Quantum coherence marks a deviation from classical physics, and has been studied as a resource for metrology and quantum computation. Finding reliable and effective methods for assessing its presence is then highly desirable. Coherence witnesses rely on measuring observables whose outcomes can guarantee that a state is not diagonal in a known reference basis. Here we experimentally measure a novel type of coherence witness that uses pairwise state comparisons to identify superpositions in a basis-independent way. Our experiment uses a single interferometric set-up to simultaneously measure the three pairwise overlaps among three single-photon states via Hong-Ou-Mandel tests. Besides coherence witnesses, we show the measurements also serve as a Hilbert-space dimension witness. Our results attest to the effectiveness of pooling many two-state comparison tests to ascertain various relational properties of a set of quantum states.
@article{arxiv.2104.09235,
title = {Witnesses of coherence and dimension from multiphoton indistinguishability tests},
author = {Taira Giordani and Chiara Esposito and Francesco Hoch and Gonzalo Carvacho and Daniel J. Brod and Ernesto F. Galvão and Nicolò Spagnolo and Fabio Sciarrino},
journal= {arXiv preprint arXiv:2104.09235},
year = {2021}
}