Enhance capability of separable ball criterion for the bipartite quantum states

The largest separable ball is a meaningful geometric sufficient condition for separability of bipartite quantum states which tells that all the states in the unit ball in Frobenius norm centered at the identity matrix are separable. In this paper, we propose an algorithm that can improve the capability of this criterion to detect the separability outside the unit ball by solving an optimization problem based on the invertible local operators, that is, to optimize ( A ⊗ B ) ρ ( A ⊗ B ) † − 1 F with respect to the invertible square matrices A and B . The numerical examples have shown that our algorithm is more powerful than the original separable ball criterion.