Fig. 2
QNG tests for heralded 1–9 photons. a Example for n = 2. Red line represents the QNG criterion, while dashed gray line is its approximation (2). The blue point represents the measured state and the dotted blue line is the path of the point if the state becomes further attenuated. For the sake of visualizing all data, we denote D n , Dn+1 as the horizontal and vertical log-distances between a measured point and the QNG threshold. b The distances D n and Dn+1 for generated n-photon states were measured on a balanced (n + 1)-channel detector (numbered points for n = 1 − 9). Reaching the point of origin at zero means that QNG is no longer recognizable. Dotted paths represent attenuation with steps of 0.5 dB. Note that these steps are not the same size for all n. The number of steps on each path is proportional to QNG depth. For QNG depth values, see Fig. 3. Both vertical and horizontal error bars are shown for all data points; in some cases they are smaller than point size. For individual depiction of each multiphoton state with its respective QNG criterion, see Fig. 2 in the Supplementary Material
