2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/90593The recent proposed realignment separability criterion for mixed is analyzed. We identify the essential part of this criterion is a swap operator followed by a partial transposition. Then we analyze the separability criterion of permutation indices of the density matrix for multipartite state which is a generalization of the realignment criterion. We give a method to solve the equivalence problem of the separability criterion of permutation indices of the density matrix. For tripartite state, we show the non-trivial separability criteria are either partial transposition criterion or realignment criterion.Revtex, 3 pagesQuantum Physicstext