title: Entanglement of Distillation for Lattice Gauge Theories.
abstract: We study the entanglement structure of lattice gauge theories from the local operational point of view, and, similar to Soni and Trivedi [J. High Energy Phys. 1 (2016) 1], 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 local operations and classical communication distillable entanglement, which is obtained by depolarizing the local superselection sectors. We demonstrate that the distillable entanglement is zero for pure Abelian gauge theories at zero gauge coupling, while it is in general nonzero for the non-Abelian 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. Finally, we also discuss the entanglement entropy of gauge fixed states and show that it has no relation to the physical distillable entropy.
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
authors.forename: Karel
authors.initials: K
authors.lastname: Van Acoleyen
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
authors.forename: Nick
authors.initials: N
authors.lastname: Bultinck
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
authors.forename: Jutho
authors.initials: J
authors.lastname: Haegeman
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
authors.forename: Michael
authors.initials: M
authors.lastname: Marien
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.
authors.forename: Volkher B
authors.initials: VB
authors.lastname: Scholz
authors.affiliation: Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, 9000 Gent, Belgium.|Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria.
authors.forename: Frank
authors.initials: F
authors.lastname: Verstraete