We determine analytically the quantum Cram\'er-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 it allows to determine 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.
@article{arxiv.2205.04258,
title = {Quantum limits for resolving Gaussian sources},
author = {Giacomo Sorelli and Manuel Gessner and Mattia Walschaers and Nicolas Treps},
journal= {arXiv preprint arXiv:2205.04258},
year = {2023}
}