Topologically-ordered states supporting excitations with non-Abelian braiding statistics are expected to occur at several observed fractional quantum Hall plateaux. I will begin by discussing our proposal for interferometric experiments designed to detect such non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read and Read-Rezayi states, which are likely candidates for the observed fractional quantum Hall plateaux at nu=5/2 and 12/5 respectively. Aside from their potential utility for experimental verification of non-Abelian anyonic statistics, such interferometric experiments appear to provide the most promising route for qubit read out in a topological quantum computation. With these potential applications in mind, I will also address interferometric measurements of states having superpositions of anyonic charges and detail their measurement collapse behavior.
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