Entanglement And Berry Phase In A Parameterized Three-Qubit System

Yang-Baxter equation (YBE) is made up of Yang and Baxter, respectively, in dealing with one-dimensional δ - function interaction model and two-dimensional statistical models when developing theory dealing with the nonlinear integrable models, then promote the related theory of the quantum algebras and the Yangian algebras by V.G.Drinfeld. Recent researches show that the unitary braiding operators can produce qubit entangled states and obtain the Greenberger-Horne-Zeilinger (GHZ) state, which is one of the most serviceable multipartite d-level maximally entangled states. On the other hand, solution of the YBE can be viewed as parameter-dependent braid group representation. In consequence unitary solutions of the braid group relation as well as unitary solutions of the YBE may be considered as universal quantum gates. Such theory inspires a new approach to study of quantum entanglement and Berry phase. This motivates us such parameterized (?) matrix can be constructed as the generalized quantum gates for multipartite d-level systems.In this paper, to reconstruct a new three-qubit system, compared the results of quantum entanglement and Berry phase under the two qubit system, we construct a parameterized form of unitary (?)1,2,3(θ1,θ2,θ3) matrix through the Yang-Baxterization method. Acting such matrix on three-qubit natural basis as a quantum gate, we can obtain a set of eight entangled states.Discussed the eight entanglement degree of entanglement of three body, two entangled concurrence, and reminding entanglement. The set of eight entangled states possess the same entanglement value depending on the parameters θ1 and θ2 . Particularly, such entangled states can produce a set of maximally entangled bases GHZ states with respect toθ1=θ2 = π/2 . Choosing a useful Hamiltonian with respect to θ1=θ2=θ, one can study the evolution of the eigenstates and investigate the result of Berry phase. It is not difficult to find that the Berry phase for this new three-qubit system consistent with the solid angle on the Bloch sphere. So we can introduce three spin operators that make up the SU(2) algebraic relation, and logogram the Hamilton of this new three-qubit system. By future discussion, we can make the solution of Yang-Baxter equation extend to multibody system, and get more valuable entangle states, in order to more clearly study of quantum entanglement and Berry phase theory.