The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology
中文速览 本文提出了一个统一的理论框架，以理解和推广洪-歐-曼德爾（Hong-Ou-Mandel, HOM）干涉效应。其核心思想在于，HOM效应的根源是输入光子态在交换空间模式时所表现出的对称性。作者将此观点从标准的双光子、双模式情况，推广至任意光子数和模式数的配置，其中传统的分束器被一个更普适的离散傅里叶变换（DFT）干涉仪所取代。这个基于对称性的框架不仅简化并统一了一系列已知的结果，还为量子计量学提供了直接的启示，使得计算特定测量方案下的精度界限（费雪信息）成为可能，从而为实现量子增强传感和探测复杂量子态的对称性开辟了新路径。 English Research Briefing Research Briefing: The Role of Symmetry in Generalized Hong-Ou-Mandel Interference and Quantum Metrology 1. The Core Contribution This paper’s central thesis is that input-state symmetry under the exchange of spatial modes is the fundamental principle governing generalized Hong-Ou-Mandel (HOM) interference. By elevating symmetry from a contributing factor to the core concept, the authors develop a unified framework that extends the standard two-photon, two-mode HOM effect to arbitrary input states and multi-mode interferometers. The primary conclusion is that a Discrete Fourier Transform (DFT) interferometer, a generalization of a beam splitter, naturally maps the cyclic permutation symmetry of an \(n\)-mode input state onto a directly measurable photon number statistic. This powerful connection provides a constructive method for designing quantum metrology protocols and yields explicit, analytical expressions for the Fisher Information, directly linking the symmetry of the probe state and the sensing Hamiltonian to the ultimate achievable precision. ...