The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information
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Quantum Physics arXiv:2512.07902 (quant-ph) [Submitted on 5 Dec 2025] Title:The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information Authors:Kagwe A. Muchane View a PDF of the paper titled The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information, by Kagwe A. Muchane View PDF HTML (experimental) Abstract:We revisit the Pauli-Clifford connection to introduce a real, grade-preserving algebraic framework for $N$-qubit quantum computation based on the tensor product structure $C\ell_{2,0}(\mathbb{R})^{\otimes N}$. In this setting the bivector $J = e_{12}$ satisfies $J^{2} = -1$ and supplies the complex structure on a minimal left ideal via right-multiplication, while Pauli operations arise as left actions of suitable Clifford elements. Adopting a canonical stabilizer mapping, the $N$-qubit computational basis state $|0\cdots 0\rangle$ is represented natively by a tensor product of real algebraic idempotents. This structural choice leads to a State-Operator Clifford Compatibility law that is stable under the geometric product for $N$ qubits and aligns symbolic Clifford multiplication with unitary evolution on the Hilbert space. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.07902 [quant-ph] (or arXiv:2512.07902v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.07902 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kagwe Muchane [view email] [v1] Fri, 5 Dec 2025 22:55:31 UTC (7 KB) Full-text links: Access Paper: View a PDF of the paper titled The State-Operator Clifford Compatibility: A Real Algebraic Framework for Quantum Information, by Kagwe A. MuchaneView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 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?)