\rangle}_{out}}}\end{gathered}$$ where the subscript $in$ and $out$ stand for the presence and absence of the target object and ${\langle \Delta^2 S_{COV} \rangle}$ is the variance of $S_{COV}$. Note that ${\langle S_{COV} \rangle}_{out}$ is always zero. To show the performance advantage of the intensity correlation protocol, previous works [@Lopaeva:2013; @He:2018] considered a similar classical intensity correlation protocol that is based on a correlated thermal twin-beam source, which has been proven to be the optimal source for classical intensity correlation [@Lopaeva:2013]. The ratio of the performance (quantified as $SNR_{COV}$) of the intensity correlation protocol and the classical intensity correlation protocol is plotted in Fig. \[PowerSNR\], as a function of mean probe photon number per pulse for different background noise and loss condition. The detail of the experimental result could be found in [@He:2018]. As can be seen, the performance advantage of the intensity correlation protocol is limited to the low mean probe photon number per pulsed regime.\

![The performance advantages (quantified as the ratio of the $\text{SNR}_{COV}$) of the intensity correlation protocol as compared to the classical intensity correlation protocol. Blue (teal) line: with (without) the additional loss and noise in the target detection channel. The detail of the experimental result and 