Sufficient and necessary condition of separability for generalized Werner states

摘要

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): W~ (d~N)_j(v) = (1 _ v).;l~(N)/ d~N v|ψ_d~N)(ψ_d~N|, where |ψ_d~N) = EU/dα_i|i _ _ _ i) is an entangled pure state of N qudits system and α_i satisfies two restric_tions: (i) Efl-olα_icx; = 1; (ii) Matrix -1(1(1) + TE,,α_ili)Ula;), where T = Min { 1 /Ica 1}, 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.