Yang–Baxter equations and quantum entanglements

Yang–Baxter equations and quantum entanglements 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- $$\frac{1}{2}$$ 1 2 and spin-1 have been shown. The extremes of $$\ell _1$$ ℓ 1 -norm of $$D$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Yang–Baxter equations and quantum entanglements

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-014-0765-3
Publisher site
See Article on Publisher Site

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- $$\frac{1}{2}$$ 1 2 and spin-1 have been shown. The extremes of $$\ell _1$$ ℓ 1 -norm of $$D$$ 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.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 5, 2014

References

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