increase of detected photon-triplet rates of at least one order of magnitude solely by accessing the full spectral bandwidth of the secondary PDC outcome. The resulting, spectrally multimode, secondary photon pairs can be deployed for example for absolute calibration of broad-band-sensitive single photon detectors in the telecommunication bands. Besides, the strong temporal correlations of our spectrally multi-mode secondary PDC photons offer energy-time-entanglement. This could be combined in future work with time-bin-entanglement schemes and would allow for the heralded generation of hyper-entangled Bell-states.

The implementation of reverse proton-exchanged waveguide structures [@Parameswaran2002] could also increase the PDC conversion efficiencies, each by at least one additional order of magnitude. Finally, higher repetition rates of the pump laser, e. g. by temporal multiplexing [@Broome2011] will lead to increasing numbers of detectable photon triplets and indicate the scalability of our integrated device. Note that state-of-the-art detector recovery times of around $75\,\mathrm{ns}$ for highly efficient MoSi-based SNSPDs [@Verma2015], in conjunction with detection efficiencies of $\eta_\mathrm{det}\sim87\%$, are still the limiting factor to date rather than available repetition rates for the pump laser. By contrast, increasing the pump pulse energy will not improve the output of photon triplets at high CAR-values, because of the growing impact of higher-order 