  We derive optimal estimators for the binned two-, three-, and four-point
correlators of statistically isotropic tensor fields defined on the sphere, in
the presence of arbitrary beams, inpainting, and masking. This is a
conceptually straightforward extension of the associated scalar field Philcox
(2023), but upgraded to include spin-$2$ fields such as Cosmic Microwave
Background polarization and galaxy shear, and parity-violating physics in all
correlators. All estimators can be realized using spin-weighted spherical
harmonic transforms and Monte Carlo summation and are are implemented in the
public code PolyBin, with computation scaling, at most, with the total number
of bins. We perform a suite of validation tests verifying that the estimators
are unbiased and, in limiting regimes, minimum variance. These facilitate
general binned analyses of higher-point functions, and allow constraints to be
placed on various phenomena, such as non-separable inflationary physics
(novelly including polarized trispectra), non-linear evolution in the late
Universe, and cosmic parity-violation.
