Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks

TL;DR

This paper explores how quantum information concepts like entanglement and coarse-graining can be used to understand the structure of quantum geometry in loop quantum gravity, focusing on the area operator and spin networks.

Contribution

It introduces a method for coarse-graining spin network states and analyzes the flow of the area operator, linking quantum information measures to geometric properties.

Findings

Coarse-graining reduces degrees of freedom in spin networks.

Entanglement correlates with geometric distance in quantum states.

Renormalisation flow of the area operator reveals geometric structure.

Abstract

After a brief review of spin networks and their interpretation as wave functions for the (space) geometry, we discuss the renormalisation of the area operator in loop quantum gravity. In such a background independent framework, we propose to probe the structure of a surface through the analysis of the coarse-graining and renormalisation flow(s) of its area. We further introduce a procedure to coarse-grain spin network states and we quantitatively study the decrease in the number of degrees of freedom during this process. Finally, we use these coarse-graining tools to define the correlation and entanglement between parts of a spin network and discuss their potential interpretation as a natural measure of distance in such a state of quantum geometry.