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In the conventional picture of quantum feedback control, sensors perform measurements on the system, a classical controller processes the results of the measurements, and actuators supply semiclassical potentials to alter the behavior of the quantum system. In this picture, the sensors tend to destroy coherence in the process of making measurements, and although the controller can use the actuators to act coherently on the quantum system, it is processing and feeding back classical information. This paper proposes an alternative method for quantum feedback control, in which the sensors, controller, and actuators are quantum systems that interact coherently with the system to be controlled. In this picture, the controller gets, processes, and feeds back quantum information. Controllers that operate using such quantum feedback loops can perform tasks such as entanglement transfer that are not possible using classical feedback. Necessary and sufficient conditions are presented for Hamiltonian quantum systems to be controllable and observable using both classical and quantum feedback.
Control Theory, quantum or classical, addresses a fundamental problem: systems do not always behave the way one wants them to behave. Engines run too fast or too slowly; rooms are too hot or too cold; atoms can decay or nuclear spins dephase more rapidly than one desires. To Improve a System’s Behavior, control theory adjoins to the system a second system, called a ‘‘Controller,’’ which interacts with the original system in a way that improves its behavior.