How to project qubits faster using quantum feedback

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.