Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions

Quantum Physics arXiv:2607.28998 (quant-ph) [Submitted on 31 Jul 2026] Title:Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions Authors:Ben-Hao Zhao, Dong-Huan Jiang, Yu-Guang Yang, Guang-Bao Xu View a PDF of the paper titled Construction of Sets of Orthogonal Quantum States with Minimal Nonlocality in Bipartite and Tripartite Systems of Unequal Local Dimensions, by Ben-Hao Zhao and 3 other authors View PDF HTML (experimental) Abstract:The research on minimal nonlocality aims to determine the minimal cardinality of nonlocal sets of quantum states. However, the construction of a nonlocal set of states in bipartite or tripartite quantum systems with unequal local dimensions remains unsolved. In this paper, we first give a method to construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb{C}^{4} \otimes \mathbb{C}^{7}$ quantum system. Then we give a general method to construct a set of orthogonal quantum states with minimal nonlocality in a bipartite quantum system with unequal local dimensions. Furthermore, we generalize the construction method to tripartite quantum system with unequal local dimensions, and construct a set of orthogonal quantum states with minimal nonlocality in $\mathbb C^{d_1} \otimes \mathbb C^{d_2}\otimes \mathbb C^{d_3}$ quantum system for $5\le d_1 new | recent | 2026-07 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?)