Unitary Solutions to the Yang-Baxter Equation in Dimension Four

Abstract

In this paper, we determine all unitary solutions to the Yang-Baxter equation in dimension four. Quantum computation motivates this study. This set of solutions will assist in clarifying the relationship between quantum entanglement and topological entanglement. We present a variety of facts about the Yang-Baxter equation for the reader unfamiliar with the equation.

30 pages, 3 figures Typos corrected in version 2

Cited by in corpus (11)

• Quantum Knots
• Entanglement Criteria - Quantum and Topological
• Teleportation, Braid Group and Temperley--Lieb Algebra
• Direct Experimental Simulation of the Yang-Baxter Equation
• Yang-Baxter operators need quantum entanglement to distinguish knots
• Factorized Three-body S-Matrix Restrained by Yang-Baxter Equation and Quantum Entanglements
• Generalized Yang-Baxter Equations and Braiding Quantum Gates
• Polyadic braid operators and higher braiding gates
• On a suggestion relating topological and quantum mechanical entanglements
• Quantum entanglement, supersymmetry, and the generalized Yang-Baxter equation
• A Self-Linking Invariant of Virtual Knots