Entanglement negativity in decohered topological states

TL;DR

This paper studies how decoherence affects topological order by analyzing entanglement negativity and mutual information, revealing universal signatures and their relation to quantum dimensions in both Abelian and non-Abelian topological states.

Contribution

It develops a replica field-theory framework linking entanglement measures to quantum dimensions and computes these measures exactly for decohered string-net states, including non-Abelian cases.

Findings

TEN and TMI relate to quantum dimensions of topological defects.

Decoherence modifies entanglement signatures in topological states.

TMI probes total quantum dimension; TEN detects modular part.

Abstract

We investigate universal entanglement signatures of mixed-state phases obtained by decohering pure-state topological order (TO), focusing on topological corrections to logarithmic entanglement negativity and mutual information: topological entanglement negativity (TEN) and topological mutual information (TMI). For Abelian TOs under decoherence, we develop a replica field-theory framework based on a doubled-state construction that relates TEN and TMI to the quantum dimensions of domain-wall defects between decoherence-induced topological boundary conditions, yielding general expressions in the strong-decoherence regime. We further compute TEN and TMI exactly for decohered $G$-graded string-net states, including cases with non-Abelian anyons. We interpret the results within the strong one-form-symmetry framework for mixed-state TOs: TMI probes the total quantum dimension of the emergent premodular anyon theory, whereas TEN detects only its modular part.