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arXiv:quant-ph/0310109 · Physics Letters A

Construction of entangled states with positive partial transposes based on indecomposable positive linear maps

Kil-Chan Ha, Seung-Hyeok Kye

Published Apr 22, 2004• 44 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2004.04.008

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We consider entanglement witnesses arising from positive linear maps which generate exposed extremal rays. We show that every entangled state can be detected by one of these witnesses, and this witness detects a unique set of entangled states among those. Therefore, they provide a minimal set of witnesses to detect any kind of entanglement in a sense. Furthermore, if those maps are indecomposable then they detect large classes of entangled states with positive partial transposes which have nonempty relative interiors in the cone generated by all PPT states. We also provide a one-parameter family of indecomposable positive linear maps which generate exposed extremal rays. This gives the first examples of such maps in three-dimensional matrix algebra.