  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.
