  We analyze the geometric phase for an open quantum system when computed by
resorting to a stochastic unravelling of the reduced density matrix (quantum
jump approach or stochastic Schrodienger equations). We show that the resulting
phase strongly depends on the type of unravelling used for the calculations: as
such, this phase is 'not' a geometric object since it depends on non-physical
parameters which are not related to the path followed by the density matrix
during the evolution of the system.
