Notions of controllability for quantum mechanical systems
Albertini, F.; Dapos;Alessandro, D.
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Volume 2, Issue , 2001 Page(s):1589 - 1594 vol.2
Digital Object Identifier   10.1109/.2001.981126
Summary:In this paper, we define three different notions of controllability for quantum mechanical systems involving the possibility of driving the evolution operator as well as the state of the system. By using general results on transitivity of transformation groups on spheres we establish the connections among these different notions of controllability. Motivated by the physical model of multilevel quantum systems, we also study the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove for the system of two interacting spin ½ particles the negative result that not every state transfer can be obtained in arbitrary time

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