An asymptotical separability criterion for bipartite density operators

Abstract

For a given density matrix $ρ$ of a bipartite quantum system an asymptotical separability criterion is suggested. Using the continuous ensemble method, a sequence of separable density matrices is built which converges to $ρ$ if and only if $ρ$ is separable. The convergence speed is evaluated and for any given tolerance parameter $κ$ an iterative procedure is suggested which decides in finite number of steps if there exists a separable density matrix $ρ_κ$ which differs from the matrix $ρ$ by at most $κ$.