### Abstract

The state of a quantum system is perturbed due to the interaction with the environment. In quantum control one tries to undo the perturbation by using measurement results to perform correction operations. The correction is perfect if the measurement results do not contain any information about the state of the system which is considered unknown. If some information is obtained then inevitably the system cannot be brought back in the initial state. We show however that the perturbation is bounded by a power of the information. We then look at the difference between in the Fisher information before and after the measurement and show that it is bounded by the perturbation. An application of these ideas is the use of squeezed states for controlling a system shown recently by L. Bouten.