  We extensively discuss the Hong-Ou-Mandel experiment taking an original
phase-space-based perspective. For this, we analyze time and frequency
variables as quantum continuous variables in perfect analogy with position and
momentum of massive particles or with the electromagnetic field's quadratures.
We discuss how this experiment can be used to directly measure the
time-frequency Wigner function and implement logical gates in these variables.
We also briefly discuss the quantum/classical aspects of this experiment
providing a general expression for intensity correlations that explicit the
differences between a classical Hong-Ou-Mandel like dip and a quantum one.
Throughout the manuscript, we will often focus and refer to a particular system
based on AlGaAs waveguides emitting photon pairs via spontaneous parametric
down-conversion, but our results can be extended to other analogous
experimental systems and to different degrees of freedom.
