paper

Quantum noise spectroscopy as an incoherent imaging problem

arXiv:2209.06104 · doi:10.1103/PhysRevA.107.012611

Abstract

I point out the mathematical correspondence between an incoherent imaging model proposed by my group in the study of quantum-inspired superresolution [Tsang, Nair, and Lu, Physical Review X 6, 031033 (2016)] and a noise spectroscopy model also proposed by us [Tsang and Nair, Physical Review A 86, 042115 (2012); Ng et al., Physical Review 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 in Ng et al. (2016) 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 -- simply unsqueeze the output field 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 Tsang and Nair (2012) and Ng et al. (2016).

arXiv comment10 pages, 4 figures. v3: extended; accepted version

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