Hardy's Paradox for Yu-Oh Set Constructed by Logically Contextual Quantum States

Quantum Physics [Submitted on 13 Mar 2026] Hardy's Paradox for Yu-Oh Set Constructed by Logically Contextual Quantum States Chang He, Yongjun Wang, Baoshan Wang, Songyi Liu, Yunyi Jia Quantum contextuality is a fundamental nonclassical property of quantum systems, regarded as a key resource that demonstrates the computational and informational advantages of quantum over classical systems. Our present work aims to construct Hardy's paradoxes, a set of possibilistic conditions witnessing contextuality, for Yu-Oh set, which is the state-independent contextual quantum system with the least number of vectors. To achieve the aim, we systematically enumerate all logically contextual pure states on Yu-Oh set, and theoretically prove that no mixed states in this scenario are logically contextual. Based on the identified logically contextual quantum states, we construct 12 Hardy's paradoxes with identical success probability SP=11.1%. Furthermore, we present corresponding observables to experimentally witness these Hardy's paradoxes. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.12738 [quant-ph]   (or arXiv:2603.12738v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.12738 Focus to learn more Submission history From: Yongjun Wang [view email] [v1] Fri, 13 Mar 2026 07:33:32 UTC (53 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)