The entanglement of distillation for gauge theories

TL;DR

This paper investigates the entanglement structure in lattice gauge theories, distinguishing between undistillable gauge parts and distillable entanglement, revealing differences between abelian and nonabelian theories and effects of matter fields.

Contribution

It provides a novel decomposition of entanglement entropy into gauge and distillable parts, and analyzes their behavior in abelian, nonabelian, and matter-coupled gauge theories.

Findings

Distillable entanglement is zero in pure abelian gauge theories at weak coupling.

Nonabelian gauge theories exhibit nonzero distillable entanglement.

Area laws with topological corrections emerge for distillable entanglement in theories with matter.

Abstract

We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi (arXiv:1510.07455), we show that the usual entanglement entropy for a spatial bipartition can be written as the sum of an undistillable gauge part and of another part corresponding to the LOCC distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure abelian gauge theories in the weak coupling limit, while it is in general nonzero for the nonabelian case. We also consider gauge theories with matter, and show in a perturbative approach how area laws -- including a topological correction -- emerge for the distillable entanglement.