SEPARABILITY: A NEW APPROACH FROM THE CONIC STRUCTURE OF POSITIVE OPERATORS
We exploit the cone structure of unnormalized quantum states to reformulate the separability problem. Firstly a convex combination of every quantum state rho in terms of a state C(rho) with the same rank and another one E(rho) with lower rank is perfomed, with weights 1 - lambda(rho) and lambda(rho), respectively. Secondly a scalar lambda(rho)* is computed. Then rho is separable if, and only if, lambda(rho) <= lambda(rho)*. The computation of lambda(rho)* has been undergone under the simplest choice for C(rho) as a product matrix and E(rho) being a pure state, valid for any bipartite and multipartite system in arbitrary dimensions. A necessary condition is also formulated when E(rho) is not pure in the bipartite case.
cone separability criteria