Inseparability inequalities for higher order moments for bipartite systems

Abstract

There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second-order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context, we study an example of a non-Gaussian state, which is a bipartite entangled state of the form ψ(x_a,x_b)∝(αx_a+βx_b)e^{-(x_a2+x_b2)/2}. Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states.