Coherence and dimension witnesses from SWAP tests

Abstract
Coherence witnesses are criteria capable of establishing that a quantum system is in a state of superposition, with respect to a reference basis. I will describe how to define a novel type of coherence witness that identifies the presence of superpositions independently of basis. The witness relies on pairwise state comparisons using a simple circuit known as a SWAP test. These comparisons can be (and indeed have been) implemented in photonics using multiple Hong-Ou-Mandel, two-photon interferometric tests tests in a single experimental set-up. These tests have applications also in photonic indistinguishability tests, dimension witnesses, and (maybe) machine learning.

References
https://arxiv.org/abs/1902.11039
https://arxiv.org/abs/1804.01334
https://arxiv.org/abs/1907.01325