Quantum limit to subdiffraction incoherent optical imaging. II. A parametric-submodel approach

Abstract

In a previous paper [M. Tsang, Phys. Rev. A 99, 012305 (2019)], I proposed a quantum limit to the estimation of object moments in subdiffraction incoherent optical imaging. In this sequel, I prove the quantum limit rigorously by infinite-dimensional analysis. A key to the proof is the choice of an unfavorable parametric submodel to give a bound for the semiparametric problem. By generalizing the quantum limit for a larger class of moments, I also prove that the measurement method of spatial-mode demultiplexing (SPADE) with just one or two modes is able to achieve the quantum limit. For comparison, I derive a classical bound for direct imaging using the parametric-submodel approach, which suggests that direct imaging is substantially inferior.

17 pages, 4 figures. v4: corrected minor typos. Published

References in corpus (8)

• Subdiffraction incoherent optical imaging via spatial-mode demultiplexing
• Super-resolution linear optical imaging in the far field
• General expressions for the quantum Fisher information matrix with applications to discrete quantum imaging
• Confocal super-resolution microscopy based on a spatial mode sorter
• Coherence effects on estimating general sub-Rayleigh object distribution moments
• Quantum-accelerated imaging of N stars
• Poisson Quantum Information
• Quantum Limited Superresolution of Extended Sources in One and Two Dimensions

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• Efficient superoscillation measurement for incoherent optical imaging
• Semiparametric estimation in Hong-Ou-Mandel interferometry