Bonderson, Parsa and Shtengel, Kirill and Slingerland, J.K.
Interferometry of non-Abelian Anyons.
Annals of Physics, 323 (11).
We develop the general quantum measurement theory of non-Abelian anyons through interference
experiments. The paper starts with a terse introduction to the theory of anyon
models, focusing on the basic formalism necessary to apply standard quantum measurement
theory to such systems. This is then applied to give a detailed analysis of anyonic
charge measurements using aMach-Zehnder interferometer for arbitrary anyon models.We
find that, as anyonic probes are sent through the legs of the interferometer, superpositions
of the total anyonic charge located in the target region collapse when they are distinguishable
via monodromy with the probe anyons, which also determines the rate of collapse. We
give estimates on the number of probes needed to obtain a desired confidence level for the
measurement outcome distinguishing between charges, and explicitly work out a number
of examples for some significant anyon models. We apply the same techniques to describe
interferometry measurements in a double point-contact interferometer realized in fractional
quantum Hall systems. To lowest order in tunneling, these results essentially match those
from the Mach-Zehnder interferometer, but we also provide the corrections due to processes
involving multiple tunnelings. Finally, we give explicit predictions describing state
measurements for experiments in the Abelian hierarchy states, the non-Abelian Moore-
Read state at v = 5/2 and Read-Rezayi state at v = 12/5.
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