Inseparability of Phase-Damped Bipartite Gaussian States

For bipartite non-Gaussian states which are prepared by applying the phase damping to Gaussian states, we use Fock subspace inseparable criterion and the Shchukin-Vogel inseparable criterion to analyze their inseparability. The lowest order of the two criteria is obtained. Fock subspace criterion is more efficient in detecting the entanglement of damped Gaussian state by numerical results. Two photon Fock subspace criterion does not improve the entanglement detecting condition.