Role of Initial Entanglement and Non-Gaussianity in the Decoherence of Photon-Number Entangled States Evolving in a Noisy Channel

We address the degradation of continuous variable (CV) entanglement in a noisy channel focusing on the set of photon-number entangled states. We exploit several separability criteria and compare the resulting separation times with the value of non-Gaussianity at any time, thus showing that in the low-temperature regime: (i) non-Gaussianity is a bound for the relative entropy of entanglement and (ii) Simon's criterion provides a reliable estimate of the separation time also for non-Gaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust against noise, i. e., it survives longer than a non-Gaussian one, and that this may be a general feature for CV systems in Markovian channels.