Stability of topological purity under random local unitaries

In this work, we provide an analytical proof of the robustness of a form of topological entanglement under a model of random local perturbations. We define the notion of topological 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 shallow quantum circuit. (C) Copyright S. E E. Oliviero et al.

Automated summary

In this work, the robustness of a form of topological entanglement under a model of random local perturbations is analytically proven. The concept of topological purity is defined, and it is shown that, in the context of quantum double models, this quantity can detect topological order and remains stable under the action of a random shallow quantum circuit.