Berry phase and entanglement of three qubits in a new Yang-Baxter system

Abstract

In this paper we construct a new 8×8 M matrix from the 4×4 M matrix, where M/M is the image of the braid group representation. The 8×8 M matrix and the 4×4 M matrix both satisfy extraspecial 2-group algebra relations. By Yang-Baxteration approach, we derive a unitary R (θ,) matrix from the M matrix with parameters and θ. Three-qubit entangled states can be generated by using the R (θ,) matrix. A Hamiltonian for three qubits is constructed from the unitary R (θ,) matrix. We then study the entanglement and Berry phase of the Yang-Baxter system. © 2009 The American Physical Society.