  We explore the covariance of redshift-space matter power spectra after a
standard density-field reconstruction. We derive perturbative formula of the
covariance at the tree-level order and find that the amplitude of the
off-diagonal components from the trispectrum decreases by reconstruction. Using
a large set of N-body simulations, we also find the similar reduction of the
off-diagonal components of the covariance and thereby the signal-to-noise ratio
(S/N) of the post-reconstructed (post-rec) power spectra significantly
increases compared to the pre-reconstructed spectra. This indicates that the
information leaking to higher-order statistics come back to the two-point
statistics by reconstruction. Interestingly, the post-rec spectra have higher
S/N than the linear spectrum with Gaussian covariance when the scale of
reconstruction characterized with the smoothing scale of the shift field is
below ~10Mpc/h where the trispectrum becomes negative. We demonstrate that the
error of the growth rate estimated from the monopole and quadrupole components
of the redshift-space matter power spectra significantly improves by
reconstruction. We also find a similar improvement of the growth rate even when
taking into account the super-sample covariance, while the reconstruction
cannot correct for the field variation of the super-sample modes.
