  The bunching of two single photons on a beam-splitter is a fundamental
quantum effect, first observed by Hong, Ou and Mandel. It is a unique
interference effect that relies only on the photons' indistinguishability and
not on their relative phase. We generalize this effect by demonstrating the
bunching of two Bell states, created in two passes of a nonlinear crystal, each
composed of two photons. When the two Bell states are indistinguishable, phase
insensitive destructive interference prevents the outcome of four-fold
coincidence between the four spatial-polarization modes. For certain
combinations of the two Bell states, we demonstrate the opposite effect of
anti-bunching. We relate this result to the number of distinguishable modes in
parametric down-conversion.
