probability $P_{fa}$ [^4] by comparing $\hat{\eta}_{p,MLE}$ to a threshold value $V$. By varying the threshold $V$, the relationship between the detection rate $P_\text{d}$ and the false alarm rate $P_\text{fa}$ (widely known as the ROC curve) could be derived. By assuming that the estimation uncertainty $\mathbf{n}(\eta_p)$ is a Gaussian random variable with variance given by the inverse of the Fisher information (FI), the theoretical prediction of the ROC curve could be obtained [@trans].

The Performance Of The Temporal Correlation Enhanced Target Detection Protocol
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Transmission estimation and Fisher information criterion are useful for characterizing the QTC protocol performance. For the QTC protocol, the detection section consists of time-resolved single-photon detectors (the probe and reference detector). Since the target detection channel could be considered as stationary, i.e. target not moving, the absolute time of each photon detection event is not informative. Therefore only time information that relates the time difference of different target detection events could be of interest. Such statistics must be the number of coincidence detections $N_c$, which is defined as detecting two photons on both the probe and reference detector, with the detection time difference less than a small coincidence window $T_c$. Two other photon detection statistics of interest 