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Kitaev's quantum double models in 2D provide some of the most commonlystudied examples of topological quantum order. In particular, the ground spaceis thought to yield a quantum error-correcting code. We offer an explicit proofthat this is the case for arbitrary finite groups. Actually a stronger claim isshown: any two states with zero energy density in some contractible region musthave the same reduced state in that region. Alternatively, the local propertiesof a gauge-invariant state are fully determined by specifying that itsholonomies in the region are trivial. We contrast this result with the factthat local properties of gauge-invariant states are not generally determined byspecifying all of their non-Abelian fluxes -- that is, the Wilson loops oflattice gauge theory do not form a complete commuting set of observables. Wealso note that the methods developed by P. Naaijkens (PhD thesis, 2012) under adifferent context can be adapted to provide another proof of the errorcorrecting property of Kitaev's model. Finally, we compute the topologicalentanglement entropy in Kitaev's model, and show, contrary to previous claimsin the literature, that it does not depend on whether the "log dim R" term isincluded in the definition of entanglement entropy.

Kitaev's quantum double model as an error correcting code