Beyond the Magic Square Game: Widening the Gap for Two Bell States

Quantum Physics [Submitted on 21 Mar 2026] Beyond the Magic Square Game: Widening the Gap for Two Bell States Tony Lau We demonstrate that the largest gap between the entangled value and the classical value for a one-round two-player nonlocal game with a perfect entangled strategy using two Bell states of entanglement is at least \frac{4}{35}, improving on the gap of \frac{1}{9} achieved by the Mermin-Peres magic square game. We do so by explicitly constructing a nonlocal game with classical value \frac{31}{35} using the full symmetry of the 2-qubit Pauli group. Comments: 26 pages, 6 figures, 3 tables Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.20748 [quant-ph]   (or arXiv:2603.20748v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.20748 Focus to learn more Submission history From: Anthony Lau [view email] [v1] Sat, 21 Mar 2026 10:36:07 UTC (22 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?)