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The Qutrit Bloch Sphere

arXiv Quantum Physics
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⚡ Quantum Brief
A new mathematical framework for visualizing three-level quantum systems (qutrits) in 3D space was proposed in a January 2026 preprint by physicist Vinod K Mishra. The work addresses a longstanding challenge: extending the Bloch sphere—a 2D qubit visualization tool—to accommodate qutrits, which require higher-dimensional representation due to their three basis states. Mishra’s model provides a concrete method to project qutrit states onto a 3D Bloch sphere, enabling intuitive geometric interpretation of their quantum properties. This advancement could simplify quantum information research by offering a unified visualization tool for both qubits and qutrits, bridging a gap in quantum state representation. The paper suggests potential applications in quantum computing, where qutrits may offer advantages over qubits in error correction and information density.
The Qutrit Bloch Sphere

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Quantum Physics arXiv:2601.06240 (quant-ph) [Submitted on 9 Jan 2026] Title:The Qutrit Bloch Sphere Authors:Vinod K Mishra View a PDF of the paper titled The Qutrit Bloch Sphere, by Vinod K Mishra View PDF Abstract:It is very important to understand if a qutrit can be visualized in a 3-dimensional Bloch sphere. In this work, a mathematical model for performing this operation is presented. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.06240 [quant-ph] (or arXiv:2601.06240v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.06240 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vinod Mishra [view email] [v1] Fri, 9 Jan 2026 16:34:57 UTC (577 KB) Full-text links: Access Paper: View a PDF of the paper titled The Qutrit Bloch Sphere, by Vinod K MishraView PDF view license Current browse context: quant-ph new | recent | 2026-01 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?)

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Source: arXiv Quantum Physics