Entanglement criterion of computable cross norm and realignment for continuous-variable bipartite symmetric states

Abstract

We provide the entanglement criterion of computable cross norm and realignment for any two-mode continuous-variable state with permutational symmetry. The entanglement criterion for a non-Gaussian state is obtained from its Gaussian kernel by employing the technique of functional analysis. The entanglement conditions turn out to be necessary and sufficient for the non-Gaussian states prepared by one-photon subtracting from or adding to symmetric Gaussian states. The entanglement criterion of non-Gaussian states evolved in thermal noise and amplitude damping environment also is obtained.