about how all these ingredients are realized in the scheme depicted in Fig. 1. An input coherent laser beam ($N$ photons) shows circular polarisation, ${\bf e}_{\mathrm{in}}=1/\sqrt{2}\,\left(
\hat{x}-i\hat{y} \right)$, and a Gaussian shape with temporal width $T_0$ (Full-width-half maximum, $\tau \ll T_0$). The normalized temporal and spectral shapes of the pulse read $$\begin{aligned}
& & \Psi(t)=\left( \frac{4 \ln 2}{\pi T_0^2}\right)^{1/4} \exp
\left(
-\frac{2 \ln 2 t^2}{T_0^2} \right) \nonumber \\
& & \Psi(f)=\left(\frac{\pi T_0^2}{\ln 2}\right)^{1/4} \exp \left(
-\frac{\pi^2 T_0^2 f^2}{2 \ln 2} \right).\end{aligned}$$ The input beam is divided into the two arms of a Michelson interferometer with the help of a polarising beam splitter (PBS$_1$). Light beams with orthogonal polarisations traversing each arm of the interferometer are delayed $\tau_0$ and $\tau_0+\tau$, respectively, which constitute the weak coupling between the two degrees of freedom. After recombination of the two orthogonal signals in the same PBS$_1$, the combination of a liquid-crystal variable retarder (LCVR) and a second polarising beam splitter (PBS$_2$) performs the post-selection of the polarisation of the output state, projecting the incoming signal into the polarisation states $\hat{u}=1/\sqrt{2} \left[
\hat{x}+\hat{y}\exp(i\theta) \right]$ and $\hat{v}=1/\sqrt{2}
\left[ \hat{x}-\hat{y}\exp(i\theta) \right]$. The amplitudes of the signals in the two output ports write (not normalized) $$\begin{aligned}
 & &  