Quantum interference lies at the basis of fundamental differences between
quantum and classical behaviors. It is thus crucial to understand the
boundaries between what interference patterns can be described by classical
wave mechanics and what, on the other hand, can only be understood with a
proper quantum mechanical description. While a lot of work has already been
done for the simple case of two-mode interference, the multi-mode case has not
been fully explored yet. Here we derive bounds for classical models of light
fields in a general scenario of intensity interferometry, and we show how they
can be violated in a quantum framework. As a consequence, this violation acts
as a non-classicality witness, able to detect the presence of sources with
sub-Poissonian photon-number statistics. We also derive a criterion for
certifying the indivisibility of a quantum interferometer and obtain a method
to simultaneously measure the average pairwise distinguishability of the input
sources.