Decoherent Histories and Quantum State Diffusion

We demonstrate a close connection between the decoherent histories approach to quantum mechanics and the quantum state diffusion picture, for open quantum systems described by a master equation of Lindblad form. The (physically unique) set of variables that localize in the quantum state diffusion picture also define an approximately decoherent set of histories in the decoherent histories approach. The degree of localization is related to the degree of decoherence, and the probabilities for histories prescribed by each approach are essentially the same.