The replica method and entropy for mixture of two-mode even and odd schrödinger cat states

Abstract: The replica method for calculating the von Neumann entropy is reviewed. Explicit expression for the entropy of the mixed coherent states $|\alpha>$ and $|\beta>$ is obtained using this method. The purity inequality for bipartite system for separable states is studied on example of even and odd Schr\"{o}dinger cat state.