Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

Abstract

In this paper we present reducible representation of the $n^2$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^2$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $9\times 9$ unitary $\breve{R}$ according to a $9\times 9$ braiding S-matrix we have constructed. The entanglement properties of $\breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}(\theta ,{\varphi }_1,{\varphi }_2)$-matrix acting on the standard basis.

9 pages

References in corpus (7)

• Braiding Operators are Universal Quantum Gates
• High Temperature Macroscopic Entanglement
• Braiding transformation, entanglement swapping and Berry phase in entanglement space
• Berry phase and quantum criticality in Yang--Baxter systems
• Entanglement of electron spins in superconductors
• Entanglement and Berry Phase in a $(3\times 3)-$dimensional Yang-Baxter system
• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices