Quantum-optimal detection of one-versus-two incoherent sources with arbitrary separation

TL;DR

This paper demonstrates that simple linear optical measurements, specifically binary spatial-mode demultiplexing and image-inversion interferometry, are optimal or near-optimal for detecting and estimating the separation of incoherent optical sources, surpassing direct imaging especially at sub-Rayleigh distances.

Contribution

The authors show that binary spatial-mode demultiplexing is quantum-optimal for all source separations, and that their measurement schemes outperform direct imaging for sub-Rayleigh separations.

Findings

Binary spatial-mode demultiplexing is quantum-optimal across all separations.

Image-inversion interferometry is near-optimal for sub-Rayleigh separations.

The proposed schemes outperform direct imaging in sub-Rayleigh regimes.

Abstract

We analyze the fundamental resolution of incoherent optical point sources from the perspective of a quantum detection problem: deciding whether the optical field on the image plane is generated by one source or two weaker sources with arbitrary separation. We investigate the detection performances of two measurement methods recently proposed by us to enhance the estimation of the separation. For the detection problem, we show that the method of binary spatial-mode demultiplexing is quantum-optimal for all values of separations, while the method of image-inversion interferometry is near-optimal for sub-Rayleigh separations. Unlike the proposal by Helstrom, our schemes do not require the separation to be given and can offer that information as a bonus in the event of a successful detection. For comparison, we also demonstrate the supremacy of our schemes over direct imaging for sub-Rayleigh separations. These results demonstrate that simple linear optical measurements can offer supremal performances for both detection and estimation.