  Weak-measurement-based experiments [Kocsis et al., Science 332 (2011) 1170]
have shown that, at least for pure states, the average evolution of independent
photons in Young's two-slit experiment is in compliance with the trajectories
prescribed by the Bohmian formulation of quantum mechanics. But, what happens
if the same experiment is repeated assuming that the wave function associated
with each particle is different, i.e., in the case of mixed (incoherent)
states? This question is investigated here by means of two alternative
numerical simulations of Young's experiment, purposely devised to be easily
implemented and tested in the laboratory. Contrary to what could be expected a
priori, it is found that even for conditions of maximal mixedness or
incoherence (total lack of interference fringes), experimental data will render
a puzzling and challenging outcome: the average particle trajectories will
still display features analogous to those for pure states, i.e., independently
of how mixedness arises, the associated dynamics is influenced by both slits at
the same time. Physically this simply means that weak measurements are not able
to discriminate how mixedness arises in the experiment, since they only provide
information about the averaged system dynamics.
