  Photons generated by spontaneous parametric down conversion (SPDC) are one of
the most useful resources in quantum information science. Two of their most
important characteristics are the purity and the indistinguishability, which
determine just how useful they are as a resource. We show how these
characteristics can both be accessed through Hong, Ou and Mandel (HOM) type
interferences using a single pair source. We also provide simple and intuitive
analytical formulas to extract their values from the depth of the resulting
interference patterns. The validity of these expressions is demonstrated by a
comparison with experimental results and numerical simulations. These results
provide an essential tool for both engineering SPDC sources and characterizing
the quantum states that they emit, which will play an increasingly important
role in developing complex quantum photonic experiments.
