Is measurement-based feedback still better for quantum control systems?

In this paper, we put forward a fundamental question concerning feedback control of quantum systems: Is measurement-based feedback control still better than open-loop control? In contrast to the classical control theory, the answer is far from obvious. This is because measurement-based feedback needs measurement to reduce the system uncertainty, whereas the measurement on a quantum system will inevitably increase the system uncertainty in turn. In fact, there is a complicated tradeoff between the uncertainty introduced and the information gained by the measurement on a quantum system. To investigate this fundamental problem, we will only focus on a typical model of coherent control mode with and without the decoherence term in the paper. By establishing some fundamental limits on the performances of both the open-loop and measurement-based feedback controls, we will demonstrate via simulation that the measurement-based feedback control of quantum systems is still superior to the open-loop control in some sense for the typical model under consideration.