  Weak gravitational lensing by the intervening large-scale structure of the
Universe induces high-order correlations in the cosmic microwave background
(CMB) temperature and polarization fields. We construct minimum variance
estimators of the intervening mass distribution out of the six quadratic
combinations of the temperature and polarization fields. Polarization begins to
assist in the reconstruction when E-mode mapping becomes possible on
degree-scale fields, i.e. for an experiment with a noise level of ~40 uK-arcmin
and beam of ~7', similar to the Planck experiment; surpasses the temperature
reconstruction at ~26 uK-arcmin and 4'; yet continues to improve the
reconstruction until the lensing B-modes are mapped to l ~ 2000 at ~0.3
uK-arcmin and 3'. Ultimately, the correlation between the E and B modes can
provide a high signal-to-noise mass map out to multipoles of L ~ 1000,
extending the range of temperature-based estimators by nearly an order of
magnitude. We outline four applications of mass reconstruction: measurement of
the linear power spectrum in projection to the cosmic variance limit out to L ~
1000 (or wavenumbers 0.002 < k < 0.2 in h/Mpc), cross-correlation with cosmic
shear surveys to probe the evolution of structure tomographically,
cross-correlation of the mass and temperature maps to probe the dark energy,
and the separation of lensing and gravitational wave B-modes.

Astrophysics