is, for the actual power of 1 $\mu$W we find a spectral mode density of $n=P/P_{max}=0.2$ which assures that we are below the single photon limit and therefore no coincidences are measured between photons of different pairs.

Experimental results
====================

CGLMP inequality {#sec:cglmp}
----------------

We assume the qudits in our experiment to be described by a symmetric noise model $$\label{eq:snmodel}
\hat{\rho}^{(d)}=\lambda_d\vert\psi\rangle^{(d)}\,^{(d)}\langle\psi\vert+\frac{(1-\lambda_d)}{d^2}\mathbbm{1}_{d^2},$$ where deviations from a pure state are quantified by the mixing parameter $\lambda_d$ and $\mathbbm{1}_{d^2}$ denotes the $d^2$-dimensional identity operator. Here, $\vert\psi\rangle^{(d)}$ is a maximally entangled state $$\label{eq:qudit_maxent_phase}
\vert\psi\rangle^{(d)}=\frac{1}{\sqrt{d}}\sum_{l=0}^{d-1}\,\e^{i l \phi_0}\vert l \rangle_i \vert l\rangle_s,$$ where $\phi_0$ accounts for small phase shifts due to non-perfectly compensated dispersion in the setup. In order to show entanglement without performing full quantum state tomography we make use of Bell test measurements. Collins *et al.* (hereafter referred to as CGLMP) introduced a dimensional dependent Bell parameter $I_d$ to study the non-classical correlations of $d$-dimensional bipartite quantum states in the context of a new family of Bell inequalities [@collins2002]. The parameter $I_d$ is related to its corresponding Bell operator $\hat{B}$ [@braunstein1992] according to $I_d=\Tr\left(\hat{B}\hat{\rho}^{(d)}\right)$ where it was shown in [@terhal2000] that $\hat{B}$ itself can be used as an entanglement witness. Consequently, the violation of 