Robust and efficient CMB lensing power spectrum from polarization surveys

Deep surveys of the CMB polarization have more information on the lensing signal than the quadratic estimators (QE) can capture. We showed in a recent work that a CMB lensing power spectrum built from a single optimized CMB lensing mass map, working in close analogy to state-of-the-art QE techniques, can result in an essentially optimal spectrum estimator at reasonable numerical cost. We extend this analysis here to account for real-life non-idealities including masking and realistic instrumental noise maps. As in the QE case, it is necessary to include small corrections to account for the estimator response to these anisotropies, which we demonstrate can be estimated easily from simulations. The realization-dependent debiasing of the spectrum remains robust, allowing unbiased recovery of the band powers even in cases where the statistical model used for the lensing map reconstruction is grossly wrong. This allows now robust and at the same time optimal CMB lensing constraints from CMB data, on all scales relevant for the inference of the neutrino mass, or other parameters of our cosmological model.