Detectability, Invasiveness and the Quantum Three Box Paradox

TL;DR

This paper investigates the quantum 3 box paradox, revealing that its core feature involves invasive but non-detectable measurements, and shows that no fully classical model can replicate this quantum phenomenon.

Contribution

It clarifies the role of invasiveness in quantum PPS paradoxes and demonstrates the impossibility of a fully classical explanation for the 3 box paradox.

Findings

Quantum PPS paradoxes require invasive, non-detectable measurements.

Classical models cannot fully replicate the 3 box paradox.

Some quasi-classical features are compatible with PPS paradoxes.

Abstract

Quantum pre- and post-selection (PPS) paradoxes occur when counterfactual inferences are made about different measurements that might have been performed, between two measurements that are actually performed. The 3 box paradox is the paradigm example of such a paradox, where a ball is placed in one of three boxes and it is inferred that it would have been found, with certainty, both in box 1 and in box 2 had either box been opened on their own. Precisely what is at stake in PPS paradoxes has been unclear, and classical models have been suggested which are supposed to mimic the essential features of the problem. We show that the essential difference between the classical and quantum pre- and post-selection effects lies in the fact that for a quantum PPS paradox to occur the intervening measurement, had it been performed, would need to be invasive but non-detectable. This invasiveness is required even for null result measurements. While some quasi-classical features (such as non-contextuality and macrorealism) are compatible with PPS paradoxes, it seems no fully classical model of the 3 box paradox is possible.