Separability criterion for density matrices

A quantum system consisting of two subsystems is separable if its density matrix can be written as rho=Sigma(A)W(A) rho(A)' x rho(A)' and rho(A) '' are density matrices for the two subsystems, and the positive weights w(A) satisfy Sigma w(A)=1. In this Letter, it is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of rho, has only non-negative eigenvalues. Some examples show that this criterion is more sensitive than Bell's inequality for detecting quantum inseparability.