Locally optimal control of quantum systems with strong feedback.

For quantum systems with high purity, we find all observables that, when continuously monitored, maximize the instantaneous reduction in the average linear entropy. This allows us to obtain all locally optimal feedback protocols with strong feedback, and explicit expressions for the best such protocols for systems of size N < or =4. We also show that for a qutrit the locally optimal protocol is the optimal protocol for observables with equispaced eigenvalues, providing the first fully optimal feedback protocol for a 3-state system.