Identifying quantum topological phases through statistical correlation

We theoretically examine the use of a statistical distance measure, the indistinguishability, as a generic tool for the identification of topological order. We apply this measure to the toric code and two fractional quantum Hall models. We find that topologically ordered states can be identified with the indistinguishability for both models. Calculations with the indistinguishability also underscore a key distinction between symmetries that underlie topological order in the toric code and quantum Hall models.