  The basic idea behind Rayleigh's criterion on resolving two incoherent
optical point sources is that the overlap between the spatial modes from
different sources would reduce the estimation precision for the locations of
the sources, dubbed Rayleigh's curse. We generalize the concept of Rayleigh's
curse to the abstract problems of quantum parameter estimation with incoherent
sources. To manifest the effect of Rayleigh's curse on quantum parameter
estimation, we define the curse matrix in terms of quantum Fisher information
and introduce the global and local immunity to the curse accordingly. We
further derive the expression for the curse matrix and give the necessary and
sufficient condition on the immunity to Rayleigh's curse. For estimating the
one-dimensional location parameters with a common initial state, we demonstrate
that the global immunity to the curse on quantum Fisher information is
impossible for more than two sources.
