of SFG detection is typically on the order of a few femtoseconds, which itself corresponds to $\tau^{coh}_{i,s}$ for broadband SPDC emission. It is guaranteed for $\Delta t_{10}>\tau^{coh}_{i,s}$ that no $\vert 0 \rangle_i \vert 1\rangle_s$ and $\vert 1 \rangle_i \vert 0\rangle_s$ events contribute to the coincidence signal. Further, to prevent (\[eq:time\_bins\_freq\]) acting as a filter on the entangled photons spectrum, $\Delta t_j$ is restricted to $\Delta t_j\ll\tau^{coh}_{i,s}$. Given the constraints on $\Delta t_{10}$ and $\Delta t_j$ are satisfied, the event that both photons of a pair, down-converted at a given time, pass time bin $f_1^{i,s}(t)$ (long arm) cannot be distinguished from two photons created after a time delay $\Delta t_{10}$ and traveling through bin $f_0^{i,s}(t)$ (short arm). The state generated by two time bins then reads $$\label{eq:psidisc_qubit_entangled}
\vert\psi\rangle^{(2)} = c_{0}\vert 0 \rangle_i \vert 0\rangle_s+c_{1}\vert 1 \rangle_i \vert 1\rangle_s.$$ To demonstrate the equivalence between Fransons (FR) interferometric scheme and the implementation of time bins in the frequency space, we consider the transfer function for a single photon in a Mach-Zehnder interferometer $$\label{eq:M_franson}
M_{FR}^{i,s}(\omega)=T+R\,\e^{i\bar{\phi}_{i,s}(\omega)},$$ where both beam splitters have transmission and reflection coefficients $T$ and $R$. The total phase shift $\bar{\phi}_{i,s}(\omega)=\omega\Delta t_{10}+\phi_{i,s}$ is the sum of the phase difference $\omega\Delta t_{10}$ between the 