Non-locality of non-Abelian anyons

  title={Non-locality of non-Abelian anyons},
  author={Gavin K. Brennen and Sofyan Iblisdir and Jiannis K. Pachos and Joost Slingerland},
  journal={New Journal of Physics},
Entangled states of quantum systems can give rise to measurement correlations of separated observers that cannot be described by local hidden variable theories. Usually, it is assumed that entanglement between particles is generated due to some distance-dependent interaction. Yet anyonic particles in two dimensions have a nontrivial interaction that is purely topological in nature. In other words, it does not depend on the distance between two particles, but rather on their exchange history… 

Nonlocality as a benchmark for universal quantum computation in Ising anyon topological quantum computers

An obstacle affecting any proposal for a topological quantum computer based on Ising anyons is that quasiparticle braiding can only implement a finite (nonuniversal) set of quantum operations. The

Quantum Walks of SU(2)_k Anyons on a Ladder

We study the effects of braiding interactions on single anyon dynamics using a quantum walk model on a quasi-1-dimensional ladder filled with stationary anyons. The model includes loss of information

Relational time in anyonic systems

In a seminal paper [Phys. Rev. D 27, 2885 (1983)], Page and Wootters suggest that time evolution could be described solely in terms of correlations between systems and clocks, as a means of dealing

Universal Quantum Computation with Abelian Anyon Models

Error Correction for Non-Abelian Topological Quantum Computation

The properties of non-Abelian error correction, in general are considered, and it is found that error correction is possible under a threshold value of 7% for the total probability of an error on each physical spin, remarkably comparable with the thresholds for Abelian models.

Fault-tolerant Greenberger-Horne-Zeilinger paradox based on non-Abelian anyons.

The construction of the Greenberger-Horne-Zeilinger paradox reveals the nonlocal property of non-Abelian anyons and results indicate that the non- Abelian fractional statistics is a pure quantum effect and cannot be described by local realistic theories.

Non-Abelian Topological Approach to Non-Locality of a Hypergraph State

To resolve the divergence in the complexity of classical and quantum representation of a hypergraph, the notion of non-amenability and its relation to combinatorics of dynamical self-organization for the case of fractal system of free group on finite generators is investigated.

Majorana bound states with chiral magnetic textures

The aim of this Tutorial is to give a pedagogical introduction into realizations of Majorana fermions, usually termed as Majorana bound states (MBSs), in condensed matter systems with magnetic

Demonstrating entanglement by testing Bell's theorem in Majorana wires

We propose an experiment that would establish the entanglement of Majorana zero modes in semiconductor nanowires by testing the Bell and Clauser-Horne-Shimony-Holt inequalities. Our proposal is

Introduction to Topological Quantum Computation

The makings of anyonic systems, their properties and their computational power are presented in a pedagogical way and special emphasis is given to the motivation and physical intuition behind every mathematical concept.



Non-Abelian Anyons and Topological Quantum Computation

Topological quantum computation has emerged as one of the most exciting approaches to constructing a fault-tolerant quantum computer. The proposal relies on the existence of topological states of

Topologically protected qubits from a possible non-Abelian fractional quantum Hall state.

Here, an experiment is proposed which can simultaneously determine the braiding statistics of quasiparticle excitations and, if they prove to be non-Abelian, produce a topologically protected qubit on which a logical Not operation is performed by qu asiparticle braiding.

Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices.

This paper shows how to simulate the creation and manipulation of Abelian and non-Abelian anyons in topological lattice models using trapped atoms in optical lattices and requires an ancilla particle which can undergo single-particle gates, be moved close to each constituent of the lattice and undergo a simple quantum gate, and be detected.

Evidence for the epistemic view of quantum states: A toy theory

We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated

Non-Abelian Anyons and Interferometry

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

The entanglement of indistinguishable particles shared between two parties

  • H. WisemanJ. Vaccaro
  • Computer Science
    2003 European Quantum Electronics Conference. EQEC 2003 (IEEE Cat No.03TH8665)
  • 2003
Entanglement of indistinguishable particles E/sub p/ shared between two separated parties is introduced and it is assumed that the state |/spl psi//sub AB/> of the indistinguishable particles contains exactly N particles.

Universal quantum computation with the v=5/2 fractional quantum Hall state

We consider topological quantum computation (TQC) with a particular class of anyons that are believed to exist in the fractional quantum Hall effect state at Landau-level filling fraction v =5/2.

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.