  Quantum simulators are attracting great interest because they promise insight
into the behavior of quantum many-body systems that are prohibitive for
classical simulations. The generic output of quantum simulators are snapshots,
obtained by means of projective measurements. A central goal of theoretical
efforts must be to predict the exact same quantities that can be measured in
experiments. Here, we report on the snapshot based calculation of particle
currents in quantum lattice models with a conserved number of particles. It is
shown how the full probability distribution of locally resolved particle
currents can be obtained from suitable snapshot data. Moreover, we investigate
the Hall response of interacting bosonic flux ladders, exploiting snapshots
drawn from matrix-product states. Flux ladders are minimal lattice models,
which enable microscopic studies of the Hall response in correlated quantum
phases and they are successfully realized in current quantum-gas experiments.
Using a specific pattern of unitary two-site transformations, it is shown that
the Hall polarization and the Hall voltage can be faithfully computed from the
snapshots obtained in experimentally feasible quench and finite-bias
simulations.
