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

TL;DR

This paper explores how quantum entanglement affects particle trajectories in a Young's two-slit experiment using Bohmian velocity fields, revealing that entanglement causes trajectories to cross and behave differently than in separable states.

Contribution

It introduces a velocity field analysis from Bohmian mechanics to study entanglement effects in bipartite Young's experiments, highlighting the deformation of trajectories due to entanglement.

Findings

Entanglement causes trajectories to cross and wander across the total space.

In separable states, velocity fields act independently on each particle.

Entangled states deform velocity fields, disrupting the non-crossing rule.

Abstract

We consider the concept of velocity fields, taken from Bohmian mechanics, to investigate the dynamical effects of entanglement in bipartite realizations of Young's two-slit experiment. In particular, by comparing the behavior exhibited by factorizable two-slit states (cat-type state analogs in the position representation) with the dynamics exhibited by a continuous-variable Bell-type maximally entangled state, we find that, while the velocity fields associated with each particle in the separable scenario are well-defined and act separately on each subspace, in the entangled case there is a strong deformation in the total space that prevents this behavior. Consequently, the trajectories for each subsystem are not constrained any longer to remain confined within the corresponding subspace; rather, they exhibit seemingly wandering behavior across the total space. In this way, within the subspace associated with each particle (that is, when we trace over the other subsystem), not only interference features are washed out, but also the so-called Bohmian non-crossing rule\linebreak (i.e., particle trajectories are allowed to get across the same point at the same time).