The simplest causal inequalities and their violation

Understand

In a scenario where two parties share, act on and exchange some physical resource, the assumption that the parties' actions are ordered according to a definite causal structure yields constraints on the possible correlations that can be established.

• We show that the set of correlations that are compatible with a definite causal order forms a polytope, whose facets define causal inequalities.
• We fully characterize this causal polytope in the simplest case of bipartite correlations with binary inputs and outputs.
• We find two families of nonequivalent causal inequalities; both can be violated in the recently introduced framework of process matrices, which extends the standard quantum formalism by relaxing the implicit assumption of a fixed causal structure.