# Bright-light detector control emulates the local bounds of Bell-type inequalities

## TL;DR

This paper presents a method using optical detector control to emulate Bell inequality violations at the theoretical detection efficiency threshold, highlighting potential security risks in quantum communication.

## Contribution

It introduces a practical approach to simulate Bell violations at the local bound using existing detector control techniques, closing the efficiency gap in previous models.

## Key findings

- Emulates CHSH violation up to the efficiency threshold
- Replicates local bounds of re-calibrated Garg-Mermin inequality
- Highlights security vulnerabilities in quantum protocols

## Abstract

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 $\eta_{\text{T}} = 2 (\sqrt{2}-1) \approx 0.8284$. 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.