  In this article, we show that the exact two-body problem can be replaced by
quantum jumps between densities written as $D=| \Psi_a \right> \left< \Psi_b |$
where $| \Psi_a \right>$ and $| \Psi_b \right>$ are vacuum for different
quasi-particles operators. It is shown that the stochastic process can be
written as a Stochastic Time-Dependent Hartree-Fock Bogoliubov theory
(Stochastic TDHFB) for the generalized density ${\cal R}$ associated to $D$
where ${\cal R}^2 = {\cal R}$ along each stochastic trajectory.
