injection efficiency of the pump into the waveguide structure is around $\eta_\mathrm{p}^\mathrm{in}=0.5\pm0.1$. By calculating $$\label{eq:04}
P^\mathrm{th}_\mathrm{triplet}=\frac{\eta_\mathrm{i1}\eta_\mathrm{s2}\eta_\mathrm{i2}\cdot P_\mathrm{PDC,1} P_\mathrm{PDC,2}\mathbf{P}_\mathrm{p}\eta_\mathrm{p}^\mathrm{in}\lambda_\mathrm{p}}{h c_\mathrm{vac} R_\mathrm{rep}}$$ with the vacuum speed of light $c_\mathrm{vac}$, we get a theoretical success probability of $P^\mathrm{th}_\mathrm{triplet}=\left(6.35\pm1.5\right)\times10^{-11}$ per pulse. This is in excellent agreement with the experimentally derived benchmark. Note that the scalability of our source is inherent to Eq. (\[eq:04\]), because for identical pulse energies the ratio $\mathbf{P}_\mathrm{p}/R_\mathrm{rep}$ and $P^\mathrm{th}_\mathrm{triplet}$ do not change, whereas the absolute number of successfully detected photon triplets increases with higher repetition rates of the pump laser. The pulsed excitation in general and in conjunction with the emission wavelengths of the triplet states make our source fully compatible with existing synchronized telecom infrastructure.

In comparison to other approaches on tripartite-state generation [@Hamel2014; @Ding2015; @Khoshnegar2015], our integrated source offers around two to four orders of magnitude less photon-triplets per unit time. The main limiting factors on the detected photon triplets rates in our setup are given by the necessity of spectral filtering in the secondary PDC output and by the individual conversion efficiencies of the two PDC stages. Further improvements of our waveguide technology can reduce their impact on the success probability in the future. We expect an 