A Bohmian model of the quantum switch

Abstract

In a paper by Araújo et al., the quantum switch was first theoretically described with the process matrix formalism where the authors claim that it is “a genuine example of ’indefinite causal order’ “. This means A superposition of event E before F (E ≺ F) with F before E (F ≺ E). The quantum switch was first experimentally implemented by Procopio et al., where the authors claim that it is “the first realization of a ’superposition of causal order’ “. In this thesis, a Bohmian Mechanical toy model is used to describe the experimental realization presented in the paper by Procopio et al. The relevant parts of the experiment are first described by quantum mechanics, thereafter the description with Bohm’s theory is made. In Bohmian Mechanics, particles always have definite positions, and are guided by the wave function. The particle’s trajectories of the particles follow from the guiding equation. The Bohmian trajectories are computed close to the first beam splitters of the Mach-Zehnder interferometer, giving insights into the trajectories for the whole experimental setup. Both the Quantum Mechanical and the Bohmian Mechanical descriptions are completely in line with the experimental outcome. Based on these descriptions, it turns out that the experimental implementation is compatible with causal order from the perspective of both Quantum Mechanics and Bohmian Mechanics. Instead of a superposition of the same two events with different causal orders, we find that there are four different events. Even the assumption of 2 events underlying the process matrix formalism in the paper by Araújo et al. seems to be broken in the experiment. It therefore seems that the claim of indefinite causal order by Procopio et al. may be too strong.