  The violation of the Cauchy-Schwarz and Bell inequalities ranks among the
major evidences of the genuinely quantum nature of an emitter. We show that by
dispensing from the usual approximation of mode correlations and studying
directly correlations between the physical reality -the photons- these
violations can be optimized. This is achieved by extending the concept of
photon correlations to all frequencies in all the possible windows of
detections, with no prejudice to the supposed origin of the photons. We
identify the regions of quantum emission as rooted in collective de-excitation
involving virtual states instead of, as previously assumed, cascaded
transitions between real states.
