Comparing the cost of violating causal assumptions in Bell experiments: locality, free choice and arrow-of-time

The causal modelling of Bell experiments relies on three fundamental assumptions: locality, freedom of choice and arrow-of-time. It turns out that nature violates Bell inequalities, which implies the failure of at least one of those assumptions. Since rejecting any of them, even partially, is sufficient to explain the observed correlations, it is natural to inquire about the cost in each case. This paper builds upon the findings in Blasiak et al. 2021 Proc. Natl Acad. Sci. USA 118, e2020569118 (doi:10.1073/pnas.2020569118) showing the equivalence between the locality and free choice assumptions. Here, we include retrocausal models to complete the picture of causal explanations of the observed correlations. Furthermore, we refine the discussion by considering more challenging causal scenarios which allow only single-arrow type violations of a given assumption. The figure of merit chosen for the comparison of the causal cost is defined as the minimal frequency of violation of the respective assumption required for a simulation of the observed experimental statistics.