Universality of finite time disentanglement

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