Unraveling of the Lindblad equation of N coupled oscillators into N independent ones

We consider a system of N bi-linearly coupled damped harmonic quantum oscillators with time-evolution governed by a Lindblad equation. We show that the corresponding stochastic quantum state diffusion equation can be transformed into a set of N independent damped harmonic oscillators. This offers a great reduction in the basis size. We investigate the numerical performance of the method and find, in particular, scaling laws for the number of stochastic trajectories needed to find a certain accuracy.