  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.
