  When one performs a continuous measurement, whether on a classical or quantum
system, the measurement provides a certain average rate at which one becomes
certain about the state of the system. For a quantum system this is an average
rate at which the system is projected onto a pure state. We show that for a
standard kind of continuous measurement, for a qubit this rate may be increased
by applying unitary operations during the measurement (that is, by using
Hamiltonian feedback), in contrast to the equivalent measurement on a classical
bit, where reversible operations cannot be used to enhance the rate of entropy
reduction. We determine the optimal feedback algorithm and discuss the
Hamiltonian resources required.
