regime [@england2019quantum].

Temporal Correlation
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For the intensity correlation protocol that is based on pulse pumped SPDC process, the correlation enhancement is limited to the low mean photon number per pulse ($\bar{n}$) regime. A way to increase the target detection performance without sacrificing the correlation enhancement is to increase the repetition rate of the probe pulses but keep the mean probe photon number per pulse $\bar{n}$ fixed. In the limit where the repetition period equals the pulse duration of the pump light, the pump light becomes CW. This generalized protocol with CW pump light will be termed the quantum temporal correlation (QTC) protocol since the probe and reference photon are generated in pairs ‘almost simultaneously’ [@liu2019enhancing]. The correlation time $\Delta t$, which is defined as the standard deviation of the time difference between the generation of probe and reference photon, quantifies the intrinsic temporal correlation. To utilize such temporal correlation, the detectors must be able to resolve the detection time of each incoming photon. It is worth noting that the detection of the probe and reference photons does not have to be simultaneous since their optical path lengths are not equal in general. The temporal correlation analysis is done in 