  The application of quantum estimation theory to the problem of imaging two
incoherent point sources has recently led to new insights and better
measurements for incoherent imaging and spectroscopy. To establish a more
general limit beyond the case of two sources, here I evaluate a quantum bound
on the Fisher information that can be extracted by any far-field optical
measurement about the moments of a subdiffraction object. The bound matches the
performance of a spatial-mode-demultiplexing (SPADE) measurement scheme in
terms of its scaling with the object size, indicating that SPADE is close to
quantum-optimal. Coincidentally, the result is also applicable to the
estimation of diffusion parameters with a quantum probe subject to random
displacements.
