Fig. 2: Model example.

Imaging two pinholes (a), separated by the distance 2d, with the n-photon entangled state of light. The n-photon coincidence detection leads to constructive interference of the light passing through the pinholes (b). The interference is absent for (n − 1)-photon detection (c). For a particular value of the transverse momentum of one of the entangled photons, the conditional detection of the remaining n − 1 photons may exhibit destructive interference (d). Dot-dashed lines represent separate contributions from the pinholes; the dashed line shows the interference signal; the solid line represents the sum of all the contributions. For the simulations, we used the PSF \(h({{{\bf{s}}}},{{{\bf{r}}}})\propto \exp [-{({{{\bf{s}}}}-{{{\bf{r}}}})}^{2}/(5{d}^{2})]\) and n = 4. Note, that the peaks in panels c and d are n/(n − 1) = 4/3 times wider than in panels b, but the image contrast is better due to the absence of constructive interference. Panel e summarizes the results, showing the total signals from panels b, c, and d for their comparison: G⁽ⁿ⁾(x) (solid line), G⁽ⁿ⁻¹⁾(x) (dot-dashed line), and G^(n−1, 1)(x) (dashed line). Panel f shows the same signals for n = 2 and PSF \(h({{{\bf{s}}}},{{{\bf{r}}}})\propto \exp [-{({{{\bf{s}}}}-{{{\bf{r}}}})}^{2}/(2.5{d}^{2})]\) with its width ensuring the same image contrast for the nth order correlations (shown by the solid line) as in previous panels. As expected for n = 2, G⁽ⁿ⁻¹⁾(x) does not outperform G⁽ⁿ⁾(x) in terms of the image contrast.