AI 中文总结
针对多中选一量子计量学中QFI矩阵奇异时传统方法失效的问题，本文推导了适用于该场景的无矩阵量子精度界，为实用量子单参数计量学提供了精细操作框架。
AI 中文摘要
实用量子单参数估计很少是纯粹的任务，几乎总是包含冗余参数，将其转化为多中选一问题。现有解决该问题的方法依赖多参数计量学，通过将矩阵量子克拉美-罗界约化得到标量量子精度极限。然而这些方法常受限于量子费舍尔信息（QFI）矩阵的复杂求逆及权重矩阵的必要选择，且当QFI矩阵奇异时会失效。本文中，我们表明对于动态多中选一估计，一条此前被忽视的求和规则将所有模型参数的QFI与时间的QFI关联起来，这要求纳入后者以考虑增广QFI矩阵，同时使其固有奇异——这正是传统方法失效的场景。为应对该挑战，我们推导了一个仅涉及标量量、适用性广泛且将现有结果作为特例包含的紧无矩阵量子精度界。在幺正和噪声场景中均得到验证，我们的发现为实用量子单参数计量学提供了更精细的操作框架。
英文摘要
Practical quantum single-parameter estimation is rarely a pristine task; it almost invariably involves nuisance parameters, casting it as a one-from-many problem. Existing approaches to this problem rely on multi-parameter metrology, reducing the matrix quantum Cramér-Rao bound to obtain scalar quantum precision limits. However, these methods are often hampered by the demanding inversion of the quantum Fisher information (QFI) matrix and the requisite choice of a weight matrix, and they break down when the QFI matrix becomes singular. Here, we show that for dynamical one-from-many estimation, a previously overlooked sum rule connecting the QFI about all model parameters to the QFI about time necessitates including the latter to consider an augmented QFI matrix while simultaneously rendering it inherently singular--precisely the scenario where conventional approaches fail. To meet this challenge, we derive a tight, matrix-free quantum precision bound that involves only scalar quantities, offers broad applicability, and subsumes existing results as special cases. Validated in both unitary and noisy settings, our findings provide a refined operational framework for practical quantum single-parameter metrology.
Comments24 pages, 8 figures, under review
