Direct measurement of the biphoton Wigner function through two-photon interference

TLDR

The Hong‑Ou‑Mandel experiment, a benchmark in quantum optics, demonstrates non‑classical photon pairs and has been generalized to bosonic and fermionic systems, while the Wigner function offers complete information for entanglement inference using established criteria. The study demonstrates that a simple modification of the standard HOM experiment enables direct measurement of the Wigner function. The authors apply the modified HOM setup to biphotons generated by parametric down‑conversion, a highly reliable quantum system. They find that a negative Wigner function value suffices to certify non‑Gaussian entanglement between photons, and that the modified HOM experiment opens new avenues for fundamental quantum tests with simple optical setups.

Abstract

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non–classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable quantum systems, consisting of biphotons generated by parametric down conversion. A consequence of our results is that a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics using simple optical set-ups.