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

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.