Stoquastic permutationally invariant Bell operators

Quantum Physics [Submitted on 23 Mar 2026] Stoquastic permutationally invariant Bell operators Jan Li, Owidiusz Makuta, Evert van Nieuwenburg, Jordi Tura As Hermitian operators, many-body Bell operators can naturally be identified as many-body Hamiltonians. An important subclass of such Hamiltonians is the stoquastic class, characterized by having nonpositive off-diagonal matrix elements in a given basis. Interestingly, this property is shared by the permutationally invariant (PI) Bell operators underlying the largest Bell-correlation experiments to date. In this work, we explore the connection between many-body PI Bell operators and stoquasticity. We introduce the stoquasticity cone, which allows for a full characterization of the stoquastic parameter regimes for any PI Bell operator. We use this to show that PI Bell operators of the binary-input binary-output scenario consisting of at most three-body correlators can always be rendered stoquastic for any set of measurement parameters. Additionally, we also provide examples that use the stoquasticity cone to optimize for the quantum-classical gap. Numerical evidence suggests that the Bell operator used in the largest experiments to date is optimal with respect to stoquasticity. To the best of our knowledge, this work establishes the first connection between PI Bell operators and stoquasticity. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.22493 [quant-ph]   (or arXiv:2603.22493v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22493 Focus to learn more Submission history From: Jan Li [view email] [v1] Mon, 23 Mar 2026 19:00:12 UTC (473 KB) Access Paper: HTML (experimental) 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?)