论文标题
混合状态量子估计的信息几何方法
Information geometric approach to mixed state quantum estimation
论文作者
论文摘要
信息几何形状促进了对统计流形的几何结构的研究，从而在科学知识的各个领域提供了一系列阐明。在物理科学，尤其是在量子理论中，这种几何方法与国家的区分性具有令人难以置信的相似之处，这是确定实施物理过程的有效性的巨大价值的能力。这为我们提供了这项工作的背景。在这里，我们将从信息几何的角度来解决单次统计推断的问题。我们将获得Cramér-Rao结合的广义Bhattacharyya高阶校正，其中统计数据由混合量子态给出。使用公正的估计器$ t $，在构成的构成与产生动态的哈密顿$ H $的同时，我们发现这些校正与估算器的特定选择无关。使用信息几何技术执行此过程，并建立与纯状态案例进行更正的连接。
Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this geometric method has an incredible parallel with the distinguishability of states, an ability of great value for determining the effectiveness in implementing physical processes. This gives us the context for this work. Here we will approach a problem of uniparametric statistical inference from an information-geometric perspective. We will obtain the generalised Bhattacharyya higher-order corrections for the Cramér-Rao bound, where the statistics is given by a mixed quantum state. Using an unbiased estimator $T$, canonically conjugated to the Hamiltonian $H$ that generates the dynamics, we find these corrections independent of the specific choice of estimator. This procedure is performed using information-geometric techniques, establishing connections with corrections to the pure states case.
