Controllability properties for finite dimensional quantum Markovian master equations

Claudio Altafini

Journal of Mathematical Physics 44(6):2357-2372, 2003 (also preprint arXiv:quant-ph/0211194).

Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.

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