THE REPRESENTATIONS OF TEMPERLEY-LIEB ALGEBRA AND ENTANGLEMENT IN A YANG-BAXTER SYSTEM
Chunfang Sun, Gangcheng Wang, Taotao Hu, Chengcheng Zhou, Qingyong Wang, Kang Xue · International Journal of Quantum Information · 2009
A method of constructing Temperley-Lieb algebra (TLA) representations has been introduced in [Xue et al. arXiv:0903.3711]. Using this method, we can obtain another series of n2 × n2 matrices U which satisfy the TLA with the single loop [Formula: see text]. Specifically, we present a 9 × 9 matrix U with [Formula: see text]. Via Yang-Baxterization approach, we obtain a unitary [Formula: see text]-matrix, a solution of the Yang-Baxter equation. This 9 × 9 Yang-Baxter matrix is universal for quantum computing.