The replica method and entropy for mixture of two-mode even and odd schr\"odinger cat states

TL;DR

This paper reviews the replica method for calculating von Neumann entropy and applies it to mixed coherent states and Schrödinger cat states, providing explicit entropy expressions and exploring purity inequalities.

Contribution

It introduces explicit entropy calculations for mixed coherent states and analyzes purity inequalities for Schrödinger cat states using the replica method.

Findings

Explicit entropy expressions for mixed coherent states derived

Purity inequality for bipartite systems studied in the context of Schrödinger cat states

The replica method effectively computes von Neumann entropy in these quantum 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.