by fiber-based coarse wavelength division multiplexers at $\left(1551\pm7\right)\,\mathrm{nm}$ and $\left(1611\pm7\right)\,\mathrm{nm}$, respectively. The three resulting fiber-coupled beams address free-running binary detectors. The data acquisition and evaluation is done by a time-tagging module and appropriate software. Legend: CWDM - coarse wavelength division multiplexer, FC - fiber coupling stage, FR-APD - free-running avalanche photodiode, HWP - half-wave plate, LPF - long-pass filter, SiF - silicon filter, SMF - single-mode fiber, SNSPD - superconducting nanowire single photon detector, TTM - time-tagging module, VAtt - variable attenuator.[]{data-label="triplet-setup"}](fig02.eps){width="0.95\linewidth"}

For testing our device, we implement the setup shown in Fig. \[triplet-setup\]. Thermal stabilization of our integrated chip at temperatures of $\theta=164.8^\circ\mathrm{C}$ ensures that the intermediate signal 1 wavelength is $\lambda_\mathrm{s1}=\lambda_\mathrm{p2}=790.3\,\mathrm{nm}$, which is required for non-degenerate secondary PDC generation (see Appendix A for detailed explanation). This setting allows for optimum mutual compatibility of the two PDC processes, and it improves the spatio-spectral separability of secondary photon pairs by using fiber-based coarse wavelength division multiplexers (CWDM). These standard components also serve as high-performance filters for noise events as well as for parasitic photons from the primary PDC stage. Otherwise, those photons could affect the detection of secondary PDC photons, because the first PDC process happens around ten million times 