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## "Non-Abelian anyons and interferometry", Parsa Bonderson, 2012

*Reviewed February 4, 2024*

*Citation:* Bonderson, Parsa Hassan. Non-Abelian anyons and interferometry. California Institute of Technology, 2012.

*Web:* https://thesis.library.caltech.edu/2447/2/thesis.pdf

*Tags:* Expository, Modular-tensor-categories, Hardware

This PhD thesis gives a lovely introduction to anyon models.
What sets this thesis apart from other introductions is the keep focus
on isotopy normalization, which allows for the immediate definition
of what a "physical state" is. To showcase the power of this normalization,
Bonderson takes up the task of computing probabilities of seeing various results
under different forms of interferometry. The ability to model
interferometers, make predictions, and give both quantities and qualitative
analysis of the observations one would obtain is very impressive.
This is a perfect reference for the statement
"the gauge-invariant phases obtained from braiding
and F-moves can be observed using interferometry".

This thesis also contains several references to experimental papers
which performed these sorts of special interferometric experiments, such as

> Neder, I., et al. "Unexpected behavior in a two-path electron interferometer." Physical Review Letters 96.1 (2006): 016804.

> Ji, Yang, et al. "An electronic mach-zehnder interferometer." Nature 422.6930 (2003): 415-418.

Of course, like all good ideas, this goes back to Kitaev:

> Feldman, D. E., and Alexei Kitaev. "Detecting non-Abelian statistics with an electronic Mach-Zehnder interferometer." Physical review letters 97.18 (2006): 186803.

Another nice tidbit I like from this thesis is that it gives
broader context to its discussions at some key moments.
For instance, he reminded the reader that the 3D world
is special because the 1/r^(D-1) force law only produces
stable orbits in 3D, both in classical mechanics and in relativity:

> Tangherlini, Frank R. "Schwarzschild field in n dimensions and the dimensionality of space problem." Il Nuovo Cimento (1955-1965) 27 (1963): 636-651.

There's also a nice quote by Gibbs at the beginning:
“A mathematician may say anything he pleases, but a physicist must be
at least partially sane.” -Josiah Willard Gibbs (1839-1903).