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

摘要

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