  We examine the degree to which observations of large-scale cosmic microwave
background (CMB) polarization can shed light on the puzzling large-scale power
modulation in maps of CMB anisotropy. We consider a phenomenological model in
which the observed anomaly is caused by modulation of large-scale primordial
curvature perturbations, and calculate Fisher information and error forecasts
for future polarization data, constrained by the existing CMB anisotropy data.
Because a significant fraction of the available information is contained in
correlations with the anomalous temperature data, it is essential to account
for these constraints. We also present a systematic approach to finding a set
of normal modes that maximize the available information, generalizing the
well-known Karhunen-Loeve transformation to take account of the constraints
from the temperature data. A polarization map covering at least $\sim 60\%$ of
the sky should be able to provide a $3\sigma$ detection of modulation at the
level favored by the temperature data. A significant fraction of the
information in such a data set is contained in the single mode that optimally
encapsulates the signal due to temperature-polarization correlation.
