Fig. 1. Diffraction limit understood in the perspective of modal transformation. Here, U is the Fourier transform and P stands for the projection that only allows low-spatial-frequency components at the Fourier plane to pass through, and U^† is the adjoint of U. The red and green grids represent the coordinate space and the frequency space in the transverse plane, respectively.

Fig. 2. Quantum statistical inference process.

Fig. 3. Results of the Bayesian filtering method. (a) The estimation results of image information under different number of measurements; (b) the evaluated CRB distribution corresponding to (a); (c) variation of both the reconstruction MSE and evaluated average CRB with the sampling number under different SNRs (adapted from Fig. 2 in Ref. [54]).

Fig. 4. (a) The FI of different parts of detection signals as a function of relative intensity β (with respect to the mean intensity of the detection signals); (b) comparison of experimental results reconstructed from 15,000 samplings using the proposed scheme (left) and vanilla correlation scheme (right) (adapted from Figs. 7 and 8 in Ref. [57]).