  We investigate the proposed experimental setup for measuring the topological
charge in a an Ising anyon system by means of Fabry-P\'erot interferometry with
a chiral edge state. We show that such an interferometer has the unintended but
not necessarily unwelcome effect of stabilizing the state of the system being
measured (i.e., a topological qubit). We show further that interactions between
the edge mode and the localized bulk quasiparticles can have the effect of
polarizing the qubit, stabilizing its state. We discuss the these results in
the context of recent interferometer experiments in the 5/2 fractional quantum
Hall state, where the first of these effects is small, but the second may be
relevant to the observed phenomena.
