An asymptotical separability criterion for bipartite density operators

TL;DR

This paper introduces an asymptotic criterion for determining the separability of bipartite quantum states, utilizing a continuous ensemble method to approximate the state with a converging sequence of separable states.

Contribution

It proposes a novel asymptotic separability criterion and an iterative procedure to efficiently decide separability within a specified tolerance.

Findings

Sequence of separable states converges to the given state if and only if it is separable.

The convergence speed of the sequence is evaluated.

An iterative method is provided to determine separability within a finite number of steps.

Abstract

For a given density matrix $\rho$ 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 $\rho$ if and only if $\rho$ is separable. The convergence speed is evaluated and for any given tolerance parameter $\kappa$ an iterative procedure is suggested which decides in finite number of steps if there exists a separable density matrix $\rho_\kappa$ which differs from the matrix $\rho$ by at most $\kappa$.