  Detecting the faint emission of a secondary source in the proximity of the
much brighter source has been the most severe obstacle for using direct imaging
in searching for exoplanets. Using quantum state discrimination and quantum
imaging techniques, we show that one can significantly reduce the probability
of error for detecting the presence of a weak secondary source, even when the
two sources have small angular separations. If the weak source has relative
intensity $\epsilon \ll 1 $ to the bright source, we find that the error
exponent can be improved by a factor of $1/\epsilon$. We also find the
linear-optical measurements that are optimal in this regime. Our result serves
as a complementary method in the toolbox of optical imaging, from astronomy to
microscopy.
