for the probe and reference light. The number of generated probe and reference photons in their respective wave packets are always equal. The detection section of the intensity correlation protocols consists of time-resolved photon-counting detectors for both the collected light and reference light. The temporal resolution of the detectors is required so that each probe light wave packet and its correlated reference light wave packet are resolved and “paired” correctly. In practical implementations, the nonlinear conversion efficiency is usually very low that the probability $\bar{n}$ of generating a probe (reference photon) in a wave packet is much less than unity. Under this approximation, the probability distribution $p_I(x,y)$ of generating $x$ probe and $y$ reference photons is given by: $$\begin{gathered}
p_I(0,0) = 1-\bar{n}\hspace{1cm}p_I(1,1) = \bar{n} \\
p_I(1,0) = p_I(0,1) = 0 \end{gathered}$$ The normalized mutual information $\text{MI}_\text{I}$ between the probe and reference photon number could be calculated according to : $$\begin{gathered}
\text{MI}_\text{I} = \frac{ -\bar{n}{\text{log}_2}(\bar{n}) - (1-\bar{n}){\text{log}_2}(1-\bar{n}) }{\bar{n}} \simeq -{\text{log}_2}\bar{n}\end{gathered}$$ As can be seen, the intensity correlation is very high with low mean probe photon number per pulse $\bar{n}$ but diminishes rapidly as $\bar{n}$ increases. Therefore for pulse pumped intensity correlation protocols, the correlation enhancement is limited to the low $\bar{n}$ 