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A note on separability criteria for multipartite state

Heng Fan
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Abstract

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.

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Heng Fan. 2002-10-24. A note on separability criteria for multipartite state. https://arxiv.org/abs/quant-ph/0210168

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