All photons are equal but some photons are more equal than others

Two photons are identical if they are prepared in the same quantum state and there is a unique way to achieve this. Conversely, there are many different ways of preparing two non-identical photons: they may differ in polarization, frequency, mode-function, etc. Thus, photon distinguishability depends upon the degree of freedom being varied. By analyzing the coincidence probability distribution in a Hong-Ou-Mandel experiment, we show that photon distinguishability can be quantified by the rate of distinguishability of photons, an experimentally measurable parameter that crucially depends on both the photon-quantum state and the degree of freedom under control.