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arXiv:quant-ph/0103003

Comment on: Necessary and sufficient condition of separability of any system

Tilo Eggeling, K. G. H. Vollbrecht, Michael M. Wolf

Published Mar 1, 2001• 1 citation
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Abstract

In a recent paper (quant-ph/0102133) Chen, Liang, Li and Huang suggest a necessary and sufficient separability criterion, which is supposedly practical in judging the separability of any mixed state. In this note we briefly recapitulate their main result and show that it is a reformulation of the problem rather than a practical criterion.

DOI
10.48550/arxiv.quant-ph/0103003

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In a recent paper (quant-ph/0102133) Chen, Liang, Li and Huang suggest a necessary and sufficient separability criterion, which is supposedly practical in judging the separability of any mixed state. In this note we briefly recapitulate their main result and show that it is a reformulation of the problem rather than a practical criterion.
Recently, a new and powerful separability criterion was introduced in [O. Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing the main idea behind the above criterion and the necessary and sufficient condition in terms of positive maps, we provide a characterization of separable states by means of linear contractions. The latter need not be positive maps. We extend the idea to multipartite systems, and find that, somewhat suprisingly, partial realigment (unlike partial transposition) can detect genuinely triparite entanglement. We also show that for multipartite system any permutation of indices of density matrix leads to separability criterion.