Interferometry versus projective measurement of anyons

TL;DR

This paper compares interferometric and projective measurement methods for topological charge in non-abelian anyonic systems, demonstrating that interferometry can simulate projective measurements with lower overhead.

Contribution

It proves that interferometric measurement is strictly more powerful than projective measurement for determining total topological charge, allowing simulation of projective protocols.

Findings

Interferometric measurement can simulate projective measurement protocols.

Projective measurement requires fusing anyons, while interferometry does not.

Interferometry offers a lower-overhead method for measuring topological charge.

Abstract

The distinct methods for measuring topological charge in a non-abelian anyonic system have been discussed in the literature: projective measurement of a single point-like quasiparticle and interferometric measurement of the total topological charge of a group of quasiparticles. Projective measurement by definition is only applied near a point and will project to a topological charge sector near that point. Thus, if it is to be applied to a \emph{group} of anyons to project to a \emph{total} charge, then the anyons must first be fused one by one to obtain a single anyon carrying the collective charge. We show that interferometric measurement is strictly stronger: Any protocol involving projective measurement can be simulated at low overhead by another protocol involving only interferometric measurement.