Violating a Bell Inequality: What to Do When You Lose Your Quantum System

Quantum Physics arXiv:2609.12604 (quant-ph) [Submitted on 11 Sep 2026] Title:Violating a Bell Inequality: What to Do When You Lose Your Quantum System Authors:Xinyu Xu, Yuqing Li, Mingze Xu, Dawei Ding View a PDF of the paper titled Violating a Bell Inequality: What to Do When You Lose Your Quantum System, by Xinyu Xu and 3 other authors View PDF HTML (experimental) Abstract:The detection loophole is a well-known loophole in Bell nonlocality motivated by the inefficiency of detectors used in Bell experiments. However, this inefficiency is actually a ubiquitous feature of any photonic platform for quantum networks since photons are readily absorbed by the surrounding environment. When the quantum system, usually a photon, is lost, what should the parties output? The most natural choice is to fall back to a deterministic strategy where each party produces an output via a function of her local input. In this paper, we study how to choose such a fallback strategy for general Bell inequalities with respect to different efficiencies $\eta$ to maximize the possible violation. We mathematically prove that for the CHSH inequality, there exists a fallback strategy that is optimal for all $\eta$. However, in general, we find that the optimal fallback strategy can vary with $\eta$, sometimes in surprising ways. For example, we find an example of a Bell inequality where the optimal fallback strategy near the threshold efficiency is not an optimal deterministic strategy in the lossless setting. Our results can reduce the efficiency requirements for closing the detection loophole and thus are useful for applications of Bell inequality violation, such as quantum telepathy or device-independent quantum key distribution. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.12604 [quant-ph] (or arXiv:2609.12604v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.12604 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Xinyu Xu [view email] [v1] Fri, 11 Sep 2026 09:00:29 UTC (1,186 KB) Full-text links: Access Paper: View a PDF of the paper titled Violating a Bell Inequality: What to Do When You Lose Your Quantum System, by Xinyu Xu and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?)