  Communicating classical information with a quantum system involves the
receiver making a measurement on the system so as to distinguish as well as
possible the alphabet of states used by the sender. We consider the situation
in which this measurement takes an appreciable time. In this case the
measurement must be described by a continuous measurement process. We consider
a continuous implementation of the optimal measurement for distinguishing
between two non-orthogonal states, and show that feedback control can be used
during this measurement to increase the rate at which the information regarding
the initial preparation is obtained. We show that while the maximum obtainable
increase is modest, the effect is purely quantum mechanical in the sense that
the enhancement is only possible when the initial states are non-orthogonal. We
find further that the enhancement in the rate of information gain is achieved
at the expense of reducing the total information which the measurement can
extract in the long-time limit.
