[2] Other contemporaneous works on wave-function-based Monte Carlo approaches to open quantum systems include those of Dum, Zoller and Ritsch, and Hegerfeldt and Wilser.
[3] QTT is compatible with the standard formulation of quantum theory, as described by the Schrödinger equation, but it offers a more detailed view.
This approach is fundamentally statistical and is useful for predicting average measurements of large ensembles of quantum objects but it does not describe or provide insight into the behaviour of individual particles.
QTT fills this gap by offering a way to describe the trajectories of individual quantum particles that obey the probabilities computed from the Schrödinger equation.
[6] The mapping from inputs to outputs is provided by a quantum stochastic process that is set up to account for a particular measurement strategy (e.g., photon counting, homodyne/heterodyne detection, etc.).
The theory suggests that "quantum jumps" are not instantaneous but happen in a coherently driven system as a smooth transition through a series of superposition states.
In their experiment they used a superconducting artificial atom to observe a quantum jump in detail, confirming that the transition is a continuous process that unfolds over time.