Quantum Bell inequalities from Information Causality -- tight for Macroscopic Locality.

Quantum generalizations of Bell inequalities are analytical expressions of correlations observed in the Bell experiment that are used to explain or estimate the set of correlations that quantum theory allows. Unlike standard Bell inequalities, their quantum analogs are rare in the literature, as no known algorithm can be used to find them systematically. In this work, we present a family of quantum Bell inequalities in scenarios where the number of settings or outcomes can be arbitrarily high. We derive these inequalities from the principle of Information Causality, and thus, we do not assume the formalism of quantum mechanics. Considering the symmetries of the derived inequalities, we show that the latter give the necessary and sufficient condition for the correlations to comply with Macroscopic Locality. As a result, we conclude that the principle of Information Causality is strictly stronger than the principle of Macroscopic Locality in the subspace defined by these symmetries.