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arXiv:2209.06104 · Physical Review A

Quantum noise spectroscopy as an incoherent imaging problem

Mankei Tsang

Published Jan 19, 2023• 16 citations

Abstract

I point out the mathematical correspondence between an incoherent imaging model proposed by my group in the study of quantum-inspired superresolution [M. Tsang, R. Nair, and X.-M. Lu, Phys. Rev. X 6, 031033 (2016)] and a noise spectroscopy model also proposed by us [M. Tsang and R. Nair, Phys. Rev. A 86, 042115 (2012); S. Ng et al., Phys. Rev. A 93, 042121 (2016)]. Both can be regarded as random displacement models, where the probability measure for the random displacement depends on unknown parameters. The spatial-mode demultiplexing (SPADE) method proposed for imaging is analogous to the spectral photon counting method proposed by Ng et al. for optical phase noise spectroscopy: Both methods are discrete-variable measurements that are superior to direct displacement measurements (direct imaging or homodyne detection) and can achieve the respective quantum limits. Inspired by SPADE, I propose a modification of spectral photon counting when the input field is squeezed: The output field is simply unsqueezed before spectral photon counting. I show that this method is quantum optimal and far superior to homodyne detection for both parameter estimation and detection, thus solving the open problems in the work of Tsang and Nair and Ng et al.

DOI: 10.1103/physreva.107.012611

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I derive classical and quantum lower error bounds for moment estimation in subdiffraction incoherent optical imaging. While the end results are similar to earlier ones [Tsang, Phys. Rev. Res. 1, 033006 (2019); Phys. Rev. A 99, 012305 (2019)], the present work avoids the flawed mathematical assumptions in the earlier works by adopting a parametric-submodel approach from semiparametric statistics. With the rigorous bounds at hand and redefining the parameter of interest, I show that an alternative measurement called spatial-mode demultiplexing (SPADE) is superior to ideal direct imaging for a subdiffraction object, even if SPADE can measure only a finite number of modes.

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