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Sci Rep. 2013 Dec 18;3:3530. doi: 10.1038/srep03530.

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

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Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162, 75013, Paris, France.
Instituto de Física, Universidade Federal do Rio de Janeiro. Caixa Postal 68528, 21941-972 Rio de Janeiro, RJ, Brazil.
Instituto de Física, Universidade Federal Fluminense, 24210-340 Niterói-RJ, Brasil and.
Univ. Paris-Sud 11, Institut de Sciences Moléculaires d'Orsay (CNRS), Bâtiment 350-Campus d'Orsay, 91405 Orsay Cedex, France.


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.

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