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 -