Multi-entropy from Linking in Chern-Simons Theory

TL;DR

This paper investigates the multipartite entanglement structure of link states in Chern-Simons theories, deriving explicit formulas for multi-entropy in Abelian cases and analyzing their entanglement properties.

Contribution

It provides explicit formulas for Rénnyi multi-entropy of link states in Abelian Chern-Simons theory and characterizes their tripartite entanglement.

Findings

Explicit formula for Rénnyi multi-entropy in Abelian theory

Link states are stabilizer states with GHZ-like entanglement

Multi-entropy quantifies genuine tripartite entanglement

Abstract

We study the multipartite entanglement structure of quantum states prepared by the Euclidean path integral over three-manifolds with multiple torus boundaries (the so-called link states) in both Abelian and non-Abelian Chern-Simons theories. For three-component link states in the Abelian theory, we derive an explicit formula for the R\'enyi multi-entropy in terms of linking numbers. We further show that the genuine multi-entropy faithfully quantifies the tripartite entanglement generated by GHZ-states, consistent with the fact that the prepared states are stabilizer states.