  In this paper we investigate how common is the phenomenon of Finite Time
Disentanglement (FTD) with respect to the set of quantum dynamics of bipartite
quantum states with finite dimensional Hilbert spaces. Considering a quantum
dynamics from a general sense, as just a continuous family of Completely
Positive Trace Preserving maps (parametrized by the time variable) acting on
the space of the bipartite systems, we conjecture that FTD happens for all
dynamics but those when all maps of the family are induced by local unitary
operations. We prove this conjecture valid for two important cases: i) when all
maps are induced by unitaries; ii) for pairs of qubits, when all maps are
unital. Moreover, we prove some general results about unitaries/CPTP maps
preserving product/pure states
