Holographic entanglement in spin network states: A focused review

Colafranceschi, Eugenia; Adesso, Gerardo

Abstract

In the long-standing quest to reconcile gravity with quantum mechanics, profound connections have been unveiled between concepts traditionally pertaining to a quantum information theory, such as entanglement, and constitutive features of gravity, like holography. Developing and promoting these connections from the conceptual to the operational level unlock access to a powerful set of tools which can be pivotal toward the formulation of a consistent theory of quantum gravity. Here, we review recent progress on the role and applications of quantum informational methods, in particular tensor networks, for quantum gravity models. We focus on spin network states dual to finite regions of space, represented as entanglement graphs in the group field theory approach to quantum gravity, and illustrate how techniques from random tensor networks can be exploited to investigate their holographic properties. In particular, spin network states can be interpreted as maps from bulk to boundary, whose holographic behavior increases with the inhomogeneity of their geometric data (up to becoming proper quantum channels). The entanglement entropy of boundary states, which are obtained by feeding such maps with suitable bulk states, is then proved to follow a bulk area law with corrections due to the entanglement of the bulk state. We further review how exceeding a certain threshold of bulk entanglement leads to the emergence of a black hole-like region, revealing intriguing perspectives for quantum cosmology.

Citation

Colafranceschi, E., & Adesso, G. (2022). Holographic entanglement in spin network states: A focused review. AVS Quantum Science, 4(2), Article 025901. https://doi.org/10.1116/5.0087122

• Journal Article Type: Article
• Acceptance Date: May 16, 2022
• Online Publication Date: Jun 7, 2022
• Publication Date: Jun 1, 2022
• Deposit Date: Jun 15, 2022
• Publicly Available Date: Jun 28, 2022
• Journal: AVS Quantum Science
• Print ISSN: 2639-0213
• Electronic ISSN: 2639-0213
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 2
• Article Number: 025901
• DOI: https://doi.org/10.1116/5.0087122
• Keywords: Electrical and Electronic Engineering, Computational Theory and Mathematics, Physical and Theoretical Chemistry, Computer Networks and Communications, Condensed Matter Physics, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials
• Public URL: https://nottingham-repository.worktribe.com/output/8398457
• Publisher URL: https://avs.scitation.org/doi/10.1116/5.0087122