Failed attempt to escape from the quantum pigeon conundrum

Abstract

A recent criticism by Kunstatter et al. [Phys. Lett. A 384, 126686 (2020)] of a quantum setup violating the pigeon counting principle [Aharonov et al. PNAS 113, 532 (2016)] is refuted. The quantum nature of the violation of the pigeonhole principle with preand postselection is clarified. In a recent paper [1] Kunstatter et al. analyzed the work [2] of Aharonov et al. which presented a violation of the pigeon counting principle (PCP) in a particular preand postselected system. Kunstatter et al. claimed “we have provided a proof that the PCP is not violated in quantum mechanics”. In this Comment we will argue that Kunstatter et al. did not resolve the PCP conundrum because they analyzed a different problem. The quantum pigeon conundrum is a paradox about the locations of preand postselected quantum particles. We prepare a particular state of three particles in two boxes and consider a possible event in which the particles are found later in another particular state. The PCP tells us that when we put three classical particles in two boxes, we must find one pair in the same box. Aharonov et al. [2] argued that for particular preand postselected quantum states, three quantum particles are put in two boxes, yet no two particles are in the same box. In standard quantum mechanics there is no definition of the location of a preand postselected particle. The proposed definitions [3, 4] led to heated controversies, and it seems that we are still very far from a consensus regarding this question. In particular, the meaning of “no two particles present in the same box” has to be carefully specified. Obviously, it does not mean that the results of strong simultaneous measurements of the locations of all pairs of particles contradict the PCP for this particular preand postselection, since the results of strong measurements correspond to classical elements of reality for which the PCP must hold. Elements of reality of quantum preand postselected systems [5], similarly to