Witnesses of coherence and dimension from multiphoton indistinguishability tests

Abstract

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.

10 pages, 7 figures

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• Semi-device independent characterization of multiphoton indistinguishability
• Geometry of sets of Bargmann invariants
• Certifying nonstabilizerness in quantum processors
• An Elementary Characterization of Bargmann Invariants
• Estimation of multivariate traces of states given partial classical information
• Convexity of noncontextual wirings and how they order the set of correlations