Genuine quantum trajectories for non-Markovian processes

A large class of non-Markovian quantum processes in open systems can be formulated through time-local master equations which are not in Lindblad form. It is shown that such processes can be embedded in a Markovian dynamics which involves a time-dependent Lindblad generator on an extended state space. If the state space of the open system is given by some Hilbert space H, the extended state space is the triple Hilbert space HxC(3) which is obtained by combining the open system with a three-state system. This embedding is used to derive an unraveling for non-Markovian time evolution by means of a stochastic process in the extended state space. The process is defined through a stochastic Schrodinger equation which generates genuine quantum trajectories for the state vector conditioned on a continuous monitoring of an environment. The construction leads to a continuous measurement interpretation for non-Markovian dynamics within the framework of the theory of quantum measurement.