  Fermi-edge singularity and Anderson's orthogonality catastrophe are
paradigmatic examples of non-equilibrium many-body physics in conductors,
appearing after a quench is created by the sudden change of a localised
potential. We investigate if the signal carried by the quench can be used to
transmit a long ranged interaction, reminiscent of the RKKY interaction, but
with the inclusion of the full many-body propagation over space and time. We
calculate the response of a conductor to two quenches induced by localised
states at different times and locations. We show that building up and
maintaining coherence between the localised states is possible only with finely
tuned interaction between the localised states and the conductor. This puts
bounds to the use of time controlled RKKY type interactions and may limit the
speed at which some quantum gates could operate.
