  The empirical correlation between the mass of a super-massive black hole
(MBH) and its host galaxy properties is widely considered to be evidence of
their co-evolution. A powerful way to test the co-evolution scenario and learn
about the feedback processes linking galaxies and nuclear activity is to
measure these correlations as a function of redshift. Unfortunately, currently
MBH can only be estimated in active galaxies at cosmological distances. At
these distances, bright active galactic nuclei (AGN) can outshine the host
galaxy, making it extremely difficult to measure the host's luminosity.
Strongly lensed AGNs provide in principle a great opportunity to improve the
sensitivity and accuracy of the host galaxy luminosity measurements as the host
galaxy is magnified and more easily separated from the point source, provided
the lens model is sufficiently accurate. In order to measure the MBH-L
correlation with strong lensing, it is necessary to ensure that the lens
modelling is accurate, and that the host galaxy luminosity can be recovered to
at least a precision and accuracy better than that of the typical MBH
measurement. We carry out extensive and realistic simulations of deep Hubble
Space Telescope observations of lensed AGNs obtained by our collaboration. We
show that the host galaxy luminosity can be recovered with better accuracy and
precision than the typical uncertainty on MBH(~ 0.5 dex) for hosts as faint as
2-4 magnitudes dimmer than the AGN itself. Our simulations will be used to
estimate bias and uncertainties on the actual measurements to be presented in a
future paper.
