The role of initial entanglement and nonGaussianity in the decoherence of photon number entangled states evolving in a noisy channel

Abstract

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' criterion provides a reliable estimate of the separation time also for nonGaussian states. We provide several evidences supporting the conjecture that Gaussian entanglement is the most robust against noise, i.e. it survives longer than nonGaussian one, and that this may be a general feature for CV systems in Markovian channels.