Causal reappraisal of the quantum three box paradox

TL;DR

This paper analyzes the quantum three box paradox from a causal perspective, clarifying the roles of measurement disturbance and realism in explaining the observed correlations and highlighting the complexity of the paradox.

Contribution

It introduces a causal framework to differentiate mechanisms behind the paradox, showing when measurement disturbance is necessary or can be avoided, depending on assumptions.

Findings

Full statistics require measurement disturbance for explanation.

Without realism, the paradox can be explained without disturbance.

Causal structures help clarify the mechanisms behind quantum correlations.

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.