Causal reappraisal of the quantum three box paradox

Abstract: Quantum three box paradox is a prototypical example of some bizarre predictions for intermediate measurements made on pre- and post-selected systems. Although in principle those effects can be explained by measurement disturbance, it is not clear what mechanisms are required to fully account for the observed correlations. In this paper, this paradox is scrutinised from the causal point of view. We consider an array of potential causal structures behind the experiment, eliminating those without enough explanatory power. This gives a means of differentiating between the various mechanisms in which measurement disturbance can propagate in the system. Specifically, we distinguish whether it is just the measurement outcome or the full measurement context that is required for the causal explanation of the observed statistics. We show that the latter is indispensable, but only when the full statistics is taken into account (which includes checking the third box too). Furthermore, we discuss the realism assumption which posits the existence of preexisting values revealed by measurements. It is shown that in this case measurement disturbance is necessary. Interestingly, without the realism assumption, the original version of the paradox (with just two boxes considered for inspection) can be explained without resorting to any measurement disturbance. These various results illustrate the richness of the paradox which is better appreciated from the causal perspective.