  We address the amount of information in the non-Gaussian regime of weak
lensing surveys by modelling all relevant covariances of the power spectra and
bispectra, using 1000 ray-tracing simulation realizations for a Lambda-CDM
model and an analytical halo model. We develop a formalism to describe the
covariance matrices of power spectra and bispectra of all triangle
configurations. In addition to the known contributions which extend up to
six-point correlation functions, we propose a new contribution `the halo sample
variance (HSV)' arising from the coupling of the lensing Fourier modes with
large-scale mass fluctuations on scales comparable with the survey region via
halo bias theory. We show that the model predictions are in good agreement with
the simulation once we take the HSV into account. The HSV gives a dominant
contribution to the covariance matrices at multipoles l > 10^3, which arises
from massive haloes with a mass of > 10^14 solar mass and at relatively low
redshifts z < 0.4. Since such haloes are easily identified from a multi-colour
imaging survey, the effect can be estimated from the data. By adding the
bispectrum to the power spectrum, the total information content or the
cumulative signal-to-noise ratio up to a certain maximum multipole of a few
10^3 is improved by 20--50 per cent, which is equivalent to a factor of
1.4--2.3 larger survey area for the power spectrum measurement alone. However,
it is still smaller than the case of a Gaussian field by a factor of 3 mostly
due to the HSV. Thus bispectrum measurements are useful for cosmology, but
using information from upcoming surveys requires that non-Gaussian covariances
are carefully estimated.
