Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

Details Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem Method of constructing braid group representation and entanglement in a Yang-Baxter sysytem

2009-03-30

arxiv.org/abs/0903.5230v4

Physics

Quantum Physics

9 pages

Scientific paper

In this paper we present reducible representation of the $n^{2}$ braid group representation which is constructed on the tensor product of n-dimensional spaces. By some combining methods we can construct more arbitrary $n^{2}$ dimensional braiding matrix S which satisfy the braid relations, and we get some useful braiding matrix S. By Yang-Baxteraition approach, we derive a $ 9\times9 $ unitary $ \breve{R}$ according to a $ 9\times9 $ braiding S-matrix we have constructed. The entanglement properties of $ \breve{R}$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $ \breve{R}(\theta, \phi_{1},\phi_{2})$-matrix acting on the standard basis.

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