  A recent paper [Z. Yu and S. Prasad, "Quantum limited superresolution of an
incoherent source pair in three dimensions," arXiv:1805.09227v2 [quant-ph]
(2018)] considered the problem of quantum limited estimation of the separation
vector for a pair of incoherent point sources in all three dimensions. Here we
extend our analysis to treat the problem of simultaneously estimating the
location of the centroid and the separation of the source pair, which is
equivalent to localizing both sources simultaneously. We first calculate the
quantum Fisher information for simultaneous pair centroid-separation estimation
and then discuss the fundamental, estimation-theoretic trade-offs between the
two tasks, which we confirm using simulations.
