YangBaxter operators need quantum entanglement to distinguish knots
Abstract
Any solution to the YangBaxter equation yields a family of representations of braid groups. Under certain conditions, identified by (Turaev 1988 Inventiones Math. 92 52753), the appropriately normalized trace of these representations yields a link invariant. Any YangBaxter solution can be interpreted as a twoqudit quantum gate. Here we show that if this gate is nonentangling, then the resulting invariant of knots is trivial. We thus obtain a connection between topological entanglement and quantum entanglement.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 February 2016
 DOI:
 10.1088/17518113/49/7/075203
 arXiv:
 arXiv:1507.05979
 Bibcode:
 2016JPhA...49g5203A
 Keywords:

 Quantum Physics;
 Mathematics  Geometric Topology
 EPrint:
 12 pages, 2 figures