Rapid State-Reduction of Quantum Systems Using Feedback Control

We consider using Hamiltonian feedback control to increase the speed at which a continuous measurement purifies (reduces) the state of a quantum system, and thus to increase the speed of the preparation of pure states. For a measurement of an observable with N equispaced eigenvalues, we show that there exists a feedback algorithm which will speed up the rate of state-reduction by at least a factor of 2(N+1)/3.