We show that the Hong-Ou-Mandel effect from quantum optics is equivalent to the SWAP test, a quantum information primitive which compares two arbitrary states. We first derive a destructive SWAP test that doesn't need the ancillary qubit that appears in the usual quantum circuit. Then, we study the Hong-Ou-Mandel effect for two photons meeting at a beam splitter and prove it is, in fact, an optical implementation of the destructive SWAP test. This result offers both an interesting simple realization of a powerful quantum information primitive and an alternative way to understand and analyse the Hong-Ou-Mandel effect.
@article{arxiv.1303.6814,
title = {The SWAP test and the Hong-Ou-Mandel effect are equivalent},
author = {Juan Carlos Garcia-Escartin and Pedro Chamorro-Posada},
journal= {arXiv preprint arXiv:1303.6814},
year = {2014}
}