Small correlation is sufficient for optimal noisy quantum metrology

TL;DR

This paper introduces a class of quantum states with optimal Fisher information scaling for noisy quantum metrology, emphasizing small but sufficient correlations and practical measurement protocols.

Contribution

It presents a new class of resource states with optimal scaling, along with efficient measurement protocols and insights into the role of spin squeezed states in noisy environments.

Findings

Resource states with large intra-group and small inter-group correlations achieve optimal Fisher information.

Time-reversal based measurement protocol is optimal and efficient.

Spin squeezed states are also optimal under general noisy conditions.

Abstract

We propose a class of metrological resource states whose quantum Fisher information scales optimally in both system size and noise rate. In these states, qubits are partitioned into sensing groups with relatively large correlations within a group but small correlations between groups. The states are obtainable from local Hamiltonian evolution, and we design a metrologically optimal and efficient measurement protocol utilizing time-reversed dynamics and single-qubit on-site measurements. Using quantum domino dynamics, we also present a protocol free of the time-reversal step that has an estimation error roughly twice the best possible value. Finally, we show that spin squeezed states are also optimal for noisy metrology under general conditions.