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This article is cited in 2 scientific papers (total in 2 papers)
Solutions of the Yang–Baxter equation associated with a topological
basis and applications in quantum information
Mo-Lin Gea, Li-Wei Yua, Kang Xueb, Qing Zhaoc a Chern Institute of Mathematics, Nankai University, Tianjin, China
b Department of Physics, Northeast Normal University, Changchun, China
c Physics College, Beijing Institute of Technology, Beijing, China
Abstract:
We discuss a new type of solutions of the Yang–Baxter equation, called type-II solutions. They are related to quantum entanglements. The action of the corresponding braiding operator on the topological basis associated with a topological quantum field theory generates a $(2J{+}1)$-dimensional matrix form of the $R$-matrix for spin $J$, i.e., the Wigner function $D$ with the spectral parameter $\theta$ denoting the entanglement degree. We present concrete examples for $J=1/2$ and $J=1$ in an explicit form. We show that the Hamiltonian related to the type-II $R$-matrix is Kitaev's toy model.
Keywords:
Yang–Baxter equation, quantum entanglement, topological quantum field theory, Wigner function $D$, Kitaev's toy model.
Received: 01.06.2014
Citation:
Mo-Lin Ge, Li-Wei Yu, Kang Xue, Qing Zhao, “Solutions of the Yang–Baxter equation associated with a topological
basis and applications in quantum information”, TMF, 181:1 (2014), 19–38; Theoret. and Math. Phys., 181:1 (2014), 1145–1163
Linking options:
https://www.mathnet.ru/eng/tmf8723https://doi.org/10.4213/tmf8723 https://www.mathnet.ru/eng/tmf/v181/i1/p19
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Abstract page: | 535 | Full-text PDF : | 163 | References: | 51 | First page: | 36 |
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