 $$\begin{aligned}  \label{eq:noiseoperators:cov:calc}   \begin{pmatrix} \delta_{\mathcal{X}}^0(t) & \delta_{\mathcal{X}\mathcal{P}}(t) \\ \delta_{\mathcal{X}\mathcal{P}}(t) & \delta_{\mathcal{P}}^0(t) \end{pmatrix} = \