Separability Criterion for Density Matrices

A quantum system consisting of two subsystems is separable if its density matrix can be written as 0ex{0ex}=0ex{0ex}A^w₀₀^'₀^'', where ₀^' and ₀^'' are density matrices for the two subsystems, and the positive weights w₀ satisfy w₀0ex{0ex}=0ex{0ex}1. In this Letter, it is proved that a necessary condition for separability is that a matrix, obtained by partial transposition of, has only non-negative eigenvalues. Some examples show that this criterion is more sensitive than Bell's inequality for detecting quantum inseparability.