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Solutions of the Yang-Baxter equation associated with a topological basis and applications in quantum information

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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 θ 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.

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Authors and Affiliations

  1. Chern Institute of Mathematics, Nankai University, Tianjin, China

    Mo-Lin Ge & Li-Wei Yu

  2. Department of Physics, Northeast Normal University, Changchun, China

    Kang Xue

  3. Physics College, Beijing Institute of Technology, Beijing, China

    Qing Zhao

Authors
  1. Mo-Lin Ge
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  2. Li-Wei Yu
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  3. Kang Xue
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  4. Qing Zhao
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Corresponding author

Correspondence to Mo-Lin Ge.

Additional information

This paper is dedicated to Professor L. D. Faddeev, who has been guiding our research. We heartily express our deepest respects to him. Faddeev and his colleagues contribute greatly not only with their scientific achievements but also with help in developing the Nankai group.

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Ge, ML., Yu, LW., Xue, K. et al. Solutions of the Yang-Baxter equation associated with a topological basis and applications in quantum information. Theor Math Phys 181, 1145–1163 (2014). https://doi.org/10.1007/s11232-014-0205-7

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