The quantum jump approach allows to characterize the stochastic dynamics associated with an open quantum system submitted to a continuous measurement action. In this paper we show that this formalism can consistently be extended to non-Markovian system dynamics. The results rely on studying a measurement process performed on a bipartite arrangement characterized by a Markovian Lindblad evolution. Both renewal and nonrenewal extensions are found. The general structure of nonlocal master equations that admit an unraveling in terms of the corresponding non-Markovian trajectories is also found. By studying a two-level system dynamics, it is demonstrated that non-Markovian effects such as an environment-to-system flow of information may be present in the ensemble dynamics.

• Received 29 May 2013

DOI:https://doi.org/10.1103/PhysRevA.88.012124