Yang-Baxter operators need quantum entanglement to distinguish knots

Abstract

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.

12 pages, 2 figures

References in corpus (1)

• Quantum Fourier Transforms and the Complexity of Link Invariants for Quantum Doubles of Finite Groups

Cited by in corpus (11)

• Towards topological quantum computer
• Braiding quantum gates from partition algebras
• Local invariants of braiding quantum gates -- associated link polynomials and entangling power
• Solutions to the constant Yang-Baxter equation in all dimensions
• The Yang-Baxter equation, Quantum computing and Quantum entanglement
• Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation
• Polyadic braid operators and higher braiding gates
• Geometric representations of braid and Yang-Baxter gates
• Generating W states with braiding operators
• A note on "eight-vertex" universal quantum gates
• Quantum teleportation and Birman-Murakami-Wenzl algebra