Birman-Wenzl-Murakami代数、拓扑参数与Berry相

Birman-Wenzl-Murakami代数及其拓扑基

Birman-Wenzl-Murakami Algebra and the Topological Basis

本文利用纠缠态构造了Temperley-Lieb代数（TLA）的9 × 9-矩阵表示，进而得到了Birman-Wenzl-Murakami代数（BWMA）的一族9 × 9-矩阵表示.在此基础上，我们找到了三种拓扑基态，并应用拓扑基态将九维BWMA重铸为三维BWMA。最后，我们发现在特殊情况下拓扑基态是自旋单重态。

Quantum teleportation and Birman-Murakami-Wenzl algebra

In this paper, we investigate the relationship of quantum teleportation in quantum information science and the Birman-Murakami-Wenzl (BMW) algebra in low-dimensional topology. For simplicity, we focus on the two spin-1/2 representation of the BMW algebra, which is generated by both the Temperley-Lieb projector and the Yang-Baxter gate. We describe quantum teleportation using the Temperley-Lieb projector and the Yang-Baxter gate, respectively, and study teleportation-based quantum computation using the Yang-Baxter gate. On the other hand, we exploit the extended Temperley-Lieb diagrammatical ap…

BWMA的拓扑基、L1-norm在量子信息中的极值及其在物理中的应用

Topological Basis Associated with BWMA, Extremes of L1-norm in Quantum Information and Applications in Physics

构造了Birman-Wenzl-Murakami代数（BWMA）的拓扑基，并给出了$S^+=S$和$S^+=S^{-1}$的编织矩阵S的三维形式.讨论了一种常见的自旋为1的与BWMA相关的编织矩阵模型。证明了L1-范数和冯诺伊曼熵的极值点$(θ=\pmπ/2$和$\pmπ)$是相互连通的.通过一般性的讨论和实例，我们指出L1-范数描述了量子纠缠。

B-M-W代数的拓扑基：两个自旋1/2的实现

Topological Basis Associated with B-M-W algebra: Two Spin-1/2 Realization

本文研究了Birman-Murakami-Wenzl（B-M-W）代数及其相应的Yang-Baxter $\breve{R}(θ,ϕ)$矩阵的双自旋1/2实现.在B-M-W代数的双自旋1/2实现的基础上，研究了由拓扑基张成的三维拓扑空间。通过这种拓扑基的实现，四维Yang-Baxter $\breve{R}(θ,ϕ)$可约化为具有$J=1$的Wigner $D^{J}$函数.讨论了谱参数空间中的纠缠和Berry相位。结果表明，通过Yang-Baxter $\breve{R}(θ,ϕ)$矩阵作用于标准基，可以得到一组纠缠基，当$\breve{R}_{i}(θ,ϕ)$变为辫子算符时，纠缠度最大.