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Comparisons between quantum open-loop control and closed-loop control

The paper first briefly introduces the current research on quantum control. Then the quantum open-loop control (no measurement introduced) and the closed-loop control (measurement introduced) was compared through a standard model of coherent control. When using quantum closed-loop control, we need measurement which inevitably brings in the reduction noise. This is different from the classical control systems. On the other hand, measurement-based feedback can reduce the influence of the system uncertainties. Thus, there is a tradeoff between the noise influence brought in by the measurement and the information got by the measurement. The paper demonstrate that in the case without decoherence, the quantum closed-loop control is superior to the open-loop control in dealing with the uncertainty in some sense. In the case with decoherence, we discuss the controllability of the quantum control through two performance indices.