S parameter versus n (bottom x axis) or the corresponding pump power in the PhC WG (top x axis). n and pump powers are calibrated by fitting the full set of transmission intensity data (Supplementary Note 3 ). The solid curve is the theoretical model (Supplementary Note 8e ) with parameters taken from the filtered power saturation g (2) measurements in Supplementary Note 4 , that is, no additional fitting was performed. The dashed black line represents the locality bound. The data in a and b are recorded for the lowest n (0.0024) or pump power (7.2 pW) in c . As we have performed single-shot measurements, the error bars shown are standard deviations obtained from Monte Carlo simulations with 1,000 samples, assuming a Poisson distribution with a mean given by the measured value (shown as markers).
