Witnesses of coherence and dimension from multiphoton indistinguishability tests

Quantum coherence is a resource with a lot of application in quantum computing and quantum information, and more in general is studied in the foundations of quantum mechanics. It is of interest to find protocols to verify its presence that are simple and reliable. Currently there exist some methods of coherence witness that are based on a family of observables whose result can check if a state is not diagonal in a given base. Here we experimentally test a novel type of coherence witness based on state comparison to detect sperpositions in a basis-independent way. Our experiment uses a linear interferometer to perform three Hong-Ou-Mandel tests simultaneously to measure pairwise overlaps between three single-photon states.
Beyond coherence witnesses we show that our experimental apparatus can be used as a Hilbert-space dimension witness. Our results validate this procedure as a new type of coherence and dimension witnesses.