Quantifying n-photon indistinguishability with a cyclic integrated interferometer

We report on a universal method to measure the genuine indistinguishability of n-photons - a crucial parameter that determines the accuracy of optical quantum computing. Our approach relies on a low-depth cyclic multiport interferometer with N = 2n modes, leading to a quantum interference fringe whose visibility is a direct measurement of the genuine n-photon indistinguishability. We experimentally demonstrate this technique for a 8-mode integrated interferometer fabricated using femtosecond laser micromachining and four photons from a quantum dot single-photon source. We measure a four-photon indistinguishability up to 0.81$\pm$0.03. This value decreases as we intentionally alter the photon pairwise indistinguishability. The low-depth and low-loss multiport interferometer design provides an efficient and scalable path to evaluate the genuine indistinguishability of resource states of increasing photon number.