the detector temporal resolution could limit the amount of intrinsic temporal correlation that could be utilized for target detection. The comparison between the normalized mutual information for different protocols is shown in Fig. \[MI\].

![Comparison between the normalized mutual information for target detection protocols enhanced by (blue) intensity correlation and (red,magenta and orange) temporal correlation. The pump pulse duration $\sigma_+$ for the temporal correlation protocol is set to 1 ns.[]{data-label="MI"}](fig2.pdf){width="0.6\columnwidth"}

FIGURE OF MERIT FOR TARGET DETECTION PROTOCOLS
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In correlation enhanced target detection protocols, multiple detectors (i.e. the probe and reference detector) are used to resolve the correlation between the probe and reference photon. Therefore the probability distribution of the different detection outcomes is multi-dimensional. However, it is generally hard to directly infer the presence or absence of the target object from the experimentally observed multidimensional distribution. Instead, a practical approach for target detection is to construct a *target detection signal*, defined in terms of the experimentally measured quantities, to quantify the probability of the presence of the target object. Based on different definitions of target detection signal, the target detection performance could also be quantified by different figures of merit. A general and suitable figure of merit for target 