Geometric phase for open quantum systems and stochastic unravellings

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