Protecting weak measurements against systematic errors

TL;DR

This paper analyzes how weak measurements in quantum metrology can be made more robust against systematic errors caused by decoherence, demonstrating that weak value amplification can significantly reduce these errors.

Contribution

It derives a first-order approximation for systematic errors in weak measurements and shows that postselected weak measurements with large weak values are more robust against decoherence.

Findings

Postselected weak measurements reduce systematic errors under decoherence.

Large weak values enhance robustness of parameter estimation.

Numerical simulations confirm analytical predictions.

Abstract

In this work, we consider the systematic error of quantum metrology by weak measurements under decoherence. We derive the systematic error of maximum likelihood estimation in general to the first-order approximation of a small deviation in the probability distribution, and study the robustness of standard weak measurement and postselected weak measurements against systematic errors. We show that, with a large weak value, the systematic error of a postselected weak measurement when the probe undergoes decoherence can be significantly lower than that of a standard weak measurement. This indicates the advantage of weak value amplification in improving the performance of parameter estimation. We illustrate the results by an exact numerical simulation of decoherence arising from a bosonic mode and compare it to the first-order analytical result we obtain.