A quantum dot can be used as a source of one- and two-photon states and of polarization entangled photon pairs. The emission of such states is investigated here from the point of view of frequency-resolved two-photon correlations. These follow from a spectral filtering of the dot emission, which can be achieved either by using a cavity or by placing a number of interference filters before the detectors. A combination of these various options is used to iteratively refine the emission in a 'distillation' process and arrive at highly correlated states with a high purity. The so-called 'leapfrog processes', where the system undergoes a direct transition from the biexciton state to the ground state by direct emission of two photons, are shown to be central to the quantum features of such sources. Optimum configurations are singled out in a global theoretical picture that unifies the various regimes of operation.