Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for multi-impurity chiral model, that scattering of an electron through impurities depends anyon's total fusion channel. Here we study correlation between spins. We argue, based a combination conformal field theory, perturbative limit with large number channels $k$, and exactly solvable two-channel case, interimpurity spin probes anyon pair correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid via consecutive measurements.