Towards unambiguous calculation of the topological entropy for mixed states

TL;DR

This paper addresses the challenge of accurately calculating topological entropy in mixed states, which can be misleading due to effective diverging correlation lengths, and proposes a new method for more reliable identification of topological order.

Contribution

The authors introduce a novel method for calculating topological entropy in mixed states, improving the reliability of detecting topological order in thermal and error-affected states.

Findings

Mixed states can cause diverging correlation lengths.

Traditional calculations may give misleading topological order results.

The proposed method enhances confidence in identifying topological order.

Abstract

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.