is that the recovered $C_l$s accurately follow the true $C_l$s only for $l \ga 50$.

Exact covariance properties {#sec:exact-cov}
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The covariance of any quadratic power spectrum estimates that derive from the pseudo-$C_l$s by linear transformations follow simply from the covariance of the latter. For this reason, in this paper we concentrate on the pseudo-$C_l$ covariance. Furthermore, we focus on the sample covariance (i.e. we neglect instrument noise) to highlight those aspects specific to CMB polarization that arise from mode-mixing on the incomplete sky. Including instrument noise is obviously important for application to near-future surveys since it will dominate sample variance. Extending the analytic results derived in this paper to include simple white noise should be straightforward (see @efstathiou04 for the case of the temperature anisotropies). However, for more realistic correlated noise, Monte-Carlo simulations will probably be required to account properly for the noise contribution to the covariances. We shall assume throughout that the CMB signal is Gaussian. If the initial fluctuations were very-nearly Gaussian, as expected in simple single-field inflation models (e.g. @bartolo04), non-linear effects will introduce only a small level of non-Gaussianity into $E$ modes on the scales of interest for primary CMB science (e.g. @mollerach04). However, if 