phase shift $\phi_0$ takes into account all uncompensated group velocity dispersion in the experimental setup. Equation (\[eq:signal\_single\]) is used to fit the experimental data in figure \[fig:time\_bin\_qudits\] for $t_1=0$ fs. Between $t_1\approx 25$ fs and $t_1\approx 50$ fs the contribution to the coincidence rate due to single photon interference decreases since $t_1$ begins to exceed the coherence time of the entangled photons. Consequently, the signal in figure \[fig:time\_bin\_qudits\] approaches the interference pattern of a maximally entangled qubit. The transformation from a non-entangled to a maximally entangled state can only be measured because sum frequency generation in a nonlinear crystal offers a coincidence window on the same time scale as $\tau_{i,s}^{coh}$. Note, that all measurements in figure \[fig:time\_bin\_qudits\] are performed for $t_1\ll\tau^{coh}_p\approx 88$ ns. To model the transition from a non-entangled qubit to a maximally entangled qubit we consider the state $$\label{eq:stat_g1_g2}
\fl\vert\psi\rangle^{(2)} = \frac{1}{\sqrt{1+2\gamma_1^2+\gamma_2^2}}\left(\vert 0 \rangle_i \vert 0\rangle_s+\gamma_1\e^{i\phi_0/2}\left[\vert 0 \rangle_i \vert 1\rangle_s+\vert 1 \rangle_i \vert 0\rangle_s\right]+\gamma_2\e^{i\phi_0}\vert 1 \rangle_i \vert 1\rangle_s\right)$$ with additional parameters $\gamma_1$ and $\gamma_2$ quantifying the contribution of the one-photon and two-photon interferences to the coincidence rate $$\begin{aligned}
\label{eq:gamma_1gamma_2}
S^{(2)}_{\gamma_1,\gamma_2}(\phi)&=&\left\vert\langle\chi\vert\psi\rangle^{(2)}\right\vert^2 \nonumber\\
&\propto &\left\vert 1+2\gamma_1\e^{i(\phi+\phi_0/2)}+\gamma_2 \e^{i(2\phi+\phi_0)}\right\vert^2.\end{aligned}$$ Equation (\[eq:gamma\_1gamma\_2\]) serves to fit the data points in figure \[fig:time\_bin\_qudits\] for $t_1>0$ 