Emergence of Jumps in Quantum Trajectories via Homogenization

In the strong noise regime, we study the homogenization of quantum trajectories i.e. stochastic processes appearing in the context of quantum measurement. When the generator of the average semigroup can be separated into three distinct time scales, we start by describing a homogenized limiting semigroup. This result is of independent interest and is formulated outside of the scope of quantum trajectories. Going back to the quantum context, we show that, in the Meyer–Zheng topology, the time-continuous quantum trajectories converge weakly to the discontinuous trajectories of a pure jump Markov process. Notably, this convergence cannot hold in the usual Skorokhod topology.