Numerical detection of Gaussian entanglement and its application to the identification of bound entangled Gaussian states

We present a numerical method for solving the separability problem of Gaussian quantum states in continuous-variable quantum systems. We show that the separability problem can be cast as an equivalent problem of determining the feasibility of a set of linear matrix inequalities. Thus, it can be efficiently solved using existent numerical solvers. We apply this method to the identification of bound entangled Gaussian states. We show that the proposed method can be used to identify bound entangled Gaussian states that could be simple enough to be producible in quantum optics.