发表机构
Center for Quantum Enabled-Computing, Center for Theoretical Physics of the Polish Academy of Sciences; International Iberian Nanotechnology Laboratory (INL); Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165/59, Université libre de Bruxelles; Instituto de Física, Universidade Federal Fluminense（波兰科学院理论物理中心量子使能计算中心; 伊比利亚纳米技术国际实验室; 布鲁塞尔自由大学布鲁塞尔理工学院量子信息与通信中心; 弗鲁米嫩塞联邦大学物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Gram矩阵层析方法，通过测量Bargmann不变量来表征光子部分可区分性，无需直接访问内部自由度，且样本复杂度与内部维度无关，适用于玻色采样等实验。
AI 中文摘要
部分可区分性影响多光子干涉，而多光子干涉是玻色采样等大规模光子实验以及量子技术中多光子态应用的核心。表征导致这种行为的内部自由度具有挑战性：在许多场景中，这些自由度无法直接访问，甚至其维度或物理性质可能先验未知。这里我们针对具有纯或近纯内部状态的独立制备光子引入Gram矩阵层析。对于纯态，Gram矩阵包含预测对内部自由度不敏感的实验统计所需的所有信息。我们从可测量的Bargmann不变量（编码重叠幅度和集体相位的量）的二次数量中重建该矩阵，直至物理上无关的相位选择。我们使用两种互补方法访问这些量：定向傅里叶干涉仪和单个随机干涉仪中测量的二体和三体光子数相关性。我们推导出显式误差界，控制任何后续对内部状态不敏感的实验中预测和实际结果分布之间的总变差距离。这些保证考虑了有限采样和与纯度的偏差。关键的是，该协议的总样本复杂度独立于内部希尔伯特空间维度，并在内部状态重叠的温和假设下呈多项式。我们的协议使用标准干涉测量，并将其转化为对部分可区分光子的稳健且操作上有根据的表征。
英文摘要
Partial distinguishability affects multiphoton interference, which is central to large-scale photonic experiments such as Boson Sampling and to applications of multiphoton states across quantum technologies. Characterizing the internal degrees of freedom responsible for this behavior is challenging: in many scenarios they cannot be accessed directly and even their dimension or physical nature may be unknown \emph{a priori}. Here we introduce Gram-matrix tomography for independently prepared photons with pure or nearly pure internal states. For pure states, the Gram matrix contains all information required to predict the statistics of experiments that are insensitive to the internal degrees of freedom. We reconstruct this matrix, up to physically irrelevant phase choices, from a quadratic number of measurable Bargmann invariants (quantities encoding overlap magnitudes and collective phases). We access these quantities using two complementary approaches: targeted Fourier interferometers and two- and three-body photon-number correlations measured in a single random interferometer. We derive explicit error bounds that control the total-variation distance between predicted and actual outcome distributions for any subsequent experiment that is insensitive to the internal states. These guarantees account for finite sampling and deviations from purity. Crucially, the total sample complexity of the protocol is independent of the internal Hilbert-space dimension and polynomial under mild assumptions on overlaps of internal states. Our protocol uses standard interferometric measurements and turns them into a robust and operationally grounded characterization of partially distinguishable photons.
