The problem of coherent control in non-Markovian open quantum systems

We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall causing insurmountable difficulties in the effective modelling of the controlled system. We show that the only way to avoid these problems is a full microscopic description of the controlled system in presence of noise. We illustrate our findings with a paradigmatic example.