Quasitriangular Hopf algebras, braid groups and quantum entanglement

Abstract

The aim of the paper is to provide an method to obtain representations of the braid group through a set of quasitriangular Hopf algebras. In particular, these algebras may be derived from group algebras of cyclic groups with additional algebraic structures. In this context, by using the flip operator, it is possible to construct R-matrices that can be regarded as quantum logic gates capable of preserving quantum entanglement.

13 pages

References in corpus (4)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Teleportation, Braid Group and Temperley--Lieb Algebra
• Entanglement and Quantum Groups

Cited by in corpus (3)

• Cyclic groups and quantum logic gates
• Solutions to the constant Yang-Baxter equation in all dimensions
• An Approach by Representation of Algebras for Decoherence-Free Subspaces