Decoherence of Anyonic Charge in Interferometry Measurements

We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target’s topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges $a$ and $a^{\prime }$ in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with $a$ to give $a^{\prime }$.

Figure 1

A Mach-Zehnder interferometer containing the target anyon(s) $A$, to be probed by the anyons $B_k$. (Detectors not shown.)