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Loop Quantum Gravity and Quantum Information

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Handbook of Quantum Gravity

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Abstract

We summarize recent developments at the interface of quantum gravity and quantum information and discuss applications to the quantum geometry of space in loop quantum gravity. In particular, we describe the notions of link entanglement, intertwiner entanglement, and boundary spin entanglement in a spin-network state. We discuss how these notions encode the gluing of quanta of space and their relevance for the reconstruction of a quantum geometry from a network of entanglement structures. We then focus on the geometric entanglement entropy of spin-network states at fixed spins, treated as a many-body system of quantum polyhedra, and discuss the hierarchy of volume-law, area-law, and zero-law states. Using information theoretic bounds on the uncertainty of geometric observables and on their correlations, we identify area-law states as the corner of the Hilbert space that encodes a semiclassical geometry and the geometric entanglement entropy as a probe of semiclassicality.

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Acknowledgements

E.B. acknowledges support from the National Science Foundation, Grant No. PHY-2207851, and from the John Templeton Foundation via the ID 62312 grant, as part of the “Quantum Information Structure of Spacetime (QISS)” project (qiss.fr).

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Authors and Affiliations

  1. Institute for Gravitation and the Cosmos, Pennsylvania State University, University Park, PA, USA

    Eugenio Bianchi

  2. Laboratoire de Physique (LP ENSL), CNRS (UMR 5672), Ecole Normale Supérieure de Lyon, Lyon, France

    Etera R. Livine

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  1. Eugenio Bianchi
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  2. Etera R. Livine
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Correspondence to Eugenio Bianchi .

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Editors and Affiliations

  1. Department of Physics, Fudan University, Shanghai, China

    Cosimo Bambi

  2. Department of Physics, Cagliari University, Monserrato (Cagliari), Italy

    Leonardo Modesto

  3. Departamento de Física, Universidade Federal de Juiz de Fora, Juiz de Fora, Minas Gerais, Brazil

    Ilya Shapiro

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Bianchi, E., Livine, E.R. (2024). Loop Quantum Gravity and Quantum Information. In: Bambi, C., Modesto, L., Shapiro, I. (eds) Handbook of Quantum Gravity. Springer, Singapore. https://doi.org/10.1007/978-981-99-7681-2_108

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