Performance-tradeoff relation for locating two incoherent optical point sources

The optimal quantum measurements for estimating individual parameters might be incompatible with each other, so they cannot be jointly performed. The tradeoff between the estimation precisions for different parameters can be characterized by information regret: the difference between the Fisher information and its quantum limit. We show that the information-regret-tradeoff relation can give us not only an intuitive picture of the potential for improving the joint scheme for estimating the centroid and the separation but also some clues to the optimal measurements for the sequential scheme. In particular, we show that, for two incoherent point sources with a very small separation, the optimal measurement for the separation must extract little information about the centroid and vice versa.