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arXiv · 2405.08743

Self-testing tilted strategies for maximal loophole-free nonlocality

Nicolas Gigena·Ekta Panwar·Giovanni Scala·Mateus Araújo·Máté Farkas·Anubhav Chaturvedi
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Abstract

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 Gr\"obner 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 Navascu\'es--Pironio--Ac\'in hierarchy to saturate the maximum quantum violation of these inequalities.

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Nicolas Gigena, Ekta Panwar, Giovanni Scala, Mateus Araújo, Máté Farkas, Anubhav Chaturvedi. 2024-05-14. Self-testing tilted strategies for maximal loophole-free nonlocality. https://doi.org/10.1038/s41534-025-01029-6

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