Essential Duality and Maximal Non-signalling Extensions in Algebraic Quantum Field Theory
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Quantum Physics arXiv:2605.00075 (quant-ph) [Submitted on 30 Apr 2026] Title:Essential Duality and Maximal Non-signalling Extensions in Algebraic Quantum Field Theory Authors:Hassan Nasreddine View a PDF of the paper titled Essential Duality and Maximal Non-signalling Extensions in Algebraic Quantum Field Theory, by Hassan Nasreddine View PDF HTML (experimental) Abstract:We show that, under additivity, the maximal von Neumann algebra extension of $\mathcal{A}(O)$ inside $B(\mathcal{H})$ whose inner automorphisms are non-signalling with respect to all spacelike-separated regions is $\mathcal{A}(O')'$. Consequently, $\mathcal{A}(O)$ is maximal with respect to this property if and only if essential duality holds. The proof is purely algebraic. When essential duality fails, we construct a proper extension all of whose inner automorphisms, and more generally all normal completely positive maps admitting Kraus operators in the algebra, are non-signalling. Under essential duality, any proper extension necessarily admits a signalling operation. An entropic formulation using Araki relative entropy provides a quantitative diagnostic of signalling, though it is not used in the proof. Additional structural results include the wedge-intersection identity $\mathcal{A}(O')' = \bigcap_{W \supset O}\mathcal{A}(W)$ and equivalent characterisations of essential duality. These results identify essential duality as an operational maximality condition within the given representation. Comments: Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) MSC classes: 46L60 (Primary), 81T05, 46L30 (Secondary) Cite as: arXiv:2605.00075 [quant-ph] (or arXiv:2605.00075v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.00075 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hassan Nasreddine [view email] [v1] Thu, 30 Apr 2026 13:45:27 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled Essential Duality and Maximal Non-signalling Extensions in Algebraic Quantum Field Theory, by Hassan NasreddineView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math-ph math.MP 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?) 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?)