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Interferometry of non-Abelian Anyons

Bonderson, Parsa and Shtengel, Kirill and Slingerland, J.K. (2008) Interferometry of non-Abelian Anyons. Annals of Physics, 323 (11). 2709-2755 . ISSN 0003-4916

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Abstract

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.

Item Type: Article
Additional Information: Preprint version of original article published in Annals of Physics Vol.323 No.11(2008) © 2008 Elsevier Inc. We thank L. Bonderson, A. Kitaev, I. Klich, and J. Preskill for illuminating discussions, and acknowledge the hospitality of the IQI, Microsoft Station Q, and the Aspen Center for Physics. This work was supported in part by the NSF under Grant No. PHY-0456720 and the ARO under Grant No. W911NF-05-1-0294.
Keywords: Interferometry; non-Abelian Anyons; quantum measurement theory; interference experiments; Anyonic charge measurement; Fractional quantum Hall effect; Topological qubit readout;
Subjects: Science & Engineering > Mathematical Physics
Item ID: 2725
Identification Number: DOI: 10.1016/j.aop.2008.01.012
Depositing User: Dr. Joost Slingerland
Date Deposited: 27 Sep 2011 13:26
Journal or Publication Title: Annals of Physics
Publisher: Elsevier
Refereed: No
URI:

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