Statistical dynamics of a non-Abelian anyonic quantum walk

TL;DR

This paper investigates the dynamics of a non-Abelian anyon quantum walk, revealing that entanglement with the environment causes its behavior to resemble a classical random walk, contrasting with Abelian anyons.

Contribution

It introduces a model of non-Abelian anyon quantum walks and links their statistical dynamics to quantum link invariants, showing a transition to classical behavior due to entanglement.

Findings

Non-Abelian anyons exhibit classical random walk behavior asymptotically.

Entanglement with fusion degrees of freedom reduces quantum coherence.

Contrast between non-Abelian and Abelian anyon dynamics is established.

Abstract

We study the single particle dynamics of a mobile non-Abelian anyon hopping around many pinned anyons on a surface. The dynamics is modelled by a discrete time quantum walk and the spatial degree of freedom of the mobile anyon becomes entangled with the fusion degrees of freedom of the collective system. Each quantum trajectory makes a closed braid on the world lines of the particles establishing a direct connection between statistical dynamics and quantum link invariants. We find that asymptotically a mobile Ising anyon becomes so entangled with its environment that its statistical dynamics reduces to a classical random walk with linear dispersion in contrast to particles with Abelian statistics which have quadratic dispersion.