Nonlocal response in Hall-shaped superconductors is studied using the time-dependent Ginzburg-Landau equations. Applying current in one pair of contacts leads to a voltage drop in another pair of contacts situated at a distance much larger than the coherence length. This effect is a consequence of the long range correlations in a one-dimensional vortex lattice squeezed in a narrow channel by screening currents. The discrete change in the number of vortices in the channel with applied magnetic field leads to a nonlocal response which is a nonmonotonous function of the magnetic field. For specific configurations of the Hall-shaped superconductor we found a rectifying effect.