technology or novel photon detection techniques [@liu2019enhancing] as shown in Fig. \[FI\_RESULT\]. This is in contrast to the intensity correlation protocol where the correlation enhancement is solely determined by the mean probe photon number per pulse $\bar{n}$ and limited to the low $\bar{n}$ regime.\

![Error bars and solid curves: the experimentally measured and theoretical predicted variance of the transmission estimation with different environment loss (top) and noise (bottom) condition for both the QTC (orange) and the CI (black) protocol. Dashed curves: theoretically predicted estimation variance for the QTC protocol with different detector temporal resolution, which equals to half of the coincidence window $T_c$. Details about the experiment result could be found in [@liu2019enhancing] []{data-label="FI_RESULT"}](fig5_top.pdf "fig:"){width="0.4\columnwidth"}\[n\] ![Error bars and solid curves: the experimentally measured and theoretical predicted variance of the transmission estimation with different environment loss (top) and noise (bottom) condition for both the QTC (orange) and the CI (black) protocol. Dashed curves: theoretically predicted estimation variance for the QTC protocol with different detector temporal resolution, which equals to half of the coincidence window $T_c$. Details about the experiment result could be found in [@liu2019enhancing] []{data-label="FI_RESULT"}](fig5_bottom.pdf "fig:"){width="0.4\columnwidth"}\[p\]

![Top and middle:the experimentally measured and theoretically predicted ROC curves for the QTC and 