  We give a full description of the problem of Multi-Boson Correlation Sampling
(MBCS) at the output of a random interferometer for single input photons in
arbitrary multimode pure states. The MBCS prob- lem is the task of sampling at
the interferometer output from the probability distribution associated with
polarization- and time-resolved detections. We discuss the richness of the
physics and the complexity of the MBCS problem for nonidentical input photons.
We also compare the MBCS problem with the standard bo- son sampling problem,
where the input photons are assumed to be identical and the system is
"classically" averaging over the detection times and polarizations.
