The SWAP test and the Hong-Ou-Mandel effect are equivalent

TL;DR

This paper demonstrates that the Hong-Ou-Mandel effect in quantum optics is fundamentally equivalent to the SWAP test in quantum information, providing a new perspective and a simplified implementation of the primitive.

Contribution

It introduces a destructive SWAP test without ancillary qubits and proves the Hong-Ou-Mandel effect as its optical realization, linking quantum optics and information.

Findings

Hong-Ou-Mandel effect is equivalent to the SWAP test

A destructive SWAP test without ancillary qubits is derived

The Hong-Ou-Mandel effect can be understood as an optical implementation of the destructive SWAP test

Abstract

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.