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We propose a novel parameter, the anyonic topological entropy, designed todetect the error correcting phase of a topological memory. Unlike similarquantities such as the topological entropy, the anyonic topological entropy isdefined using the states of the anyon occupations. As such, though theparameter deals with phases and phase transitions that are quantum in nature,it can be calculated solely from classical probability distributions. In manycases, these calculations will be tractable using efficient classicalalgorithms. The parameter therefore provides a new avenue for efficient studiesof anyonic systems.

A witness for topological order and stable quantum memories in abelian anyonic systems