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 $2(N+1)/3$.

• Received 17 August 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.010504