Photon addition ($|{\psi }_{+}⟩=a^{†}|\psi ⟩/\sqrt{⟨N⟩+1}$)

Ideal conditional application of a creation operator, followed by normalization. It reweights the input number distribution as well as raising each occupied number by one. A heralded physical implementation has a success probability; the algebraic creation operator alone is not a trace-preserving deterministic quantum operation.