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Yang–Baxter equations and quantum entanglements

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Abstract

In this paper some results associated with a new type of Yang–Baxter equation (YBE) are reviewed. The braiding matrix of Kauffman–Lomonaco has been extended to the solution (called type-II) of Yang–Baxter equation (YBE) and the related chain Hamiltonian is given. The Lorentz additivity for spectral parameters is found, rather than the Galilean rule for the familiar solutions (called type-I) of YBE associated with the usually exact solvable models. Based on the topological basis, the N-dimensional solution of YBE is found to be the Wigner D-functions. The explicit examples for spin-\(\frac{1}{2}\) and spin-1 have been shown. The extremes of \(\ell _1\)-norm of \(D\)-functions are introduced to distinguish the type-I from type-II of braiding matrices that also correspond to those of von Neumann entropy for quantum information.

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Acknowledgments

This work is in part supported by NSF of China with No. 11275024 and No. 11075077.

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Authors and Affiliations

  1. Chern Institute of Mathematics, Nankai University, Tianjin, 300071, China

    Mo-Lin Ge & Ruo-Yang Zhang

  2. Department of physics, Northeast Normal University, Changchun, 130024, China

    Kang Xue

  3. Physics College, Beijing Institute of Technology, Beijing, 100081, China

    Qing Zhao

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  1. Mo-Lin Ge
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Correspondence to Mo-Lin Ge.

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Ge, ML., Xue, K., Zhang, RY. et al. Yang–Baxter equations and quantum entanglements. Quantum Inf Process 15, 5211–5242 (2016). https://doi.org/10.1007/s11128-014-0765-3

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