Decoherence of charge anyons in non-Abelian quantum double models

We study non-Abelian topological order in the presence of decoherence that proliferates non-Abelian charge anyons. We propose statistical-mechanical models for information-theoretic quantities and for the probabilities of non-Abelian charge syndromes in the quantum double of any finite group. These models admit a local-spin representation, which can be used to obtain numerical bounds on decoding thresholds for various non-Abelian states. Specializing to the quantum double of $S_3$, we derive from the decohered state disordered net models based on probabilities of both anyon syndromes and their syndrome fusion channels, generalizing prior loop-model results for the quantum double of $D_4.$ As a whole, this work sharpens the picture of how non-Abelian memory breaks down in open systems and establishes benchmarks for non-Abelian error-correction schemes.