Giovanni Scala

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 Jordan's lemma and Grobner 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 Navascues-Pironio-Acin hierarchy to saturate the maximum quantum violation of these inequalities.

We propose a characteristic–function approach to Bell inequalities implemented with interferometric multiport measurements. By encoding d-valued outcomes as roots of unity, Bell functionals become linear combinations of Fourier correlators. This unified scheme reproduces CHSH, CGLMP, and MABK inequalities, and systematically generates new ones in higher-dimensional and multi setting scenarios. Optimizing over entangled states and multiport phase shifts provides explicit quantum strategies. Our framework thus offers a compact, experimentally natural route to Bell tests beyond the standard families.