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We review the replica method for calculating the von Neumann entropy and obtain an explicit expression for the entropy of the mixed coherent states |α〉 and |β〉 employing this method. We study the purity inequality for a bipartite system for separable states on the example of even and odd Schrödinger cat state.

The Replica Method and Entropy for a Mixture of Two-Mode Even and Odd Schrödinger Cat States