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.

arXiv comment13 pages

References in corpus (8)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Braiding Operators are Universal Quantum Gates
• Anyon computers with smaller groups
• Discrete non-Abelian gauge theories in two-dimensional lattices and their realizations in Josephson-junction arrays
• 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