Quantum nonlocal correlations of anomalous weak values

Quantum Physics arXiv:2607.01491 (quant-ph) [Submitted on 1 Jul 2026] Title:Quantum nonlocal correlations of anomalous weak values Authors:Ron Cohen, Avshalom C. Elitzur, Eliahu Cohen View a PDF of the paper titled Quantum nonlocal correlations of anomalous weak values, by Ron Cohen and 1 other authors View PDF HTML (experimental) Abstract:Violations of Bell inequalities are a hallmark of entanglement, with only entangled states capable of exceeding classical bounds in standard Bell tests. Here we analyze anomalous weak values of the CHSH operator in pre- and post-selected (PPS) quantum ensembles, treating them as generalized bounds on Bell-type nonlocal correlations in the presence of post-selection. Fixing the overlap between the pre- and post-selected states, we compare three scenarios: unrestricted boundary states, one separable boundary state, and both boundary states separable. For each case, we derive both the maximal weak value for a fixed Bell operator and the maximal bound obtained by further optimizing over all CHSH operators. Our results show that post-selection and entanglement are distinct operational resources: post-selection alone can enhance correlations, but entanglement is necessary to exceed the corresponding separable PPS bounds, and their combination yields the strongest attainable correlations. We further show that the enhancement beyond the separable bound closely tracks the concurrence of the states that optimize the bounds, identifying entanglement as the source of the additional correlation strength. Finally, we show that nonlocal weak values provide post-selected entanglement witnesses, and we give a constructive protocol that detects every pure two-qubit source state with nonzero concurrence in the ideal state-adapted setting, even in regimes where the corresponding standard CHSH entanglement test is inconclusive. In this state-adapted setting, we explicitly construct the post-selection and CHSH measurements that achieve the largest possible separation from the separable PPS bound. More broadly, our results motivate hybrid protocols that combine post-selection and entanglement, with possible applications to improved quantum sensing, weak-value amplification, and quantum information processing. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2607.01491 [quant-ph] (or arXiv:2607.01491v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.01491 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Eliahu Cohen [view email] [v1] Wed, 1 Jul 2026 21:42:18 UTC (224 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum nonlocal correlations of anomalous weak values, by Ron Cohen and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph 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?)