2024/05/14 by N. Gigena, Ekta Panwar, Gigena, Nicolas +9 · 5 citations
Mathematics · Physics and Astronomy · #Bell test experiments #Bell's theorem #FOS: Physical sciences #Inequality #Mathematical analysis #Mathematics #Physics #Quantum #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum entanglement #Quantum mechanics #Quantum nonlocality #Theoretical physics
paper · pdf · doi:10.48550/arxiv.2405.08743
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/05/14 · openalex created_date 2024/05/16 · openalex updated_date 2026/07/30
The degree of experimentally attainable nonlocality, as gauged by the loophole-free or effective violation of Bell inequalities, remains severely limited due to inefficient detectors. We address an experimentally motivated question: Which quantum strategies attain the maximal loophole-free nonlocality in the presence of inefficient detectors? For any Bell inequality and any specification of detection efficiencies, the optimal strategies are those that maximally violate a tilted version of the Bell inequality in ideal conditions. In the simplest scenario, we demonstrate that the quantum strategies that maximally violate the doubly-tilted versions of Clauser-Horne-Shimony-Holt inequality are unique up to local isometries. We utilize a Jordan's lemma and Gröbner basis-based proof technique to analytically derive self-testing statements for the entire family of doubly-tilted CHSH inequalities and numerically demonstrate their robustness. These results enable us to reveal the insufficiency of even high levels of the Navascués--Pironio--Acín hierarchy to saturate the maximum quantum violation of these inequalities.