Entanglement And Berry Phase In A (3×3)-dimensional Yang-Baxter System

Due to the quantum entanglement in quantum information of potentialapplications, there are many theories to study entanglement of qualitative andquantitative description. Yang-Baxter Equation (YBE) and relevant algebraiccomputation about Berry phase and entanglement is domain branch in recent years .In this paper, the quantum Berry phase and quantum entanglement in the 3×3Yang-Baxter system are discussed respectively.This paper consists five chapters, the core of this paper is composed ofChaps.2-4.Chap.2,concentrates on Yang-Baxterization of M algebra. First of all, aM algebra is given to construct a braid group algebra,we get a unitarysolution R (x) i∨of the Yang-Baxter Equation. In the same way we obtain a unitarysolutionYBE via Yang-Baxterization acting on the solution. In Chap.3, We present a9×9 unitary∨R?matrix, solution of the Yang-Baxter Equation, is obtained inthispaper. Entanglement properties of∨Rmatrix is investigated, and the arbitrary degreeof entanglement for two-qutrit entangled states can be generated via-matrix actingon the standard basis. In Chap.4, a Yang-Baxter Hamiltonian can be constructed fromunitary matrix.Then the geometric properties of this system is studied. The resultsshowed that the Berry phase of this system can be represented under the framework ofSU(2) algebra.