Towards unambiguous calculation of the topological entropy for mixed states

Calculation of topological order parameters, such as the topological entropy and topological mutual information, are used to determine whether states possess topological order. Their calculation is expected to give reliable results when the ground states of gapped Hamiltonians are considered, since non-topological correlations are suppressed by a finite correlation length. However, studies of thermal states and the effects of incoherent errors require calculations involving mixed states. Here we show that such mixed states can effectively lead to a diverging correlation length, and hence may give misleading results when these order parameters are calculated. To solve this problem, we propose a novel method to calculate the quantity, allowing topologically ordered states to be identified with greater confidence.