Planck intermediate results. XLVI. Reduction of large-scale systematic
  effects in HFI polarization maps and estimation of the reionization optical
  depth
  This paper describes the identification, modelling, and removal of previously
unexplained systematic effects in the polarization data of the Planck High
Frequency Instrument (HFI) on large angular scales, including new mapmaking and
calibration procedures, new and more complete end-to-end simulations, and a set
of robust internal consistency checks on the resulting maps. These maps, at
100, 143, 217, and 353 GHz, are early versions of those that will be released
in final form later in 2016.
  The improvements allow us to determine the cosmic reionization optical depth
$\tau$ using, for the first time, the low-multipole $EE$ data from HFI,
reducing significantly the central value and uncertainty, and hence the upper
limit. Two different likelihood procedures are used to constrain $\tau$ from
two estimators of the CMB $E$- and $B$-mode angular power spectra at 100 and
143 GHz, after debiasing the spectra from a small remaining systematic
contamination. These all give fully consistent results.
  A further consistency test is performed using cross-correlations derived from
the Low Frequency Instrument maps of the Planck 2015 data release and the new
HFI data. For this purpose, end-to-end analyses of systematic effects from the
two instruments are used to demonstrate the near independence of their dominant
systematic error residuals.
  The tightest result comes from the HFI-based $\tau$ posterior distribution
using the maximum likelihood power spectrum estimator from $EE$ data only,
giving a value $0.055\pm 0.009$. In a companion paper these results are
discussed in the context of the best-fit Planck $\Lambda$CDM cosmological model
and recent models of reionization.
