Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure

Quantum Physics arXiv:2512.19806 (quant-ph) [Submitted on 22 Dec 2025] Title:Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure Authors:Alberto Spalvieri, Sébastien Christophe Garmier, Flaminia Giacomini View a PDF of the paper titled Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure, by Alberto Spalvieri and 1 other authors View PDF Abstract:Quantum information has become a powerful tool for probing the structure of quantum field theories, yet its application to gauge theories remains subtle. On the one hand, quantum information theory assumes subsystem locality, i.e.~the factorization of the total Hilbert space into subsystems. On the other hand, gauge constraints prevent the total Hilbert space to decompose into a spacetime-local tensor product structure. Because the Hilbert space structure of gauge theories does not accommodate the subsystem decomposition used in quantum information theory, standard information-theoretic results, such as the Local Operations and Classical Communication (LOCC) theorem, cannot be used straightforwardly in the context of gauge theories. In this work, we bridge this gap in the case of a two-dimensional lattice gauge model that captures key features of electromagnetism. In particular, we construct gauge-invariant local algebras and derive a physically meaningful decomposition of the Hilbert space, providing an operationally consistent notion of locality in the absence of a local tensor-product structure. We apply this framework to field-mediated entanglement protocols relevant to proposed tests of the quantum nature of gravity. We show that the discretized version of electromagnetism satisfies an analogue of the LOCC theorem: entanglement cannot be generated without genuine quantum field interactions, even in the absence of a spacetime-local tensor product factorization of the Hilbert space. This may point towards an operational way to define a subsystem structure for gauge theories. Comments: Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2512.19806 [quant-ph] (or arXiv:2512.19806v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.19806 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Alberto Spalvieri [view email] [v1] Mon, 22 Dec 2025 19:02:14 UTC (106 KB) Full-text links: Access Paper: View a PDF of the paper titled Local Operations and Field Mediated Entanglement without a Local Tensor Product Structure, by Alberto Spalvieri and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: gr-qc References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)