Simultaneous estimation of multiple parameters near classical precision limit is of fundamental importance to measurement sciences and applications. The associated tasks constitute mainly of two aspects: finding an input quantum state capable of realizing the optimal precision limited by the laws of quantum mechanics, and finding a corresponding measurement scheme that saturates this precision. The latter aspect is typically challenging and usually requires optimization on a case by case basis. Focusing on achieving the precision of the classical limit, or the standard quantum limit, with uncorrelated particles and mutually commuting phase measurements, we present a generic and experimentally feasible Ramsey-like multi-mode interferometer that fulfils the aforementioned tasks. The proposed interferometer features a beam splitting process by a unitary transformation $U$ (with all matrix elements real), and a recombining process by $ U^†$. How such transformations $U$ can be constructed experimentally for both optical and atomic based measurements are discussed, opening up practically useful implementations for multi-mode optical and atomic sensing.

中文翻译：

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使用多模拉姆齐干涉测量法进行多参数估计

同时估计接近经典精度极限的多个参数对于测量科学和应用具有根本重要性。相关任务主要包括两个方面：寻找能够实现量子力学定律所限制的最佳精度的输入量子态，以及寻找使该精度饱和的相应测量方案。后一方面通常具有挑战性，通常需要根据具体情况进行优化。专注于通过不相关粒子和相互交换相位测量实现经典极限或标准量子极限的精度，我们提出了一种通用且实验上可行的类似拉姆齐的多模干涉仪，它可以完成上述任务。所提出的干涉仪的特点是通过酉变换 $U$（所有矩阵元素为实数）进行光束分裂，并通过 $U^†$ 进行重组。讨论了如何通过实验为基于光学和原子的测量构建这种转换 $U$，为多模光学和原子传感开辟了实用的实现方式。