Quantum limits for resolving Gaussian sources

Abstract

We determine analytically the quantum Cramér-Rao bound for the estimation of the separation between two point sources in arbitrary Gaussian states. Our analytical expression is valid for arbitrary sources brightness, and determining how different resources, such as mutual coherence (induced by thermal correlations or displacement) or squeezing, affect the scaling of the ultimate resolution limit with the mean number of emitted photons. In practical scenarios, we find coherent states of the sources to achieve quantum optimal resolution.