  Due to physical orientations and birefringence effects, practical quantum
information protocols utilizing optical polarization need to handle
misalignment between preparation and measurement reference frames. For any such
capable system, an important question is how many resources -- e.g., measured
single photons -- are needed to reliably achieve alignment precision sufficient
for the desired quantum protocol. Here we study the performance of a
polarization-frame alignment scheme used in prior laboratory and field quantum
key distribution (QKD) experiments by performing Monte Carlo numerical
simulations. The scheme utilizes, to the extent possible, the same
single-photon-level signals and measurements as for the QKD protocol being
supported. Even with detector noise and imperfect sources, our analysis shows
that only a small fraction of resources from the overall signal -- a few
hundred photon detections, in total -- are required for good performance,
restoring the state to better than 99% of its original quality.
