arXiv subjects

Chunfang Sun

Publications and source records attributed to Chunfang Sun.

23 records · Page 2Linked to original sources

arXiv2009

Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate

A method of constructing $n^{2}\times n^{2}$ matrix solutions(with $n^{3}$ matrix elements) of Temperley-Lieb algebra relation is presented in this paper. The single loop of these solutions are $d=\sqrt{n}$. Especially, a $9\times9-$matrix solution with single loop d=$\sqrt{3}$ is discussed in detail. An unitary Yang-Baxter $\breve{R}(θ,q_{1},q_{2})$ matrix is obtained via the Yang-Baxterization process. The entanglement property and geometric property (\emph{i.e.} Berry Phase) of this Yang-Baxter system are explored.

quant-ph↗

arXiv2009

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.

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arXiv2009

Entanglement and Berry Phase in a $(3\times 3)-$dimensional Yang-Baxter system

Based on the method which is given in Ref. [Sun et.al. arXiv:0904.0092v1], we present another $9\times 9$ unitary $\breve{R}-$matrix, solution of the Yang-Baxter Equation, is obtained in this paper. The entanglement properties of $\breve{R}-$matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $\breve{R}$-matrix acting on the standard basis. A Yang-Baxter Hamiltonian can be constructed from unitary $\breve{R}-$matrix. Then the geometric properties of this system is studied. The results showed that the Berry phase of this system can be represented under the framework of SU(2) algebra.

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arXiv2009

The representations of Temperley-Lieb algebras and entanglement in a Yang-Baxter system

A method of constructing Temperley-Lieb algebras(TLA) representations has been introduced in [Xue \emph{et.al} arXiv:0903.3711]. Using this method, we can obtain another series of $n^{2}\times n^{2}$ matrices $U$ which satisfy the TLA with the single loop $d=\sqrt{n}$. Specifically, we present a $9\times9$ matrix $U$ with $d=\sqrt{3}$. Via Yang-Baxterization approach, we obtain a unitary $ \breve{R}(θ,φ_{1},φ_{2})$-matrix, a solution of the Yang-Baxter Equation. This $9\times9$ Yang-Baxter matrix is universal for quantum computing.

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arXiv2009

Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $ 9\times9 $ unitary $ \breve{R}$ according to a $ 9\times9 $ braiding S-matrix we have constructed. The entanglement properties of $ \breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $ \breve{R}(θ, ϕ_{1},ϕ_{2})$-matrix acting on the standard basis.

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