Quantum limits for resolving Gaussian sources

TL;DR

This paper derives the quantum Cramér-Rao bound for estimating the separation of two Gaussian sources, revealing how quantum resources influence resolution limits across different source states.

Contribution

It provides an analytical expression for the quantum resolution limit applicable to any Gaussian state, highlighting the role of quantum resources like coherence and squeezing.

Findings

Coherent states achieve quantum optimal resolution.

The resolution limit depends on quantum resources such as squeezing.

Analytical bounds are valid for arbitrary source brightness.

Abstract

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.