Detecting quantum non-Gaussianity of noisy Schrodinger cat states

Highly quantum nonlinear 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 Schrodinger'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 Schrodinger cat states evolving in a lossy bosonic channel. We prove that the quantum non-Gaussianity can be effectively detected for high values of losses and for large coherent amplitudes of the cat states.