The effects of different quantum feedback operator types on the parameter precision of detection efficiency in optimal quantum estimation

•The effects of different quantum feedback types on the estimation precision of the detection efficiency are studied.•The precision can be more effective enhanced by a certain feedback type.•The precision has a positive relation with detection efficiency for a dynamic balance state.

The effects of different quantum feedback types on the estimation precision of the detection efficiency are studied. It is found that the precision can be more effective enhanced by a certain feedback type through comparing these feedbacks and the precision has a positive relation with detection efficiency for the optimal feedback when the system reach the state of dynamic balance. In addition, the bigger the proportion of |1〉 is the higher the precision is and we will not obtain any information about the parameter to be estimated if |0〉 is chosen as initial state for the feedback type λσz.