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

TL;DR

This paper investigates how various quantum feedback operators influence the precision of detection efficiency estimation, revealing that optimal feedback can enhance precision and that initial states significantly impact information gain.

Contribution

It introduces a comparative analysis of different quantum feedback types on parameter estimation precision, highlighting the conditions for optimal feedback effectiveness.

Findings

Optimal feedback improves estimation precision.

Precision positively correlates with detection efficiency.

Certain initial states yield no information about the parameter.

Abstract

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 is the higher the precision is and we will not obtain any information about the parameter to be estimated if is chosen as initial state for the feedback type {\lambda}{\sigma}_z.