Non-Gaussianity dynamics of two-mode squeezed number states subject to different types of noise based on cumulant theory

We provide a measure to characterize the non-Gaussianity of phase-space function of bosonic quantum states based on the cumulant theory. We study the non-Gaussianity dynamics of two-mode squeezed number states by analyzing the phase-averaged kurtosis for two different models of decoherence:amplitude damping model and phase damping model. For the amplitude damping model, the non-Gaussianity is very fragile and completely vanishes at a finite time. For the phase damping model, such states exhibit rich non-Gaussian characters. In particular, we obtain a transition time that such states can transform from sub-Gaussianity into super-Gaussianity during the evolution. Finally, we compare our measure with the existing measures of non-Gaussianity under the independent dephasing environment.