Interference of Quantum Trajectories

Abstract: We extend quantum trajectory theory to encompass the evolution of a large class of open quantum systems interacting with an environment at {arbitrary coupling strength}. Specifically, we prove that general time-local quantum master equations admit an unraveling described by ordinary jump-stochastic differential equations. The sufficient condition is to weigh the state vector Monte Carlo averages by a probability pseudo-measure which we call the "influence martingale". The influence martingale satisfies a $ 1d $ stochastic differential equation enslaved to the ones governing the quantum trajectories. Our interpretation is that the influence martingale models interference effects between distinct realizations of quantum trajectories at strong system-environment coupling. Our result proves the existence of a Markovian quantum trajectory picture in the Hilbert space of the system for completely bounded divisible dynamical maps. Furthermore, our result provides a new avenue to numerically integrate systems with large numbers of degrees of freedom by naturally extending the existing theory.