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We use time-frequency continuous variables as the standard framework todescribe states of light in the subspace of individual photons occupyingdistinguishable auxiliary modes. We adapt to this setting the interplay betweenmetrological properties and the phase space picture already extensively studiedfor quadrature variables. We also discuss in details the Hong-Ou-Mandelinterferometer, which was previously shown to saturate precision limits, andprovide a general formula for the coincidence probability of a generalizedversion of this experiment. From the obtained expression, we systematicallyanalyze the optimality of this measurement setting for arbitrary unitarytransformations applied to each one of the input photons. As concrete examples,we discuss transformations which can be represented as translations androtations in time-frequency phase space for some specific states.

Time-frequency metrology with two single-photon states: phase space picture and the Hong-Ou-Mandel interferometer