Supermaps on generalised theories
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Quantum Physics arXiv:2602.23865 (quant-ph) [Submitted on 27 Feb 2026] Title:Supermaps on generalised theories Authors:Matt Wilson, James Hefford, Timothée Hoffreumon View a PDF of the paper titled Supermaps on generalised theories, by Matt Wilson and 2 other authors View PDF Abstract:Categorical supermaps generalise higher-order quantum operations from finite-dimensional quantum theory to arbitrary circuit theories. In this paper, we establish the Yoneda lemma for categorical supermaps, which states that whenever a physical theory has a suitable notion of channel-state duality, then categorical supermaps on that theory can be concretely represented in terms of that duality. This lemma eliminates any guesswork or ambiguity when defining the appropriate notion of supermap for these theories. As a concrete application, we show that the recently proposed higher-order processes on boxworld can be obtained as a particular instance of categorical supermaps, and put forward a stable definition of higher-order real quantum theory. Subjects: Quantum Physics (quant-ph); Logic in Computer Science (cs.LO); Category Theory (math.CT) Cite as: arXiv:2602.23865 [quant-ph] (or arXiv:2602.23865v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.23865 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Matthew Wilson Mr [view email] [v1] Fri, 27 Feb 2026 10:05:24 UTC (259 KB) Full-text links: Access Paper: View a PDF of the paper titled Supermaps on generalised theories, by Matt Wilson and 2 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cs cs.LO math math.CT 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?)