frequency bin $\vert u_k\vert\doteq\vert u^i_k\vert=\vert u^s_k\vert$ is then adjusted with the SLM such that all $S_k$ are equal to $S_{min}=\min\limits_{k=0,\ldots, d-1}\{S_k\}$ within the statistical uncertainties. To minimize the photon loss, the Procrustean filtering is accompanied with an optimization of the bin widths $\Delta \omega_j$ where bins at the far end of the spectrum are chosen to be wider than bins located at the center of the spectrum. The measurement time for each $S_k$ was 300 s with a SPCM background coincidence rate of about 11 Hz. Two-photon interference fringes were then measured by a projection onto the state (\[eq:chi\_phi\]) with the SLM using the transfer function (\[eq:mslm\]) corresponding to frequency bins and scanning the phase parameter $\phi$ in discrete steps while detecting coincidence counts. Note, that $j \phi$ is the resulting absolute phase associated with bin $j=0,\ldots, d-1$ on the idler side of the spectrum. Analogue, we have $k \phi$ for bin $k=0,\ldots, d-1$ in the spectral domain of the signal photon. Figure \[fig:freq\_bin\_qudits\] depicts the measured two-photon interference curves for qudits up to $d=4$.

![\[fig:freq\_bin\_qudits\] Frequency-bin basis: Two-photon interferences for a maximally entangled qubit (blue, top left), qutrit (green, top right) and ququart (red, bottom). Shown are background-subtracted coincidence 