  Fundamental limits on the controllability of quantum mechanical systems are
discussed in the light of quantum information theory. It is shown that the
amount of entropy-reduction that can be extracted from a quantum system by
feedback controller is upper bounded by a sum of the decrease of entropy
achievable in open-loop control and the mutual information between the quantum
system and the controller. This upper bound sets a fundamental limit on the
performance of any quantum controllers whose designs are based on the
possibilities to attain low entropy states. An application of this approach
pertaining to quantum error correction is also discussed.
