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Links and Quantum Entanglement

By A. I. Solomon and C. -L. Ho


We discuss the analogy between topological entanglement and quantum entanglement, particularly for tripartite quantum systems. We illustrate our approach by first discussing two clearly (topologically) inequivalent systems of three-ring links: The Borromean rings, in which the removal of any one link leaves the remaining two non-linked (or, by analogy, non-entangled); and an inequivalent system (which we call the NUS link) for which the removal of any one link leaves the remaining two linked (or, entangled in our analogy). We introduce unitary representations for the appropriate Braid Group ($B_3$) which produce the related quantum entangled systems. We finally remark that these two quantum systems, which clearly possess inequivalent entanglement properties, are locally unitarily equivalent.Comment: 8 pages, 4 figures. Appeared in the Proceedings of the Conference in honour of Murray Gell-Mann's 80th birthday (24-26 Feb 2010, NTU, Singapore),pg.646-66

Topics: Quantum Physics, Mathematical Physics, Mathematics - Group Theory
Year: 2011
DOI identifier: 10.1142/9789814335614_0070
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