Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Our approach employs the total variation distance to find those transformations that minimize the error probability in discriminating the behaviors of distinguishable and indistinguishable photons. In particular, we show that so-called Sylvester interferometers are near-optimal for this task. By using Bayesian tests and inference, we numerically show that Sylvester transformations largely outperform most Haar-random unitaries in terms of sample size required. Furthermore, we experimentally demonstrate the efficacy of the transformation using an efficient 3D integrated circuits in the single- and multiple-source cases. We then discuss the extension of this approach to a larger number of photons and modes. These results open the way to the application of Sylvester interferometers for optimal assessment of multiphoton interference experiments.

粒子不可区分性是量子统计的核心，它调节基本现象，例如固体的电子能带结构、玻色-爱因斯坦凝聚和超导性。此外，它在线性光学量子计算和模拟等实际应用中是必要的，特别是对于玻色子采样设备。因此，开发工具来证明多个源之间的真正多光子干扰至关重要。我们的方法使用总变差距离来找到那些在区分可区分和不可区分光子的行为时最小化错误概率的变换。特别是，我们表明所谓的西尔维斯特干涉仪对于这项任务来说接近最佳。通过使用贝叶斯测试和推理，我们在数值上表明，就所需样本量而言，西尔维斯特变换在很大程度上优于大多数 Haar 随机单一变换。此外，我们通过实验证明了在单源和多源情况下使用高效 3D 集成电路的转换效果。然后我们讨论将这种方法扩展到更多的光子和模式。这些结果为应用西尔维斯特干涉仪对多光子干涉实验进行最佳评估开辟了道路。