Quantum trajectories generalized

Summary form only given. Quantum trajectories of state vectors can be used to describe open systems that otherwise can only be described using a density matrix. Besides the numerical advantage, quantum trajectories provide insight in the actual evolution of a system under continuous observation. Two distinct methods are usually considered, the quantum-jump method, associated with direct photodetection, and the quantum state diffusion (QSD) method, associated with homodyne or heterodyne mixing. We derive a general stochastic equation for quantum trajectories.