  Superposition and indistinguishablility between probability amplitudes have
played an essential role in observing quantum interference effects of
correlated photons. The Hong-Ou-Mandel interference and interferences of the
path-entangled photon number state are of special interest in the field of
quantum information technologies. However, a fully generalized two-photon
quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and
path-entangled photon number states has not yet been proposed. Here we report
the experimental demonstrations of the generalized two-photon interferometry
with both the interferometric properties of the Hong-Ou-Mandel effect and the
fully unfolded version of the path-entangled photon number state using
photon-pair sources, which are independently generated by spontaneous
parametric down-conversion. Our experimental scheme explains two-photon
interference fringes revealing single- and two-photon coherence properties in a
single interferometer setup. Using the proposed interferometric measurement, it
is possible to directly estimate the joint spectral intensity of a photon pair
source.
