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19 April 2024
 
  » arxiv » 0903.5230

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Methods of constructing braid group representation and entanglement in a Yang-Baxter sysytem
Taotao HU ; Gangcheng Wang ; Chunfang Sun ; Chengcheng Zhou ; Qingyong Wang ; kang Xue ;
Date 30 Mar 2009
AbstractIn 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 imes9 $ unitary $ reve{R}( heta, phi_{1},phi_{2})$ according to a $ 9 imes9 $ braiding S-matrix we have constructed with parameters $phi_{1}$, $phi_{2}$ and $ heta$. The entanglement properties of $ reve{R}( heta, phi_{1},phi_{2})$-matrix is investigated, and the arbitrary degree of entanglement for two-qutrit entangled states can be generated via $ reve{R}( heta, phi_{1},phi_{2})$-matrix acting on the standard basis.
Source arXiv, 0903.5230
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