Intertwiner Entanglement Excitation and Holonomy Operator

TL;DR

This paper explores how intertwiner entanglement in loop quantum gravity is affected by the holonomy operator, revealing links between quantum geometry, entanglement dynamics, and boundary observables.

Contribution

It demonstrates the relationship between entanglement excitation and holonomy operator dispersion, connecting quantum geometry with boundary dynamics in loop quantum gravity.

Findings

Intertwiner entanglement relates to quantum geometry curvature.

Holonomy operator influences bipartite and multipartite entanglement.

Entanglement dynamics reflect geometric and boundary properties.

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.