output arms.

We quantify the impact of accidentals by comparing the number of three-fold coincidences in the center spot of the graph in Fig. \[16-bin\], where we suspect our photon-triplets to reside, with the average number of accidental three-folds in the $41$ bins, where neighboring pulses are involved. By division of the two results we infer a coincidences-to-accidentals-ratio of $CAR=9.4\pm1.9$. This means that the influence of higher-order photon contributions and other accidentals from the primary PDC stage is not negligible, but very low.

Additionally, we perform a statistical analysis of the $210000$, $1.317\mathrm{ns}$-wide, time-bins in order to answer the question: how many three-fold coincidences occur how often. Our intention for this analysis method is to identify noise-related contributions, genuine photon triplets, and also accidental three-fold coincidences. Besides our expectation, that the photon triplets overcome the noise background significantly, the distribution of the accidentals should also deviate from the noise statistics, because those pseudo-time-correlated accidental events are generated by the same pulsed pump that generates the photon triplets.

![Histogram of the absolute frequencies of three-fold coincidences per $1.317\,\mathrm{ns}$-wide time bin: the logarithmic plot exhibits a Poisson-like distribution, underlined by the fit curve. Only one time bin contains $N_\mathrm{triplet}=33\pm5.7$ three-fold coincidences. Compared 