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

Abstract: 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 entails the failure of at least one of those assumptions. Since rejecting any of them - even partially - proves to be enough to explain the observed correlations, it is natural to ask about the cost in each case. This paper follows up on the results in PNAS 118 e2020569118 (2021), showing the equivalence between the locality and free choice assumptions, adding to the picture retro-causal models explaining the observed correlations. Here, we consider 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.