International Journal of Quantum Information

A REPRESENTATION OF SPECIALIZED BIRMAN-WENZL-MURAKAMI ALGEBRA AND BERRY PHASE IN YANG-BAXTER SYSTEM

Lidan Gou, Kang Xue, Qingyong Wang, Gangcheng Wang, Chunfang Sun

Published Oct 1, 2010• 2 citations

Abstract

We present an S-matrix, a solution of the braid relation. A matrix representation of specialized Birman-Wenzl-Murakami algebra is obtained. Based on which, a unitary [Formula: see text]-matrix is generated via the Yang-Baxterization approach. Then we construct a Yang-Baxter Hamiltonian through the unitary [Formula: see text]-matrix. Berry phase of this Yang-Baxter system is investigated in detail.

DOI: 10.1142/s0219749910006320

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International Journal of Quantum Information

A REPRESENTATION OF SPECIALIZED BIRMAN-WENZL-MURAKAMI ALGEBRA AND BERRY PHASE IN YANG-BAXTER SYSTEM

Lidan Gou, Kang Xue, Qingyong Wang, Gangcheng Wang, Chunfang Sun

Published Oct 1, 2010• 2 citations

Publisher

Abstract

DOI: 10.1142/s0219749910006320

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Entanglement and Berry Phase in a $9\times 9$ Yang-Baxter systemEntanglement and Berry Phase in a $9\times 9$ Yang-Baxter system

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A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang-Baxterization approach, we obtain a unitary solution $\breve{R}(θ,φ_{1},φ_{2})$ of Yang-Baxter Equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $\breve{R}$ -matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $\breve{R}$ -matrix, and Berry phase of the Yang-Baxter system is investigated. Specifically, for $ φ_{1}=φ_{2}$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang-Baxterization approach, we obtain a unitary solution $\breve{R}(θ,φ_{1},φ_{2})$ of Yang-Baxter Equation. It is shown that any pure two-qutrit entangled states can be generated via the universal $\breve{R}$-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the $\breve{R}$-matrix, and Berry phase of the Yang-Baxter system is investigated. Specifically, for $ φ_{1}=φ_{2}$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.

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International Journal of Quantum InformationSep 1, 200918 citations

Entanglement and Berry Phase in a

9\times 9

Yang-Baxter system

A M-matrix which satisfies the Hecke algebraic relations is presented. Via the Yang-Baxterization approach, we obtain a unitary solution

\breve{R}(θ,φ_{1},φ_{2})

of Yang-Baxter Equation. It is shown that any pure two-qutrit entangled states can be generated via the universal

\breve{R}

-matrix assisted by local unitary transformations. A Hamiltonian is constructed from the

\breve{R}

-matrix, and Berry phase of the Yang-Baxter system is investigated. Specifically, for $ φ_{1}=φ_{2}$, the Hamiltonian can be represented based on three sets of SU(2) operators, and three oscillator Hamiltonians can be obtained. Under this framework, the Berry phase can be interpreted.