Improving the precision of weak measurements by postselection measurement

TL;DR

This paper investigates how postselection in weak measurements can enhance precision, revealing that nonclassical pointer states and optimal system states can significantly improve measurement accuracy and Fisher information.

Contribution

It clarifies the conditions under which postselected weak measurements outperform standard ones, highlighting the role of nonclassical states and estimation strategies in precision enhancement.

Findings

Squeezed coherent states improve signal-to-noise ratio in postselected measurements.

Quantum Fisher information is generally higher in postselected weak measurements.

Proper system state choice can close the Fisher information gap.

Abstract

Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.