  We investigate the nonlocal property of the fractional statistics in Kitaev's
toric code model. To this end, we construct the Greenberger-Horne-Zeilinger
paradox which builds a direct conflict between the statistics and local
realism. It turns out that the fractional statistics in the model is purely a
quantum effect and independent of any classical theory.We also discuss a
feasible experimental scheme using anyonic interferometry to test this
contradiction.
