  The 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.
