Pre- and post-selected measurements with coupling-strength-dependent modulation

TL;DR

This paper introduces a coupling-strength-dependent modulation scheme for pre- and post-selected measurements, enabling high sensitivity and precision across all coupling strengths, thus enhancing practical quantum metrology.

Contribution

It proposes a novel modulated PPS measurement method that maintains optimal sensitivity and precision regardless of coupling strength, supported by Fisher information analysis.

Findings

Achieves high measurement sensitivity for arbitrary coupling strength.

Derives optimal states and modulation strategies using Fisher information.

Demonstrates advantages over standard PPS measurement schemes.

Abstract

Pre- and post-selected (PPS) measurement, especially the weak PPS measurement, is a useful protocol for amplifying small physical parameters. However, it is difficult to retain both the attainable highest measurement sensitivity and precision with the increase of the parameter to be measured. Here, a modulated PPS measurement scheme based on coupling-strength-dependent modulation is presented with the highest sensitivity and precision retained for an arbitrary coupling strength. This idea is demonstrated by comparing the modulated PPS measurement scheme with standard PPS measurementv scheme, respectively, in the cases of balanced pointer and unbalanced pointer. By using the Fisher information metric, we derive the optimal pre- and post-selected states, as well as the optimal coupling-strength-dependent modulation without any restriction on the coupling strength. We also give the specific strategy of performing the modulated PPS measurement scheme, which may promote practical application of this scheme in precision metrology.