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Unitary Solutions to the Yang–Baxter Equation in Dimension Four

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Abstract

In this paper, we determine all unitary solutions to the Yang–Baxter equation in dimension four. Quantum computation motivates this study. This set of solutions will assist in clarifying the relationship between quantum entanglement and topological entanglement. We present a variety of facts about the Yang–Baxter equation for the reader unfamiliar with the equation.

PACS: 02.10.Yn; 02.10.Kn; 03.65.Ud; 03.67.Hk

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References

  1. L. Kauffman and S. J. Lomonaco, New Journal of Physics, 4, (2002) URL: stacks.iop.org/1367-2630/4/73 (electronic) www.arxiv.orgquant-ph/0205137

  2. J. Hietarinta, Phys. Lett. A, 165, 245(1992).

    Google Scholar 

  3. C. Kassel, Quantum Groups Graduate Texts in Mathematics (Springer-Verlag, New York, 1995).

    Google Scholar 

  4. L. Kauffman, Knots and Physics, 3rd ed. (World Scientific Publishing Co., Inc 2001).

  5. L. Kauffman and S. J. Lomonaco, Questions about Quantum and Topological Entanglement (in preparation).

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 South Morgan St., Chicago, IL, 60607-7045

    H. A. Dye

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  1. H. A. Dye
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Dye, H.A. Unitary Solutions to the Yang–Baxter Equation in Dimension Four. Quantum Information Processing 2, 117–152 (2003). https://doi.org/10.1023/A:1025843426102

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  • DOI: https://doi.org/10.1023/A:1025843426102

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