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arXiv · 0904.0090

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

Chunfang Sun·Gangcheng Wang·Taotao Hu·Chengcheng Zhou·Qingyong Wang·Kang Xue
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Abstract

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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Chunfang Sun, Gangcheng Wang, Taotao Hu, Chengcheng Zhou, Qingyong Wang, Kang Xue. 2009-04-19. The representations of Temperley-Lieb algebras and entanglement in a Yang-Baxter system. https://arxiv.org/abs/0904.0090

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