Quantum Advantage for Single-Photon State Characterization

We propose a multiphoton interference protocol that characterizes the pairwise overlaps of the internal modes of single photons more efficiently than pairwise Hong-Ou-Mandel characterization experiments. We experimentally implement this protocol to characterize three photons. We show that our implementation of the characterization protocol outperforms the pairwise Hong-Ou-Mandel characterization, even if the Hong-Ou-Mandel characterization would have been performed in a noiseless, perfect experiment. We demonstrate this via the Fisher information matrix. Surprisingly, this advantage persists at arbitrary nonzero transmission, demonstrating the viability of this protocol for real-world characterization of single photons.