  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.

Quantum Physics