the entangled photons is always larger than $\Delta t_j$ and is thus the limiting factor for the minimal $t_{1}$. Figure \[fig:time\_bin\_qudits\] depicts qubit interference traces for various positions $t_1$ of time bin $f_1^{i,s}(t)$. Again, the phase $\phi_i=\phi_s=\phi$ is varied by the SLM.

![\[fig:time\_bin\_qudits\] Time-bin basis: Normalized two-photon interferences for a qubit encoded in time bins. The width of the bins is chosen to be $\Delta t_0=\Delta t_1=0$ fs and $t_0$ is fixed to $t_0=0$ fs. Shown are background-subtracted and normalized coincidence counts (normalized net counts). For $t_1=0$ fs the experimental data are fitted with (\[eq:signal\_single\]) (solid line). Since the visibility of the measured signal is equal to one no additional fitting parameter is needed. All measurements for $t_1>0$ fs are fitted with (\[eq:gamma\_1gamma\_2\]) (solid lines) which involves the fitting parameters $\gamma_1$ and $\gamma_2$ depicted in the inset of figure \[fig:I2\].](time_bins_qudits_dtscan.eps){width="80.00000%"}

If both bins completely overlap, i.e. $t_1=0$ fs, the coincidence signal obviously consists of a product of two single photon interference rates $$\begin{aligned}
\label{eq:signal_single}
S^{(2)}(\phi)&=&\left\vert\langle\chi\vert\psi\rangle^{(2)}\right\vert^2 \nonumber\\
&\propto & \left\vert 1+\e^{i(\phi+\phi_0/2)}\right\vert^2 \left\vert 1+\e^{i(\phi+\phi_0/2)}\right\vert^2\nonumber\\
&\propto & \cos^4\left(\frac{\phi+\phi_0/2}{2}\right)\end{aligned}$$ with $$\label{eq:stat_sep_state}
\vert\psi\rangle^{(2)} = \frac{1}{2}\left(\vert 0 \rangle_i +\e^{i\phi_0/2}\vert 1 \rangle_i \right)\left(\vert 0 \rangle_s +\e^{i\phi_0/2}\vert 1 \rangle_s \right)$$ and $\vert\chi\rangle$ of (\[eq:chi\_phi\]). As in (\[eq:qudit\_maxent\_phase\]), the 