Weak-value amplification as an optimal metrological protocol

TL;DR

This paper demonstrates that optimal post-selection in weak-value amplification maximizes information extraction about a quantum system's coupling, achieving quantum Fisher information saturation and unifying signal amplification with quantum estimation theory.

Contribution

It derives an optimal post-selection strategy that saturates quantum Fisher information, unifying weak-value amplification with quantum metrology principles.

Findings

Optimal post-selection maximizes information extraction.

Weak-value amplification saturates quantum Fisher information.

Most pre-selected states allow full information from meter data alone.

Abstract

The implementation of weak-value amplification requires the pre- and post-selection of states of a quantum system, followed by the observation of the response of the meter, which interacts weakly with the system. Data acquisition from the meter is conditioned to successful post-selection events. Here we derive an optimal post-selection procedure for estimating the coupling constant between system and meter, and show that it leads both to weak-value amplification and to the saturation of the quantum Fisher information, under conditions fulfilled by all previously reported experiments on the amplification of weak signals. For most of the pre-selected states, full information on the coupling constant can be extracted from the meter data set alone, while for a small fraction of the space of pre-selected states, it must be obtained from the post-selection statistics.