Intertwiner entanglement excitation and holonomy operator

Abstract

In the loop quantum gravity framework, spin network states carry entanglement between quantum excitations of the geometry at different space points. This intertwiner entanglement is gauge-invariant and comes from quantum superposition of spins and intertwiners. Bipartite entanglement can be interpreted as a witness of distance, while multipartite entanglement reflects the curvature of the quantum geometry. The present work investigates how the bipartite and multipartite intertwiner entanglement changes under the action of the holonomy operator, which is the basic building block of loop quantum gravity's dynamics. We reveal the relation between entanglement excitation and the dispersion of the holonomy operator. This leads to a new interesting connection between bulk geometry and boundary observables via the dynamics of entanglement.