  The quantum jump approach, where pairs of state vectors follow Stochastic
Schroedinger Equation (SSE) in order to treat the exact quantum dynamics of two
interacting systems, is first described. In this work the non-uniqueness of
such stochastic Schroedinger equations is investigated to propose strategies to
optimize the stochastic paths and reduce statistical fluctuations. In the
proposed method, called the 'adaptative noise method', a specific SSE is
obtained for which the noise depends explicitly on both the initial state and
on the properties of the interaction Hamiltonian. It is also shown that this
method can be further improved by introduction of a mean-field dynamics. The
different optimization procedures are illustrated quantitatively in the case of
interacting spins. A significant reduction of the statistical fluctuations is
obtained. Consequently a much smaller number of trajectories is needed to
accurately reproduce the exact dynamics as compared to the SSE without
optimization.
