Continuous optimal ensembles II. Reducing the separability condition to numerical equations

TL;DR

This paper introduces a method to determine robust separability of bipartite quantum states by reducing the problem to solving finite numerical equations, enabling continuous mixture representations of such states.

Contribution

It presents a novel approach that simplifies identifying robustly separable states through finite numerical equations using the continuous ensemble method.

Findings

Solution exists for all robustly separable states

Provides a continuous mixture of pure product states

Reduces the separability condition to numerical equations

Abstract

A density operator of a bipartite quantum system is called robustly separable if it has a neighborhood of separable operators. Given a bipartite density matrix, its property to be robustly separable is reduced, using the continuous ensemble method, to a finite number of numerical equations. The solution of this system exists for any robustly separable density operator and provides its representation by a continuous mixture of pure product states.