Complete Criterion for Separability Detection

Using new results on the separability properties of bosonic systems, we provide a new complete criterion for separability. This criterion aims at characterizing the set of separable states from the inside by means of a sequence of efficiently solvable semidefinite programs. We apply this method to derive arbitrarily good approximations to the optimal measure-and-prepare strategy in generic state estimation problems. Finally, we report its performance in combination with the criterion developed by Doherty, Parrilo, and Spedarlieri for the calculation of the entanglement robustness of a relevant family of quantum states whose separability properties were unknown.