Time asymmetry of probabilities versus relativistic causal structure: an arrow of time

There is an incompatibility between the symmetries of causal structure in relativity theory and the signaling abilities of probabilistic devices with inputs and outputs: while time reversal in relativity will not introduce the ability to signal between spacelike separated regions, this is not the case for probabilistic devices with spacelike separated input-output pairs. We explicitly describe a nonsignaling device which becomes a perfect signaling device under time reversal, where time reversal can be conceptualized as playing backwards a videotape of an agent manipulating the device. This leads to an arrow of time that is identifiable when studying the correlations of events for spacelike separated regions. Somewhat surprisingly, although the time reversal of Popescu-Rohrlich boxes also allows agents to signal, it does not yield a perfect signaling device. Finally, we realize time reversal using postselection, which could to lead experimental implementation.