Fig. 2: The second-order coherence for various post-selected measurements in the far field.

The x-axis is how the g⁽²⁾ changes as a function of \(\nu =L{{\Delta }}X/\left(\lambda z\right)\) while keeping L, λ and z fixed. As the detectors move further apart, the spatial correlations created by the polarization grating decrease until they diminish entirely at ν ≈ 2.7. In addition, certain post-selected measurements allow us to quantify the coherence between two fields that possess sub-Poissonian-like statistics, suggesting the possibility of sub-shot-noise measurements. Note, these measurements can be also performed using quantum state tomography⁵⁷.