Stability of topological purity under random local unitaries

TL;DR

This paper proves that topological entanglement remains stable under random local perturbations in quantum double models, demonstrating the robustness of topological order through a new measure called average topological subsystem purity.

Contribution

It introduces and analytically proves the robustness of a new measure, average topological subsystem purity, for detecting topological order under random local unitaries.

Findings

Topological order is robust under shallow-depth random quantum circuits.

Average topological subsystem purity detects topological order.

Topological entanglement remains stable under local perturbations.

Abstract

In this work, we provide an analytical proof of the robustness of topological entanglement under a model of random local perturbations. We define a notion of average topological subsystem purity and show that, in the context of quantum double models, this quantity does detect topological order and is robust under the action of a random quantum circuit of shallow depth.