的POVM对于任意纯状态或具有固定特征本征的概率分布变化的秩为2的混合状态，其QCRB饱和。但是，没有经典通信的本地测量通常不会使QCRB饱和。