  We evaluate the ability of future cosmic microwave background (CMB)
experiments to measure the power spectrum of large scale structure using
quadratic estimators of the weak lensing deflection field. We calculate the
sensitivity of upcoming CMB experiments such as BICEP, QUaD, BRAIN, ClOVER and
PLANCK to the non-zero total neutrino mass M_nu indicated by current neutrino
oscillation data. We find that these experiments greatly benefit from lensing
extraction techniques, improving their one-sigma sensitivity to M_nu by a
factor of order four. The combination of data from PLANCK and the SAMPAN
mini-satellite project would lead to sigma(M_nu) = 0.1 eV, while a value as
small as sigma(M_nu) = 0.035 eV is within the reach of a space mission based on
bolometers with a passively cooled 3-4 m aperture telescope, representative of
the most ambitious projects currently under investigation. We show that our
results are robust not only considering possible difficulties in subtracting
astrophysical foregrounds from the primary CMB signal but also when the minimal
cosmological model (Lambda Mixed Dark Matter) is generalized in order to
include a possible scalar tilt running, a constant equation of state parameter
for the dark energy and/or extra relativistic degrees of freedom.
