  We describe a method for precise estimation of the polarization of a
mesoscopic spin ensemble by using its coupling to a single two-level system.
Our approach requires a minimal number of measurements on the two-level system
for a given measurement precision. We consider the application of this method
to the case of nuclear spin ensemble defined by a single electron-charged
quantum dot: we show that decreasing the electron spin dephasing due to nuclei
and increasing the fidelity of nuclear-spin-based quantum memory could be
within the reach of present day experiments.
