to as the CI (classical intensity) protocol in the rest of the paper. In the case of radars, it is possible to do better than this using match filtering. However, that is not easily possible in the optical regime. Hence, such a direct intensity detection scheme for LIDAR can be considered as the baseline for comparison.\

![image](fig1.pdf){width="0.8\columnwidth"}

The key aspect of correlation enhanced target detection protocols is the correlation between the probe and reference light. To date, the most widely adopted approach to generate correlated twin beams is spontaneous parametric down conversion (SPDC). The generated probe and reference light could be correlated in multiple degrees of freedom, based on which different types of target detection protocols could be designed. To give an intuitive and quantitative comparison between different protocols, it is instructive to quantify the strength of different types of correlation. Assuming the detection outcome of the two detectors obey the joint distribution $p(x,y)$, the correlation between the probe light and the reference light could be quantified as the *mutual information* (MI) [@bavaud2005introduction]: $$\begin{gathered}
\text{MI} = \sum\limits_{x\in \mathcal{X},y\in\mathcal{Y}} p(x,y)\text{log}_2(\frac{p(x,y)}{p(x)p(y)})\label{MIEQ}\end{gathered}$$ where $\mathcal{X},\mathcal{Y}$ are the spaces of detection outcome $x,y$ for the probe and reference detector. Since the target detection performance is 