TY - JOUR
T1 - Yang-Baxter operators need quantum entanglement to distinguish knots
JF - Journal of Physics A
Y1 - 2016
A1 - Gorjan Alagic
A1 - Michael Jarret
A1 - Stephen P. Jordan
AB - Any solution to the Yang-Baxter equation yields a family of representations of braid groups. Under certain conditions, identified by Turaev, the appropriately normalized trace of these representations yields a link invariant. Any Yang-Baxter solution can be interpreted as a two-qudit quantum gate. Here we show that if this gate is non-entangling, then the resulting invariant of knots is trivial. We thus obtain a general connection between topological entanglement and quantum entanglement, as suggested by Kauffman et al.
VL - 49
U4 - 075203
UR - http://arxiv.org/abs/1507.05979
CP - 7
U5 - 10.1088/1751-8113/49/7/075203
ER -