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 May 9, 2025)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
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
Issues
If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.
Created January 12, 2016, Updated June 2, 2021