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 June 3, 2023)
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Yang-Baxter operators need quantum entanglement to distinguish knots
Published
Author(s)
, 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
Pub Type
Journals
Keywords
knot theory, quantum entanglement
Citation
Created January 12, 2016, Updated June 2, 2021