Dynamics, locality and weak measurements: trajectories and which-way information in the case of a simplified double-slit setup

Abstract: Understanding how the interference pattern produced by a quantum particle in Young's double-slit setup builds up -- the "only mystery" of quantum mechanics according to Feynman -- is still a matter of discussion and speculation. Recent works have revisited the possibility of acquiring which-way information based on weak measurements. Weak measurements preserve the interference pattern due to their minimally perturbing character while still leading to a final position detection. Here we investigate a simplified double-slit setup by including weakly coupled pointers. We examine how the information provided by the weak pointers can be interpreted to infer the dynamics within a local picture through "weak trajectories". We contrast our approach with non-local dynamical accounts, such as the modular momentum approach to weak values and the trajectories defined by the de Broglie-Bohm picture.