Quantum limit of superresolution with a noisy imaging system*

Rayleigh criterion for resolving two incoherent point sources is most widely used for assessing the resolution of an imaging system. After a remarkable proposal of a scheme to beat the Rayleigh limit using a structured coherent measurement [1], the superresolution technique has been paid attention to both theoretically and experimentally, while studies for the effect of noise on superresolution are limited yet. Here, we demonstrate the impact of noise, such as thermal noise and dark counts, on the superresolution scheme to resolve two identical point sources of an arbitrary state and show by using Fisher information that the ultimate resolution drops rapidly in the presence of noise [2]. As an example, we provide an analysis of the effect of noise on resolving two thermal objects. Finally, we show that a spatial mode multiplexing method is nearly optimal to resolve two thermal point sources in the presence of noise.

[1] M. Tsang et al., Phys. Rev. X 6, 031033 (2016).
[2] C. Oh et al., arXiv:2008.11339 (2020).