Unitary Equivalence of Quantum States in a Bipartite System

Abstract

Abstract If two quantum states are unitarily equivalent then their von Neumann entropies are same. Converse statement also holds, which was proved by Kan He et al. [Applied Mathematics Letters, 2012;25(8):1391–1393 [1]]. In this paper, we extend it to bipartite quantum system and prove a sufficient and necessary condition of unitary equivalence of quantum states associated with the von Neumann entropy of the composite states. A sufficient condition is also provided which involves the von Neumann entropy of the quantum state of the component subsystems. Bipartite quantum system is of interest in quantum cryptography and quantum information processing. Quantum key distribution also uses a bipartite quantum system shared between two parties namely Alice and Bob.KeywordsQuantum statesUnitary equivalenceVon Neumann entropy