标题： 高斯态之间量子保真度的最佳测量及其在量子计量学中的相关性 显示英文标题

标题： Optimal measurements for quantum fidelity between Gaussian states and its relevance to quantum metrology

摘要： 量子保真度是用来量化两个量子态接近程度的度量。 从操作意义上讲，它是测量结果的概率分布之间的最小重叠，其中最小值是在所有可能的正算子测度（POVMs）中取得的。 量子保真度已在各种科学领域中被研究，但尽管其在实际应用中具有重要意义，相关的最优测量识别却常常被忽视。 我们在此找到了多模高斯态之间量子保真度的最优POVMs的封闭解析形式。 我们的普遍发现适用于特定感兴趣的单模高斯态，并我们识别出三种类型的最优测量：数分辨探测、对算子$\hat{x}\hat{p}+\hat{p}\hat{x}$的本征基的投影以及平方探测，每种测量分别应用于不同类型的单模高斯态。 我们还展示了量子保真度的最优测量与量子参数估计的最优测量之间的等价性，使得可以利用高斯态轻松找到位移、相位、压缩和损耗参数估计的最优测量。 显示英文摘要

摘要： Quantum fidelity is a measure to quantify the closeness of two quantum states. In an operational sense, it is defined as the minimal overlap between the probability distributions of measurement outcomes and the minimum is taken over all possible positive-operator valued measures (POVMs). Quantum fidelity has been investigated in various scientific fields, but the identification of associated optimal measurements has often been overlooked despite its great importance for practical purposes. We find here the optimal POVMs for quantum fidelity between multi-mode Gaussian states in a closed analytical form. Our general finding is specified for selected single-mode Gaussian states of particular interest and we identify three types of optimal measurements: a number-resolving detection, a projection on the eigenbasis of operator $\hat{x}\hat{p}+\hat{p}\hat{x}$, and a quadrature detection, each of which is applied to distinct types of single-mode Gaussian states. We also show the equivalence between optimal measurements for quantum fidelity and those for quantum parameter estimation, enabling one to easily find the optimal measurements for displacement, phase, squeezing, and loss parameter estimations using Gaussian states.