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The quantum jump approach, where pairs of state vectors follow StochasticSchroedinger Equation (SSE) in order to treat the exact quantum dynamics of twointeracting systems, is first described. In this work the non-uniqueness ofsuch stochastic Schroedinger equations is investigated to propose strategies tooptimize the stochastic paths and reduce statistical fluctuations. In theproposed method, called the 'adaptative noise method', a specific SSE isobtained for which the noise depends explicitly on both the initial state andon the properties of the interaction Hamiltonian. It is also shown that thismethod can be further improved by introduction of a mean-field dynamics. Thedifferent optimization procedures are illustrated quantitatively in the case ofinteracting spins. A significant reduction of the statistical fluctuations isobtained. Consequently a much smaller number of trajectories is needed toaccurately reproduce the exact dynamics as compared to the SSE withoutoptimization.Comment: 12 pages, 5 figures, revised versio

Optimizing stochastic trajectories in exact quantum-jump approaches of interacting systems