ar X iv : q ua nt - p h / 98 07 08 2 v 1 2 9 Ju l 1 99 8 Heisenberg picture operators in the quantum state diffusion model

A stochastic simulation algorithm for the computation of multitime correlation functions which is based on the quantum state diffusion model of open systems is developed. The crucial point of the proposed scheme is a suitable extension of the quantum master equation to a doubled Hilbert space which is then unraveled by a stochastic differential equation. PACS numbers: 42.50.Lc,02.70.Lq Heisenberg picture operators in the quantum state diffusion model 2 Within the framework of the recently developed stochastic wave function approach to open quantum systems [1, 2, 3, 4, 5, 6, 7, 8] the state of a system is not described by a reduced density matrix but by a pure stochastic state vector ψt whose covariance matrix is equal to the reduced density matrix of the system. One of these models which was motivated by a dynamical description of the measurement process [9] is the quantum state diffusion model introduced by Gisin and Percival [5, 6]. In this approach, the time-evolution of the wave function ψt is governed by the Ito stochastic differential equation dψt = − iHψtdt+ 1 2 ∑ j [ 2〈L†j〉ψtLj − L † jLj − 〈Lj〉ψt〈L † j〉ψt ] ψtdt