Logical Bell inequalities, magic states and lambda polytopes

We investigate the role of logical Bell inequalities in identifying quantum states useful for magic state distillation. Our approach provides an alternative route to characterizing contextuality as a resource, entirely within the logical framework. In particular, we derive logical Bell inequalities that delineate the faces of the simulable polytope of a single qudit \textemdash the set of states non-negatively represented by the discrete Wigner function. This formulation highlights how logical Bell inequalities can serve as a tool for pinpointing non-stabilizer states relevant to quantum computational advantage, and it opens a pathway toward relating contextuality-based characterizations of magic to lambda-polytopes.