Sufficient and necessary condition of separability for generalized Werner states Original Research Article

In a celebrated paper [Optics Communications 179, 447, 2000], A.O. Pittenger and M.H. Rubin presented for the first time a sufficient and necessary condition of separability for the generalized Werner states. Inspired by their ideas, we generalized their method to a more general case. We obtain a sufficient and necessary condition for the separability of a specific class of N d-dimensional system (qudits) states, namely special generalized Werner state (SGWS): image, where image is an entangled pure state of N qudits system and image satisfies two restrictions: (i) image; (ii) Matrix image, where image, is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.