The Collapse Before a Quantum Jump Transition

We may infer a transition $|n rangle to |m rangle$ between energy eigenstates of an open quantum system by observing the emission of a photon of Bohr frequency $omega_{mn} = (E_n-E_m) / hbar$. In addition to the collapses to the state $|mrangle$, the measurement must also have brought into existence the pre-measurement state $|n rangle$. As quantum trajectories are based on past observations, the condition state will jump to $| m rangle$, but the state $|nrangle$ does not feature in any essential way. We resolve this paradox by looking at quantum smoothing and derive the time-symmetric model for quantum jumps.