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Recently, a new approach for the controllability of a two-dimensional quantum system has been proposed, based on its interaction with an initially uncorrelated two-dimensional probe whose initial state can be arbitrarily modified. Following this scheme and considering a particular model for the environment, we show that, in some specific cases, the environment-induced entanglement is rich enough to completely control the dynamics of . Under suitable conditions on the interaction of , , and the environment, we prove that the state of can be driven to an arbitrary target state by varying the initial state of .