This thesis is primarily a study of the measurement theory of non-Abelian anyons through interference experiments. We give an introduction to the theory of anyon models, providing all the formalism necessary to apply standard quantum measurement theory to such systems. This formalism is then applied to give a detailed analysis of a Mach-Zehnder interferometer for arbitrary anyon models. In this treatment, we find that the collapse behavior exhibited by a target anyon in a superposition of states is determined by the monodromy of the probe anyons with the target. Such measurements may also be used to gain knowledge that would help to properly identify the anyon model describing an unknown system. The techniques used and results obtained from this model interferometer have general applicability, and we use them to also describe the interferometry measurements in a two point-contact interferometer proposed for non-Abelian fractional quantum Hall states. Additionally, we give the complete description of a number of important examples of anyon models, as well as their corresponding quantities that are relevant for interferometry. Finally, we give a partial classification of anyon models with small numbers of particle types.This thesis is primarily a study of the measurement theory of non-Abelian anyons through interference experiments. We give an introduction to the theory of anyon models, providing all the formalism necessary to apply standard quantum measurement theory to such systems. This formalism is then applied to give a detailed analysis of a Mach-Zehnder interferometer for arbitrary anyon models. In this treatment, we find that the collapse behavior exhibited by a target anyon in a superposition of states is determined by the monodromy of the probe anyons with the target. Such measurements may also be used to gain knowledge that would help to properly identify the anyon model describing an unknown system. The techniques used and results obtained from this model interferometer have general applicability, and we use them to also describe the interferometry measurements in a two point-contact interferometer proposed for non-Abelian fractional quantum Hall states. Additionally, we give the complete description of a number of important examples of anyon models, as well as their corresponding quantities that are relevant for interferometry. Finally, we give a partial classification of anyon models with small numbers of particle types.

Jun 4, 2007169 citations

Physics And Mathematics of Anyons

Shiing-Shen Chern, C. W. Chu, C. S. Ting

Jun 1, 19915 citations

Twisted Interferometry: the topological perspective

Parsa Bonderson, Lukasz Fidkowski, Michael Hartley Freedman +1 more

Three manifold topology is used to analyze the effect of anyonic interferometers in which the probe anyons' path along an arm crosses itself, leading to a "twisted" or braided space-time trajectory for the probe anyons. In the case of Ising non-Abelian anyons, twisted interferometry is shown to be able to generate a topologically protected $π/8$ -phase gate, which cannot be generated from quasiparticle braiding.Three manifold topology is used to analyze the effect of anyonic interferometers in which the probe anyons' path along an arm crosses itself, leading to a "twisted" or braided space-time trajectory for the probe anyons. In the case of Ising non-Abelian anyons, twisted interferometry is shown to be able to generate a topologically protected $π/8$-phase gate, which cannot be generated from quasiparticle braiding.

arXiv:1601.08225Jan 29, 20161 citation

Fault-Tolerant Greenberger-Horne-Zeilinger Paradox Based on Non-Abelian Anyons

Dong-Ling Deng, Chunfeng Wu, Jing‐Ling Chen +1 more

We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense "fault-tolerant" and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.We propose a scheme to test the Greenberger-Horne-Zeilinger paradox based on braidings of non-Abelian anyons, which are exotic quasiparticle excitations of topological states of matter. Because topological ordered states are robust against local perturbations, this scheme is in some sense "fault-tolerant" and might close the detection inefficiency loophole problem in previous experimental tests of the Greenberger-Horne-Zeilinger paradox. In turn, the construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons. Our results indicate that the non-Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories. Finally, we present a possible experimental implementation of the scheme based on the anyonic interferometry technologies.

Physical Review LettersAug 4, 201010 citations

PHASES IN THE PHYSICS OF ANYONS

Carlo A. Trugenberger

Foundations of Quantum MechanicsApr 1, 19920 citations

π/8

-phase gate, which cannot be generated from quasiparticle braiding.