  The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics,
evidencing the quantum nature of the photon. In order to go deeper, and obtain
the complete information about the quantum state of a system, for instance,
composed by photons, the direct measurement or reconstruction of the Wigner
function or other quasi--probability distribution in phase space is necessary.
In the present paper, we show that a simple modification in the well-known HOM
experiment provides the direct measurement of the Wigner function. We apply our
results to a widely used quantum optics system, consisting of the biphoton
generated in the parametric down conversion process. In this approach, 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. We analyze our results using two
examples of parametric down conversion processes taken from recent experiments.
The present work offers a new vision of the HOM experiment that further
develops its possibilities to realize fundamental tests of quantum mechanics
involving decoherence and entanglement using simple optical set-ups.
