  As a method to extract information from optical system, imaging can be viewed
as a parameter estimation problem. The fundamental precision in locating one
emitter or estimating the separation between two incoherent emitters is bounded
below by the multiparameter quantum Cramer-Rao bound (QCRB).Multiparameter QCRB
gives an intrinsic bound in parameter estimation. We determine the ultimate
potential of quantum-limited imaging for improving the resolution of a
far-field, diffraction-limited within the paraxial approximation. We show that
the quantum Fisher information matrix (QFIm) about one emitter's position is
independent on the true value of it. We calculate the QFIm of two
unequal-brightness emitters' relative positions and intensities, the results
show that only when the relative intensity and centroids of two point sources
including longitudinal and transverse direction are known exactly, the
separation in different directions can be estimated simultaneously with finite
precision. Our results give the upper bounds on certain far-field imaging
technology and will find wide applications from microscopy to astrometry.
