  We consider qubit purification under simultaneous continuous measurement of
the three non-commuting qubit operators \sigma_x, \sigma_y, \sigma_z. The
purification dynamics is quantified by (i) the average purification rate, and
(ii) the mean time of reaching given level of purity, (1-\epsilon). Under ideal
measurements (detector efficiency \eta=1), we show in the first case an
asymptotic mean purification speed-up of 4 as compared to a standard
(classical) single-detector measurement. However by the second measure --- the
mean time of first passage T(\epsilon) of the purity --- the corresponding
speed-up is only 2. We explain these speed-ups using the isotropy of the qubit
evolution that provides an equivalence between the original measurement
directions and three simultaneous measurements, one with an axis aligned along
the Bloch vector and the other with axes in the two complementary directions.
For inefficient detectors, \eta=1-\delta <1 the mean time of first passage
T(\delta,\epsilon) increases since qubit purification competes with an
isotropic qubit dephasing. In the asymptotic high-purity limit (\epsilon,
\delta << 1) we show that the increase possesses a scaling behavior: \Delta
T(\delta,\epsilon) is a function only of the ratio {\delta}/{\epsilon}. The
increase \Delta T({\delta}/{\epsilon}) is linear for small argument but becomes
exponential ~ exp({\delta}/2{\epsilon}) for {\delta}/{\epsilon} large.
