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Quantum theory in a global space-time gives rise to non-local correlations,which cannot be explained causally in a satisfactory way; this motivates thestudy 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, isassumed beyond the absence of logical paradoxes. It was shown for the two-partycase, however, that a global causal order always emerges in the classicallimit. Quite naturally, it has been conjectured that the same also holds in themulti-party setting. We show that counter to this belief, classicalcorrelations locally compatible with classical probability theory exist thatallow for deterministic signaling between three or more parties incompatiblewith any predefined causal order.

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