Quantum entanglement, unitary braid representation and TemperleyLieb algebra
Abstract
Important developments in faulttolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco that a specific braiding operator from the solution of the YangBaxter equation, namely the Bell matrix, is universal implies that in principle all quantum gates can be constructed from braiding operators together with single qubit gates. In this paper we present a new class of braiding operators from the TemperleyLieb algebra that generalizes the Bell matrix to multiqubit systems, thus unifying the Hadamard and Bell matrices within the same framework. Unlike previous braiding operators, these new operators generate directly, from separable basis states, important entangled states such as the generalized GreenbergerHorneZeilinger states, clusterlike states, and other states with varying degrees of entanglement.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 November 2010
 DOI:
 10.1209/02955075/92/30002
 arXiv:
 arXiv:1011.6229
 Bibcode:
 2010EL.....9230002H
 Keywords:

 Quantum Physics;
 Mathematical Physics;
 Mathematics  Group Theory
 EPrint:
 5 pages, no figure