Past exam of the laser science and quantum information processing course of the University of Oxford / 2018 / 3 / d / Solution

The conditional probability of the atomic ground state is the squared ground-state amplitude divided by the five-photon event probability:For $z\ne 0$, $|c_5{|}^2=|z{|}^2|c_4{|}^2/5$, giving the equivalent expressionIt applies only when the conditioning denominator is nonzero. The distinct $\sqrt{5}$ and $\sqrt{6}$ factors reflect the two different initial photon-number blocks.