  When three or more particles are considered, quantum correlations can be
stronger than the correlations generated by so-called hybrid local hidden
variable models, where some of the particles are considered as a single block
inside which communication and signaling is allowed. We provide an exhaustive
classification of Bell inequalities to characterize various hybrid scenarios in
four- and five-particle systems. In quantum mechanics, these inequalities
provide device-independent witnesses for the entanglement depth. In addition,
we construct a family of inequalities to detect a non-locality depth of (n-1)
in n-particle systems. Moreover, we present two generalizations of the original
Svetlichny inequality, which was the first Bell inequality designed for hybrid
models. Our results are based on the cone-projection technique, which can be
used to completely characterize Bell inequalities under affine constraints;
even for many parties, measurements, and outcomes.
