Entanglement And Berry Phase In Yang-Baxter System

With the development of quantum information (QI) theory, quantum entanglement and geometric phase have been studied extensively because of their wide applications in QI. In this thesis, the quantum geometric phase and quantum entanglement in the Yang-Baxter system are discussed respectively. This discussion leads to some interesting results, which are helpful for the understanding of the physical implications of quantum geometric phase and quantum entanglement.This paper consists five chapters. The whole paper discusses the entanglement and the physical significance of the geometric phase in the Yang-Baxter system, as well as they are how to realize and how to correlate. The core of this paper is composed of Chaps.2-4. Chap.2 concentrates on introducing the Yang-Baxter system. First of all, a M algebra is given to construct a braid group algebra, we get a unitary solution R(θ,φ) of the Yang-Baxter Equation (YBE). Secondly, the paper presents a new -matrix directly according to our recent research results and obtains a solution of the braid relation. In the same way we obtain a unitary solution Yang-Baxter of the YBE via Yang-Baxterization acting on the solution. Chap.3 concentrates on discussing the question of the entanglement. Derived from the solution of YBE in Chap.2, we show that arbitrary entanglement states can be achieved by relating the unitary matrix R(θ,φ) to entanglement. Then the dynamics of entanglement as well as the maximum entanglement states are studied. Chap.4 concentrates on discussing an oscillator Hamiltonian which can be constructed from the solution R(θ,φ) matrix of YBE , as well as the physical significance of the Berry phase in Yang-Baxter system.Finally the summary and prospect are presented.