Photon-starved polarimetry via functional classical shadows

Polarimetry and optical imaging techniques face challenges in photon-starved scenarios, where the low number of detected photons imposes a trade-off between image resolution, integration time, and sample sensitivity. Here we introduce a quantum-inspired method, functional classical shadows, for reconstructing a polarization profile in the low photon-flux regime. Our method harnesses correlations between neighbouring datapoints, based on the recent realisation that machine learning can estimate multiple physical quantities from a small number of non-identical samples. This is applied to the experimental reconstruction of polarization as a function of the wavelength. Although the quantum formalism helps structuring the problem, our approach suits arbitrary intensity regimes.