Fig. 2
Bell’s theorem for temporal order. A bipartite system, made of subsystems S1 and S2, is sent to two groups of agents. Operations on S1 (S2) are performed at events A1, B1 (A2, B2). At event C1 (C2), a measurement with setting i1 (i2) and outcome o1 (o2) is performed. Events A1, B1 are space-like separated from A2, B2 and C1 is space-like to C2; light cones are marked by dashed yellow lines. The order of events Aj, Bj, j = 1, 2, is described by a variable λ defined by a system M. The system M is measured at event D, producing an output bit z. If the initial state of the systems S1, S2, M is separable, and λ is a classical variable (possibly dynamical and probabilistic), the resulting bipartite statistics of the outcomes o1, o2 cannot violate any Bell inequality, even if conditioned on z
