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

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 ( 2 J+ 1 )-dimensional matrix...

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Bibliographic Details
Published in:Theoretical and mathematical physics 2014-10, Vol.181 (1), p.1145-1163
Main Authors: Ge, Mo-Lin, Yu, Li-Wei, Xue, Kang, Zhao, Qing
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary: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 ( 2 J+ 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.
ISSN:0040-5779
1573-9333
DOI:10.1007/s11232-014-0205-7