  Highly quantum non-linear interactions between different bosonic modes lead
to the generation of quantum non-Gaussian states, i.e. states that cannot be
written as mixtures of Gaussian states. A paradigmatic example is given by
Schroedinger's cat states, that is coherent superpositions of coherent states
with opposite amplitude. We here consider a novel quantum non-Gaussianity
criterion recently proposed in the literature and prove its effectiveness on
Schroedinger cat states evolving in a lossy bosonic channel. We prove that
quantum non-Gaussianity can be effectively detected for high values of losses
and for large coherent amplitudes of the cat states.
