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Spin network Entanglement and Bulk-Boundary Map in Loop Quantum Gravity

jeu 17 nov 2022



Soutenance de M. CHEN Qian sous la direction de M. LIVINE Etera

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Description générale

The notion of locality in loop quantum gravity is still an open question. Indeed, the naive locality is in absence due to the presence of di↵eomorphism. This thesis is dedicated to the study of way-out under the prescriptions of quasi-locality and relational perspective, in which the insights from quasi-local holography (i.e. for a bounded region of space-time with a non-empty boundary) and entanglement are rooted respectively. On one hand, the local holography takes root in the holographic principle, which conjectures that the geometry and the dynamic of a space-time region can be entirely described by a theory living on the boundary of this given region. On the other hand, the entanglement encodes the relational observables, reflecting relative locality between subsystems, thus geometry could be emerged/reconstructed from quantum information. The objective is to put the entanglement into the mathematical framework of bulk-boundary relation, which defined boundary states via spin network states.

We study the spin networks with non-empty boundaries from the viewpoint of bulk-boundary maps, then investigate quasi-local descriptions via the approaches of coarse-graining. From one of coarse-graining approaches, i.e. tracing over bulk degrees of freedom, we prove and show how the bulk can be reconstructed (universally but non-uniquely) from boundary states. From another coarse-graining approach, i.e., gauge-fixing, we show how the multipartite entanglement is related to bulk curvature and boundary closure defect under a simple dynamics generated by loop holonomy operator, which allows us to glimpse curvature from entanglement. Moreover, we prove that spin network entanglement is preserved under the coarse-graining in the case of this simple dynamics. Furthermore, we study the dynamics of correlation and entanglement under a real loop quantum gravity dynamics. Together, these researches allow to envisage the foundation of quantum gravity that is established on the quasi-local holography and relative locality

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