Maximal incompatibility of locally classical behavior and global causal order in multi-party scenarios

Abstract: Quantum theory in a global space-time gives rise to non-local correlations, which cannot be explained causally in a satisfactory way; this motivates the study of theories with reduced global assumptions. Oreshkov, Costa, and Brukner (2012) proposed a framework in which quantum theory is valid locally but where, at the same time, no global space-time, i.e., predefined causal order, is assumed beyond the absence of logical paradoxes. It was shown for the two-party case, however, that a global causal order always emerges in the classical limit. Quite naturally, it has been conjectured that the same also holds in the multi-party setting. We show that counter to this belief, classical correlations locally compatible with classical probability theory exist that allow for deterministic signaling between three or more parties incompatible with any predefined causal order.