  Different non-classicality criteria expressed in the form of inequalities
among intensity moments and elements of photon-number distributions are applied
to noisy twin beams and other two-mode states obtained from a twin beam by
using a beam splitter. Their performance in revealing the non-classicality is
judged in comparison with the exact results provided by suitable entanglement
and local non-classicality quantifiers. Whereas the non-classicality of noisy
twin beams is always revealed by these criteria, not all the nonclassical
states obtained at the output of the beam splitter can be identified by these
experimentally easily reachable criteria.
