Quality analysis for precision metrology based on joint weak measurements without discarding readout data

Abstract

We present a theoretical analysis for the metrology quality of joint weak measurements (JWMs), in close comparison with the weak-value-amplification technique. We point out that the difference probability function employed in the JWM scheme cannot be used to calculate the uncertainty variance and Fisher information (FI). In order to carry out the metrological precision, we reformulate the problem in terms of difference-combined stochastic variables, which makes all calculations well defined. We reveal that, in general, the metrological precision of the JWM scheme cannot reach that indicated by the total FI, despite that all the readouts are collected without discarding. We also analyze the effect of technical noise, showing that the technical noise cannot be removed by the subtracting procedure, which yet can be utilized to outperform the conventional measurement, when considering the imaginary weak value measurement.