Abstract: The quantum precision measurement technology based on the theory of quantum parameter estimation has attracted extensive attention due to its detection advantages beyond the standard quantum limit. In many application scenarios, it often involves the simultaneous and precise detection of multiple parameters. However, since the generators of multiple parameters to be estimated are generally noncommutative, this leads to a trade-off in the estimation precision among different parameters, making it challenging to achieve simultaneous optimal estimation for all parameters. In recent years, instead of preparing large-scale entangled states, squeezed states or designing complex quantum measurement schemes, researchers have started from the perspective of optimizing the evolution of quantum dynamics by introducing quantum control to each component of quantum dynamics systems to adjust the evolution of quantum states. This kind of method can achieve simultaneous optimal estimation of multiple parameters, so the trade-off between multiple estimation precisions can be overcome, and a better quantum Cramér-Rao bound can be reached. In this paper, we summarize the quantum multiparameter estimation methods based on feedback control, expound on the improvement effect of feedback control on the simultaneous optimal estimation of multiple parameters from multiple perspectives, and demonstrate the potential of this technology in practical applications. Finally, the future research trends of quantum multiparameter estimation are summarized and prospected.

Key words: quantum information, quantum precision measurement, multiparameter estimation theory, quantum control, quantum Cramér-Rao bound