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arXiv:0709.1306 · International Journal of Theoretical Physics

Necessary and Sufficient Condition for Greenberger-Horne-Zeilinger Diagonal States to Be Full N-partite Entangled

Koji Nagata

Published Sep 15, 2009• 5 citations
arXivHTMLPDF
DOI
10.1007/s10773-009-0139-2

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We present a broad class of NNN-qubit Greenberger-Horne-Zeilinger (GHZ)-diagonal states such that nonpositivity under the partial transpose operation is necessary and sufficient for the presence of entanglement, including many naturally arising instances such as dephased GHZ states. Furthermore, our proof directly leads to an entanglement witness which saturates this bound. The witness is applied to thermal GHZ states to prove that the entanglement can be extremely robust to system imperfections.