Higher-Order Quantum Objects are Strong Profunctors
Summarize this article with:
Quantum Physics arXiv:2603.11221 (quant-ph) [Submitted on 11 Mar 2026] Title:Higher-Order Quantum Objects are Strong Profunctors Authors:Matt Wilson, James Hefford View a PDF of the paper titled Higher-Order Quantum Objects are Strong Profunctors, by Matt Wilson and 1 other authors View PDF Abstract:We explore the sense in which the existing constructions for higher-order maps on quantum theory based on causality constraints and compositionality constraints respectively, coincide. More precisely, we construct a functor F : Caus(C) -> StProf(C1) from higher-order causal categories to the category of strong profunctors over first-order causal processes that is lax-lax duoidal, full, faithful, and strongly closed whenever C is additive. When C = CP this embedding is furthermore strong on the sequencer for duoidal categories, expressing the possibility to interpret one-way signalling (but not general non-signalling) constraints in terms of the coend calculus for profunctors. We conclude that insofar as compositional constraints can be used to express causality constraints, the profunctorial approach generalises higher-order quantum theory to a construction over general symmetric monoidal categories. Subjects: Quantum Physics (quant-ph); Category Theory (math.CT) Cite as: arXiv:2603.11221 [quant-ph] (or arXiv:2603.11221v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.11221 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Matthew Wilson Mr [view email] [v1] Wed, 11 Mar 2026 18:35:59 UTC (140 KB) Full-text links: Access Paper: View a PDF of the paper titled Higher-Order Quantum Objects are Strong Profunctors, by Matt Wilson and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: 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?)