Young's experiment with entangled bipartite systems: The role of underlying quantum velocity fields

The Bohmian concept of local velocity field is used here to investigate the dynamical effects of entanglement in experiments involving two spatially separated subsystems, in particular, in bipartite realizations of Young's two-slit experiment. In this analysis, single-slit diffraction states are represented by Gaussian wave packets, used here as the basis to construct more general two-party factorizable and entangled states. Physically, these states describe the dynamics along the transverse direction, where interference (and its suppression) take place. The dynamics exhibited by a continuous-variable Bell-type maximally entangled state is thus investigated and compared to the behavior exhibited by factorizable two-slit states (i.e., cat-type states in the position representation). It is found that, while the velocity fields associated with each particle in the separable scenario are well defined and act separately on each coordinate, in the entangled case there is a strong deformation that prevents this behavior. This provokes that particles initially associated with the same subspace gradually move away from it, displaying a wandering behavior across the extended two-dimensional space. Consequently, not only interference features are washed out within the respective particle subspaces, but also the well-known Bohmian non-crossing rule is apparently violated, as different particle trajectories seem to get across the same point at the same time (within such subspaces). This behavior thus coincides with what one might expect from a classical point of view: the trajectories leaving one slit are unaware of the dynamics displayed by the trajectories leaving the other slit, and vice versa.