LAUSR

It is well-known that no local model—in theory—can simulate the outcome statistics of a Bell-type experiment as long as the detection efficiency is higher than a threshold value. For the Clauser–Horne–Shimony–Holt (CHSH) Bell inequality this theoretical threshold value is ηT=2(2-1)≈0.8284\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _{\text {T}} = 2 (\sqrt{2}-1) \approx 0.8284$$\end{document}. On the other hand, Phys. Rev. Lett. 107, 170404 (2011) outlined an explicit practical model that can fake the CHSH inequality for a detection efficiency of up to 0.5. In this work, we close this gap. More specifically, we propose a method to emulate a Bell inequality at the threshold detection efficiency using existing optical detector control techniques. For a Clauser–Horne–Shimony–Holt inequality, it emulates the CHSH violation predicted by quantum mechanics up to ηT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta _{\text {T}}$$\end{document}. For the Garg–Mermin inequality—re-calibrated by incorporating non-detection events—our method emulates its exact local bound at any efficiency above the threshold. This confirms that attacks on secure quantum communication protocols based on Bell violation is a real threat if the detection efficiency loophole is not closed.