摘要：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 $$\eta _{\text {T}} = 2 (\sqrt,-1) \approx 0.8284$$ . 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 $$\eta _{\text {T}}$$ . 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.
