The non-Abelian nature of this Moore-Read state comes from the collective degeneracy of the quasiparticles in this state. The simplest of the wave functions proposed by Moore and Read corresponds to a spin-polarized p-wave pairing Bardeen-Cooper-Schrieffer state for a fixed number of composite fermions. If a system has a large set of non-Abelian states, the repeated application of the braiding transformation, A ij ab, would allow the approximation of any unitary transformation to arbitrary accuracy. For some pairs of quasiparticles, the matrices, A 12 ab and A 23 ab, do not commute such quasiparticles obey non-Abelian matrix statistics.
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