  We present a number of rapid-purification feedback protocols for optical
homodyne detection of a single optical qubit. We derive first a protocol that
speeds up the rate of increase of the average purity of the system, and find
that like the equivalent protocol for a non-disspative measurement, this
generates a deterministic evolution for the purity in the limit of strong
feedback. We also consider two analogues of the Wiseman-Ralph
rapid-purification protocol in this setting, and show that like that protocol
they speed up the average time taken to reach a fixed level of purity. We also
examine how the performance of these algorithms changes with detection
efficiency, being an important practical consideration.
