Francesca Albertini, Domenico D'Alessandro
In coherent feedback control schemes a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled indirectly through the interaction with A. The system S is said to be indirectly controllable if every unitary transformation can be performed on the state of S with this scheme. In this paper we show how indirect controllability of S is equivalent to complete controllability of the combined system S+A, if the dimension of A is larger than 3. In the case where the dimension of A is equal to 2, it is possible to have indirect controllability without having complete controllability of S+A and we give sufficient conditions for this to happen. We conjecture that these conditions are also necessary. The results of the paper extend the result of arXiv:1210.4953 and expand the results of arXiv:1203.0887 to systems of arbitrary dimensions.
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http://arxiv.org/abs/1210.5449
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