a visibility [@thew2004] according to $$\label{eq:cglmp_lamb}
V_d=\frac{d\lambda_d}{2+\lambda_d (d-2)}.$$ Entanglement between idler and signal photon is then present if $$\label{eq:cglmp_vis}
V_d>V_d(\lambda_d^c)\doteq V_d^c.$$ The values for the critical visibility $V_d^c$ are listed in table \[tab:freq\_bin\]. To relate CGLMP’s inequality to the visibility of interference fringes has the advantage that a possible phase shift $\phi_0$ present in the experiments has no influence on the violation of a Bell inequality. This would be the case if single projection measurements at fixed phase settings were used to determine the value of a Bell parameter.

Frequency-bin basis
-------------------

With the goal to maximize the entanglement in $$\vert\psi\rangle^{(d)} = \sum_{j=0}^{d-1} c_{j}\vert j \rangle_i \vert j\rangle_s$$ we make use of the Procrustean method of entanglement concentration [@bennett1996]. In general, this method equalizes the amplitudes in a partially entangled state through local operations where contributions with higher probabilities are diminished by appropriate filtering. One is then left with a maximally entangled state according to (\[eq:qudit\_maxent\_phase\]) with all amplitudes being equal. For a bin structure according to (\[eq:freq\_bins\]) we experimentally equate the $\vert c_j\vert$ by performing single projection measurements onto $\vert\chi_k\rangle=\vert u_k\vert^2\vert  k\rangle_i\vert k\rangle_s$ for $k=0,\ldots, d-1$ with corresponding coincidence signals $S_k=\left\vert\vert u_k\vert^2 \vert c_k\vert\right\vert^2$. The amplitude of the $k$-th 