  We measure the covariance of the non-linear matter power spectrum from N-body
simulations using two methods. In the first case, the covariance of power is
estimated from the scatter over many random realizations of the density field.
In the second, we use a novel technique to measure the covariance matrix from
each simulation individually by re-weighting the density field with a carefully
chosen set of functions. The two methods agree at linear scales, but
unexpectedly they disagree substantially at increasingly non-linear scales.
Moreover, the covariance of non-linear power measured using the re-weightings
method changes with box size. The numerical results are consistent with an
explanation given in a companion paper, which argues that the cause of the
discrepancy is beat-coupling, in which products of Fourier modes separated by a
small wavevector couple by gravitational growth to the large-scale beat mode
between them. We calculate the information content of the non-linear power
spectrum (about the amplitude of the initial, linear power spectrum) using both
methods and confirm the result of a previous paper, that at translinear scales
the power spectrum contains little information over and above that in the
linear power spectrum, but that there is a marked increase in information at
non-linear scales. We suggest that, in real galaxy surveys, the covariance of
power at non-linear scales is likely to be dominated by beat-coupling to the
largest scales of the survey and that, as a result, only part of the
information potentially available at non-linear scales is actually measurable
from real galaxy surveys.
