Multiparameter Quantum Metrology of Incoherent Point Sources: Towards Realistic Superresolution

TL;DR

This paper derives the quantum Cramér-Rao bound for estimating parameters of two incoherent optical sources, demonstrating that superresolution is achievable beyond the Rayleigh limit with optimal measurement strategies, especially relevant for astronomy.

Contribution

It establishes the multiparameter quantum Cramér-Rao bound for incoherent sources and shows how optimal measurements can surpass classical resolution limits.

Findings

The Rayleigh limit is not fundamental and can be overcome with proper measurement strategies.

Optimal detection provides quadratic improvement over intensity measurements.

Information about separation diminishes for unequally bright sources, but superresolution remains possible.

Abstract

We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright sources, the Cram\'er-Rao bound is independent of the source separation, which confirms that the Rayleigh resolution limit is just an artifact of the conventional direct imaging and can be overcome with an adequate strategy. For the general case of unequally bright sources, the amount of information one can gain about the separation falls to zero, but we show that there is always a quadratic improvement in an optimal detection in comparison with the intensity measurements. This advantage can be of utmost important in realistic scenarios, such as observational astronomy.