复合状态的量测诱导Fisher信息的层次性
Hierarchy of measurement-induced Fisher information for composite states
摘要：
量子费舍尔信息作为量子态的一个本征量，是量子探测和估计中的一个核心概念。当对量子态进行量子测量时，经典概率分布出现，这反过来又导致经典Fisher信息。在这篇文章中，我们利用经典的量子测量诱导的Fisher信息，并揭示了这种测量诱导的Fisher信息的丰富的层次结构。我们建立了一个一般的框架，分布和转移的Fisher信息。特别是，我们说明了三个极值分布类型的Fisher信息：本地拥有型，本地不可访问型，和完全共享型。此外，我们指出了Fisher信息的分布和流动在一些物理问题中所起的重要作用，例如，开放量子过程的非马尔可夫性、环境辅助计量学、克隆和广播等。
英文摘要：
Quantum Fisher information, as an intrinsic quantity for quantum states, is a central concept in quantum detection and estimation. When quantum measurements are performed on quantum states, classical probability distributions arise, which in turn lead to classical Fisher information. In this article, we exploit the classical Fisher information induced by quantum measurements, and reveal a rich hierarchical structure of such measurement-induced Fisher information. We establish a general framework for the distribution and transfer of the Fisher information. In particular, we illustrate three extremal distribution types of the Fisher information: the locally owned type, the locally inaccessible type, and the fully shared type. Furthermore, we indicate the significant role played by the distribution and flow of the Fisher information in some physical problems, e.g., the non-Markovianity of open quantum processes, the environment-assisted metrology, the cloning and broadcasting, etc.
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