The indirect controllability of an arbitrary finite-dimensional quantum system (N-dimensional qudit) through a quantum accessor is investigated. Here, the qudit is coupled to a quantum accessor, which is modeled as a fully controllable spin chain with nearest-neighbor (anisotropic) XY coupling. The complete controllability of such an indirect control system is investigated in detail. The general approach is applied to the indirect controllability of two- and three-dimensional quantum systems. For two- and three-dimensional systems, a simpler indirect control scheme is also presented.
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