A witness for topological order and stable quantum memories in abelian anyonic systems

TL;DR

The paper introduces the anyonic topological entropy, a new parameter that detects the error correcting phase in topological memories using classical probability distributions, enabling efficient analysis of anyonic systems.

Contribution

It proposes a novel, classically computable parameter for identifying topological order and error correction phases in abelian anyonic systems, distinct from existing measures.

Findings

The parameter can be calculated from classical probability distributions.

It provides an efficient method to study topological phases.

It detects error correcting phases in topological quantum memories.

Abstract

We propose a novel parameter, the anyonic topological entropy, designed to detect the error correcting phase of a topological memory. Unlike similar quantities such as the topological entropy, the anyonic topological entropy is defined using the states of the anyon occupations. As such, though the parameter deals with phases and phase transitions that are quantum in nature, it can be calculated solely from classical probability distributions. In many cases, these calculations will be tractable using efficient classical algorithms. The parameter therefore provides a new avenue for efficient studies of anyonic systems.