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Yang-Baxter operators need quantum entanglement to distinguish knots

Published

Author(s)

Stephen P. Jordan, Gorjan Alagic, Michael Jarret

Abstract

Solutions to the Yang-Baxter equation yield representations of braid groups. Under certain conditions, identified by Turaev, traces of these representations yield link invariants. The matrices satisfying the Yang-Baxter equation, if unitary, can be interpreted as quantum gates. Here we show that if the gate is non-entangling, then the resulting invariant of knots is trivial. Thus we obtain a connection between topological entanglement and quantum entanglement, as proposed by Kauffman et al..
Citation
Journal of Physics A-Mathematical and General
Volume
49

Keywords

knot theory, quantum entanglement

Citation

Jordan, S. , Alagic, G. and Jarret, M. (2016), Yang-Baxter operators need quantum entanglement to distinguish knots, Journal of Physics A-Mathematical and General (Accessed April 13, 2024)
Created January 12, 2016, Updated June 2, 2021