A Minimum-Cardinality Genuinely Unextendible Product Basis in Three Qutrits

Quantum Physics arXiv:2608.12785 (quant-ph) [Submitted on 13 Aug 2026] Title:A Minimum-Cardinality Genuinely Unextendible Product Basis in Three Qutrits Authors:Fei Shi, Ge Bai, Xiande Zhang, Qi Zhao, Lvzhou Li View a PDF of the paper titled A Minimum-Cardinality Genuinely Unextendible Product Basis in Three Qutrits, by Fei Shi and 4 other authors View PDF HTML (experimental) Abstract:It has remained an open question whether a genuinely unextendible product basis (GUPB) exists. We resolve this problem by constructing an explicit three-qutrit GUPB of cardinality fourteen in the smallest tripartite Hilbert space in which a GUPB can exist. Together with the nonexistence of three-qutrit GUPBs of cardinality less than fourteen, our construction proves that fourteen is the minimum cardinality. A padding procedure further extends the construction to all tripartite systems whose local dimensions are at least three. As applications, the normalized projector onto the thirteen-dimensional orthogonal complement of the three-qutrit GUPB is positive under partial transposition and bound entangled across every bipartition, while the GUPB exhibits strong quantum nonlocality without entanglement. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2608.12785 [quant-ph] (or arXiv:2608.12785v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2608.12785 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Fei Shi [view email] [v1] Thu, 13 Aug 2026 03:45:58 UTC (29 KB) Full-text links: Access Paper: View a PDF of the paper titled A Minimum-Cardinality Genuinely Unextendible Product Basis in Three Qutrits, by Fei Shi and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-08 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?) 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?)