Inequivalent classes of interference experiments with non-abelian anyons

Abstract

We present a theoretical analysis of inequivalent classes of interference experiments with non-abelian anyons using an idealized Mach-Zender type interferometer. Because of the non-abelian nature of the braid group action one has to distinguish the different possibilities in which the experiment can be repeated, which lead to different interference patterns. We show that each setup will, after repeated measurement, lead to a situation where the two-particle (or multi-particle) state gets locked into an eigenstate of some well defined operator. Also the probability to end up in such an eigenstate is calculated. Some representative examples are worked out in detail.