Conditional photon-number bias
= Conditional photon-number bias
{title2=$\bar n_-=\mu-1+\operatorname{Var}N/\mu$}
A subtraction event weights initial occupation $n$ by $n$ before removing one <photon>. Thus its conditional output mean is $\langle N(N-1)\rangle/\mu$, giving the displayed identity for $\mu>0$. If the initial <variance> exceeds its mean, this biased selection can offset the removed <photon>. The unconditional ensemble includes unsuccessful events and has a different <energy> balance.