Heisenberg scaling based on population coding

TL;DR

This paper investigates Heisenberg scaling in quantum metrology through population coding, proposing mutual information as a more suitable figure of merit than Fisher information, and demonstrating models that achieve this scaling.

Contribution

It introduces mutual information as a new figure of merit for Heisenberg scaling in quantum metrology within population coding, addressing limitations of Fisher information.

Findings

Mutual information effectively captures global structure in quantum metrology.

Several unitary models achieve Heisenberg scaling with mutual information.

Mutual information correlates with the number of distinguishable parameter elements.

Abstract

We study Heisenberg scaling of quantum metrology in the viewpoint of population coding. Although Fisher information has been used for a figure of merit to characterize Heisenberg scaling in quantum metrology, several studies pointed out it does not work as a figure of merit because it does not reflect the global structure. As an alternative figure of merit, we propose the mutual information, which connects the number of distinguishable elements of the parameter space in the viewpoint of population coding. We show that several unitary models achieve Heisenberg scaling in this context.