Separability Criterion for Density Matrices

1996/08/19 by Asher Peres · 180 citations
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Computing Algorithms and Architecture

paper · doi:10.1103/physrevlett.77.1413

Abstract

A quantum system consisting of two subsystems is separable if its density matrix can be written as \ensuremathρ\phantom\rule0ex0ex=\phantom\rule0ex0ex\ensuremathΣAw_A\ensuremathρ_A^\ensuremath'\ensuremath\bigotimes\ensuremathρ_A^\ensuremath'\ensuremath', where \ensuremathρ_A^\ensuremath' and \ensuremathρ_A^\ensuremath'\ensuremath' are density matrices for the two subsystems, and the positive weights w_A satisfy \ensuremathΣw_A\phantom\rule0ex0ex=\phantom\rule0ex0ex1. In this Letter, it is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of \ensuremathρ, has only non-negative eigenvalues. Some examples show that this criterion is more sensitive than Bell's inequality for detecting quantum inseparability.

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