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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.
Quantum Information Processing – Springer Journals
Published: Jul 5, 2014
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