The three-box paradox revisited

Abstract

The classical three-box paradox of Kirkpatrick (2003 J. Phys. A: Math. Gen. 36 4891) is compared to the original quantum three-box paradox of Aharonov and Vaidman (1991 J. Phys. A: Math. Gen. 24 2315). It is argued that the quantum three-box experiment is a ‘quantum paradox’ in the sense that it is an example of a classical task which cannot be accomplished using classical means, but can be accomplished using quantum devices. It is shown that Kirkpatrick's card game is analogous to a different game with a particle in three boxes which does not contain paradoxical features.

Measurements, disturbances and the quantum three box paradox

“…We have also argued that the classical models of [Kir03,LS05a,RV07] fail to reproduce a key feature of the PPS paradoxes.…”

“…As we show in the appendix, none of the classical models of pre-and post-selection paradoxes presented in the literature [Kir03,LS05a,RV07] are non-detectable. All involve intervening measurements which change the statistics of the final post-selection measurement.…”

“…We now highlight an important property of a PPS paradox, absent from the discussion of [Kir03,LS05a,RV07]: that Bob's measurements should be non-detectable by Alice.…”

“…Re-writing the classical models for PPS paradoxes considered in [Kir03,LS05a,RV07] in the ontic model formalism, shows how all involve detectable measurement disturbances.…”

“…Ravon and Vaidman [RV07] have rejected these classical comparisons, on the basis that they introduce a measurement disturbance. They argue that the essence of the 3 Box Paradox is that in the classical case there is no reason to suppose the measurement could introduce such a disturbance.…”