  Fractionalized quasiparticles - anyons - bear a special role in present-day
physics. At the same time, they display properties of interest both
foundational, with quantum numbers that transcend the spin-statistics laws, and
applied, providing a cornerstone for decoherence-free quantum computation. The
development of platforms for realization and manipulation of these objects,
however, remains a challenge. Typically these entail the zero-temperature
ground-state of incompressible, gapped fluids. Here, we establish a strikingly
different approach: the development and probing of anyon physics in a gapless
fluid. The platform of choice is a chiral, multichannel, multi-impurity
realization of the Kondo effect. We discuss how, in the proper limit, anyons
appear at magnetic impurities, protected by an asymptotic decoupling from the
fluid and by the emerging Kondo length scale. We discuss possible experimental
realization schemes using integer quantum Hall edges. The gapless and charged
degrees of freedom coexistent with the anyons suggest the possibility of
extracting quantum information data by transport and simple correlation
functions. To show that this is the case, we generalize the fusion ansatz of
Cardy's boundary conformal field theory, now in the presence of multiple
localized perturbations. The generalized fusion ansatz captures the idea that
multiple impurities share quantum information non-locally, in a way formally
identical to anyonic zero modes. We display several examples supporting and
illustrating this generalization and the extraction of quantum information data
out of two-point correlation functions. With the recent advances in mesoscopic
realizations of multichannel Kondo devices, our results imply that exotic anyon
physics may be closer to reach than presently imagined.
