Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality

Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality Anubhav Chaturvedi, Nicolas Gigena, Ekta Panwar, Giovanni Scala, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4420780/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 May, 2025 Read the published version in npj Quantum Information → Version 1 posted You are reading this latest preprint version Abstract The degree of experimentally attainable nonlocality, as gauged by the amount of loophole-free violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. However, self-testing via the standard sum of squares decomposition method turns out to be analytically intractable since even high levels of the Navascués--Pironio--Acín hierarchy are insufficient to saturate the maximum quantum violation of these inequalities. Instead, we utilize a novel Jordan's lemma-based proof technique to obtain robust analytical self-testing statements for the entire family of tilted-Bell inequalities. These results allow us to unveil intriguing aspects of the effect of inefficient detectors and the complexity of characterizing the set of quantum correlations, in the simplest Bell scenario. Physical sciences/Physics/Quantum physics/Quantum information Physical sciences/Physics/Quantum physics/Single photons and quantum effects Full Text Additional Declarations (Not answered) Cite Share Download PDF Status: Published Journal Publication published 19 May, 2025 Read the published version in npj Quantum Information → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4420780","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":318399361,"identity":"ded54b24-b936-4bbc-aa10-401cfc700699","order_by":0,"name":"Anubhav 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We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. However, self-testing via the standard sum of squares decomposition method turns out to be analytically intractable since even high levels of the Navascués--Pironio--Acín hierarchy are insufficient to saturate the maximum quantum violation of these inequalities. Instead, we utilize a novel Jordan's lemma-based proof technique to obtain robust analytical self-testing \r\nstatements for the entire family of tilted-Bell inequalities. These results allow us to unveil intriguing aspects of the effect of inefficient detectors and the complexity of characterizing the set of quantum correlations, in the simplest Bell scenario.","manuscriptTitle":"Robust self-testing of Bell inequalities tilted for maximal loophole-free nonlocality","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-07-16 02:15:03","doi":"10.21203/rs.3.rs-4420780/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"28d80e50-29ba-4b4e-9edf-b78396c67951","owner":[],"postedDate":"July 16th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":33666284,"name":"Physical sciences/Physics/Quantum physics/Quantum information"},{"id":33666285,"name":"Physical sciences/Physics/Quantum physics/Single photons and quantum effects"}],"tags":[],"updatedAt":"2025-05-20T07:08:50+00:00","versionOfRecord":{"articleIdentity":"rs-4420780","link":"https://doi.org/10.1038/s41534-025-01029-6","journal":{"identity":"npj-quantum-information","isVorOnly":false,"title":"npj Quantum Information"},"publishedOn":"2025-05-19 04:00:00","publishedOnDateReadable":"May 19th, 2025"},"versionCreatedAt":"2024-07-16 02:15:03","video":"","vorDoi":"10.1038/s41534-025-01029-6","vorDoiUrl":"https://doi.org/10.1038/s41534-025-01029-6","workflowStages":[]},"version":"v1","identity":"rs-4420780","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4420780","identity":"rs-4420780","version":["v1"]},"buildId":"cBFmMYwuxLRRLfASyISRj","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}