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CHSH inequality always holds in bipartite qutrits with spin-1 observables

arXiv Quantum Physics
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⚡ Quantum Brief
Hyunho Cha has mathematically proven that the CHSH inequality—key for testing quantum nonlocality—always holds for all bipartite qutrit systems when measurements are restricted to spin-1 observables, resolving a longstanding conjecture. The result extends beyond pure states, showing even mixed qutrit states cannot violate CHSH under these conditions, strengthening earlier claims limited to nonseparable pure states by Hanotel and Loubenets. This work closes a theoretical gap by confirming spin-1 measurements inherently constrain qutrit correlations, aligning with classical bounds despite quantum mechanics’ typical nonlocality potential. Published in March 2026, the proof uses rigorous quantum information techniques, offering a universal bound applicable to any two-qutrit system regardless of entanglement or state preparation. The findings deepen understanding of quantum correlations’ limits, with implications for device-independent protocols and foundational tests of quantum mechanics in higher-dimensional systems.
CHSH inequality always holds in bipartite qutrits with spin-1 observables

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Quantum Physics arXiv:2603.10296 (quant-ph) [Submitted on 11 Mar 2026] Title:CHSH inequality always holds in bipartite qutrits with spin-1 observables Authors:Hyunho Cha View a PDF of the paper titled CHSH inequality always holds in bipartite qutrits with spin-1 observables, by Hyunho Cha View PDF HTML (experimental) Abstract:We resolve a conjecture of Hanotel and Loubenets concerning CHSH inequality in bipartite qutrits. It states that nonseparable pure states of two qutrits do not violate the CHSH inequality when each party is restricted to spin-1 observables. We prove a stronger result that \emph{all} bipartite states on $\mathbb{C}^3 \otimes \mathbb{C}^3$ satisfy the CHSH inequality under spin-1 measurements, regardless of whether the state is pure or mixed. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.10296 [quant-ph] (or arXiv:2603.10296v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.10296 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hyunho Cha [view email] [v1] Wed, 11 Mar 2026 00:36:33 UTC (5 KB) Full-text links: Access Paper: View a PDF of the paper titled CHSH inequality always holds in bipartite qutrits with spin-1 observables, by Hyunho ChaView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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