Separability Criterion for Density Matrices

Abstract

A quantum system consisting of two subsystems is separable if its density matrix can be written as $ρ=\sum_A w_A\,ρ_A'\otimesρ_A''$, where $ρ_A'$ and $ρ_A''$ are density matrices for the two subsytems. In this Letter, it is shown that a necessary condition for separability is that a matrix, obtained by partial transposition of $ρ$, has only non-negative eigenvalues. This criterion is stronger than Bell's inequality.