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

TL;DR

This paper provides a theoretical analysis of joint weak measurements (JWM) for precision metrology, comparing it with weak-value amplification (WVA), and discusses the limitations and advantages of JWM in the presence of technical noise.

Contribution

It reformulates the metrological analysis of JWM using difference-combined stochastic variables and clarifies the conditions under which JWM can outperform traditional methods.

Findings

JWM cannot always reach the precision suggested by total Fisher information.

Technical noise cannot be eliminated by subtracting readouts in JWM.

JWM can outperform conventional measurement when considering imaginary weak values.

Abstract

We present a theoretical analysis for the metrology quality of joint weak measurements (JWM), in close comparison with the weak-value-amplification (WVA) 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 WV measurement.