# Fusion channels of non-Abelian anyons from angular-momentum and density-profile measurements

## TL;DR

This paper introduces a static measurement-based method to identify non-Abelian anyons by linking angular momentum and density profiles, demonstrated on the Moore-Read state, enabling new ways to characterize these exotic particles.

## Contribution

The paper proposes a novel, interference-free approach to detect non-Abelian anyons using angular momentum and density measurements, applicable to experimental and theoretical studies.

## Key findings

- Successfully identified different fusion channels of non-Abelian anyons
- Linked angular momentum properties to anyonic statistics in the Moore-Read state
- Demonstrated density-profile measurements can reveal non-Abelian features

## Abstract

We present a method to characterize non-Abelian anyons that is based only on static measurements and that does not rely on any form of interference. For geometries where the anyonic statistics can be revealed by rigid rotations of the anyons, we link this property to the angular momentum of the initial state. We test our method on the paradigmatic example of the Moore-Read state, that is known to support excitations with non-Abelian statistics of Ising type. As an example, we reveal the presence of different fusion channels for two such excitations, a defining feature of non-Abelian anyons. This is obtained by measuring density-profile properties, like the mean square radius of the system or the depletion generated by the anyons. Our study paves the way to novel methods for characterizing non-Abelian anyons, both in the experimental and theoretical domains.