2017/03/19 by Fabio M. Mele, Mele, Fabio M.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph) #gr-qc #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1703.06415
162 pages, 11 figures, Master Thesis
arxiv created 2017/03/19 · openalex publication_date 2017/03/19 · arxiv updated 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the formalism of Geometric Quantum Mechanics (GQM) to give a tensorial characterization of entanglement on spin network states. Our analysis focuses on the simple case of a single link graph (Wilson line state) for which we define a dictionary to construct a Riemannian metric tensor and a symplectic structure on the space of states. The manifold of (pure) quantum states is then stratified in terms of orbits of equally entangled states and the block-coefficient matrices of the corresponding pulled-back tensors fully encode the information about separability and entanglement. In particular, the off-diagonal blocks define an entanglement monotone interpreted as a distance with respect to the separable state. As such, it provides a measure of graph connectivity. Finally, in the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link. This suggests a connection between the GQM formalism and the (simplicial) geometric properties of spin network states through entanglement.