分布式多参数量子传感中最优探针态的几何构造

中文摘要 AI 辅助

探针态的选择对于在量子计量学中实现极限精度至关重要。对于单一参数，与最大和最小生成元本征值相关的本征态的等权叠加是最优的。这种简单构造不能直接扩展到多参数情形，因为不同参数可能偏好不同的探针。我们通过分布式量子传感中多参数估计的最优探针的几何构造来解决这一难题。在此设定下，生成元对易且共享共同本征基，因此每个共同本征态定义了一个生成元本征值向量。我们证明，这些向量的最小包围球和最小包围椭球分别决定了最大总量子Fisher信息和最小加权协方差。在两种情况下，凸体的边界识别出可能对最优探针有贡献的共同本征态，而其中心和形状则规定了这些本征态布居数必须满足的条件。我们的结果为设计最优探针态提供了一种系统方法，将参数生成元的结构直接与多参数量子计量学中可达到的精度联系起来。

英文摘要

The choice of probe state is essential to achieving ultimate precision in quantum metrology. For a single parameter, an equal superposition of eigenstates associated with the largest and smallest generator eigenvalues is optimal. This simple construction does not directly extend to multiple parameters, since different parameters can favor different probes. We address this difficulty through a geometric construction of optimal probes for multiparameter estimation in distributed quantum sensing. In this setting, the generators commute and share a common eigenbasis, so each common eigenstate defines a vector of generator eigenvalues. We show that the minimal enclosing balls and ellipsoids of these vectors determine the maximal total quantum Fisher information and the minimum weighted covariance, respectively. In both cases, the boundary of the convex body identifies the common eigenstates that can contribute to an optimal probe, and its center and shape specify the conditions that their populations must satisfy. Our results provide a systematic approach to designing optimal probe states, linking the structure of the parameter generators directly to the attainable precision in multiparameter quantum metrology.

发表机构

• Shenzhen University（深圳大学）
• The Chinese University of Hong Kong（香港中文大学）

机构由 AI 辅助整理，请以论文原文为准。