Unilateral determination of causal order in a cyclic process

Abstract: The recent years have seen interest into the possibility for (classical as well as quantum) causal structures that, while remaining logically consistent, feature a cyclic causal order between events, opening intriguing possibilities for new physics. In the cyclic processes displayed so far, the global causal order is determined jointly by the operations performed by agents at each event, a feature that can be certified through the introduction of causal games and (the violation of) causal inequalities. This raises the question of whether there exist processes in which an agent acting at a single event can unilaterally determine her causal ordering with respect to some other events. We answer this question in the affirmative, by introducing a process in which any party may be put in a position to pick, on her own, any other party to lie in her future. We certify this behaviour by displaying a related causal inequality that the process allows to maximally violate.