Exponentially decreasing critical detection efficiency for any Bell inequality

[2204.11726] Exponentially decreasing critical detection efficiency for any Bell inequality Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Quantum Physics arXiv:2204.11726 (quant-ph) [Submitted on 25 Apr 2022 ( v1 ), last revised 10 Apr 2026 (this version, v4)] Title: Exponentially decreasing critical detection efficiency for any Bell inequality Authors: Nikolai Miklin , Anubhav Chaturvedi , Mohamed Bourennane , Marcin Pawłowski , Adán Cabello View a PDF of the paper titled Exponentially decreasing critical detection efficiency for any Bell inequality, by Nikolai Miklin and 4 other authors View PDF HTML (experimental) Abstract: We address the problem of closing the detection efficiency loophole in Bell experiments, which is crucial for real-world applications. Every Bell inequality has a critical detection efficiency $\eta$ that must be surpassed to avoid the detection loophole. Here, we propose a general method for reducing the critical detection efficiency of any Bell inequality to arbitrary low values. This is accomplished by entangling two particles in $N$ orthogonal subspaces (e.g., $N$ degrees of freedom) and conducting $N$ Bell tests in parallel. Furthermore, the proposed method is based on the introduction of penalized $N$-product (PNP) Bell inequalities, for which the so-called simultaneous measurement loophole is closed, and the maximum value for local hidden-variable theories is simply the $N$th power of the one of the Bell inequality initially considered. We show that, for the PNP Bell inequalities, the critical detection efficiency decays exponentially with $N$. The strength of our method is illustrated with a detailed study of the PNP Bell inequalities resulting from the Clauser-Horne-Shimony-Holt inequality. Comments: 5 + 2 pages, 2 figures. v4: Construction of PNP Bell inequalities is improved Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2204.11726 [quant-ph] (or arXiv:2204.11726v4 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2204.11726 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Phys. Rev. Lett. 129, 230403 (2022) Related DOI : https://doi.org/10.1103/PhysRevLett.129.230403 Focus to learn more DOI(s) linking to related resources Submission history From: Nikolai Miklin [ view email ] [v1] Mon, 25 Apr 2022 15:32:53 UTC (61 KB) [v2] Thu, 25 Aug 2022 13:59:28 UTC (57 KB) [v3] Thu, 1 Dec 2022 11:59:53 UTC (57 KB) [v4] Fri, 10 Apr 2026 10:01:55 UTC (53 KB) Full-text links: Access Paper: View a PDF of the paper titled Exponentially decreasing critical detection efficiency for any Bell inequality, by Nikolai Miklin and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2022-04 References & Citations INSPIRE HEP NASA ADS Google 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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