The entanglement of distillation for gauge theories

TL;DR

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 local operations and classical communication distillableEntanglement, which is obtained by depolarizing the local superselection sectors.

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.

Figures (1)

• Figure 1: (a) The setting of lattice gauge theory: the action of a gauge transformation $U_v$ is determined by the orientation of the edges. (b) A bipartite cut: the edges along the cut are labeled by irreducible representations $r_1,\ldots,r_6$ of the group action at the 6 different boundary vertices (thick points), giving rise to a direct sum structure. Fixing theses irreducible representations produces a direct product structure on each boundary edge, with one factor lying on the inside and one factor on the outside.