\begin{equation}
\label{Eq: Unitary-U}
\begin{aligned}
\mathcal{U} & = \begin{bmatrix}
1 & 0 & 0 & 0\\
0 & \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}} & 0\\
0 & \frac{1}{\sqrt{2}} & - \frac{1}{\sqrt{2}} & 0\\
0 & 0 & 0 & 1
\end{bmatrix} .
\end{aligned}
\end{equation}