Parameter accuracy analysis of weak-value amplification process in the presence of noise* *Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0305200), the National Natural Science Foundation of China (Grant Nos. 11674234 and 11605205), the Natural Science Foundation of Chongqing (Grant Nos. cstc2015jcyjA00021 and cstc2018jcyjAX0656), the Innovation Project of Sichuan University (Grant No. 2018SCUH0021), the

Abstract

We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre- and post-selected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.