Quantum Fuzzy Sets Revisited: Density Matrices, Decoherence, and the Q-Matrix Framework
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Quantum Physics arXiv:2603.26739 (quant-ph) [Submitted on 22 Mar 2026] Title:Quantum Fuzzy Sets Revisited: Density Matrices, Decoherence, and the Q-Matrix Framework Authors:Mirco A. Mannucci View a PDF of the paper titled Quantum Fuzzy Sets Revisited: Density Matrices, Decoherence, and the Q-Matrix Framework, by Mirco A. Mannucci View PDF HTML (experimental) Abstract:In 2006 we proposed Quantum Fuzzy Sets, observing that states of a quantum register could serve as characteristic functions of fuzzy subsets, embedding Zadeh's unit interval into the Bloch sphere. That paper was deliberately preliminary. In the two decades since, the idea has been taken up by researchers working on quantum annealers, intuitionistic fuzzy connectives, and quantum machine learning, while parallel developments in categorical quantum mechanics have reshaped the theoretical landscape. The present paper revisits that programme and introduces two main extensions. First, we move from pure states to density matrices, so that truth values occupy the entire Bloch ball rather than its surface; this captures the phenomenon of semantic decoherence that pure-state semantics cannot express. Second, we introduce the Q-Matrix, a global density matrix from which individual quantum fuzzy sets emerge as local sections via partial trace. We define a category QFS of quantum fuzzy sets, establish basic structural properties (monoidal structure, fibration over Set), characterize the classical limit as simultaneous diagonalizability, and exhibit an obstruction to a fully internal Frobenius-algebra treatment. Comments: Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI) Cite as: arXiv:2603.26739 [quant-ph] (or arXiv:2603.26739v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.26739 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Mirco A. Mannucci [view email] [v1] Sun, 22 Mar 2026 19:51:08 UTC (14 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Fuzzy Sets Revisited: Density Matrices, Decoherence, and the Q-Matrix Framework, by Mirco A. MannucciView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 Change to browse by: cs cs.AI 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?)