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We present a method to characterize non-Abelian anyons that is based only onstatic measurements and that does not rely on any form of interference. Forgeometries where the anyonic statistics can be revealed by rigid rotations ofthe anyons, we link this property to the angular momentum of the initial state.We test our method on the paradigmatic example of the Moore-Read state, that isknown to support excitations with non-Abelian statistics of Ising type. As anexample, we reveal the presence of different fusion channels for two suchexcitations, a defining feature of non-Abelian anyons. This is obtained bymeasuring density-profile properties, like the mean square radius of the systemor the depletion generated by the anyons. Our study paves the way to novelmethods for characterizing non-Abelian anyons, both in the experimental andtheoretical domains.

Fusion channels of non-Abelian anyons from angular-momentum and density-profile measurements