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.

27 pages, 12 figures, RevTex4

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• Bulk Entropy in Loop Quantum Gravity
• Intertwiner Entanglement on Spin Networks
• Fisher Metric, Geometric Entanglement and Spin Networks
• Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model
• Generic degeneracy and entropy in loop quantum gravity
• Dynamical evaporation of quantum horizons
• Spectroscopy of a canonically quantized horizon
• On the fate of the Hoop Conjecture in quantum gravity
• Holographic maps from quantum gravity states as tensor networks
• Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
• Entanglement entropy and correlations in loop quantum gravity
• The entropic boundary law in BF theory
• Renormalization of lattice-regularized quantum gravity models I. General considerations
• Statistical discrete geometry
• Elementary Particles as Gates for Universal Quantum Computation
• Entanglement entropy of physical states in hypercuboidally truncated spin foam quantum gravity