Assembling Extensive Quantum Fisher Information in Stabilizer Systems

TL;DR

This paper presents a systematic method to construct nonlocal observables with extensive quantum Fisher information in stabilizer codes, revealing phase transitions in QFI scaling related to string order and measurement effects.

Contribution

It introduces a new framework linking stabilizer generators to dual Ising spins, enabling the detection of QFI transitions in monitored quantum codes.

Findings

Identifies QFI scaling transitions in monitored cluster and toric codes.

Connects string order parameters to nonlocal observables with high QFI.

Reveals measurement-driven phase transitions in quantum information properties.

Abstract

We introduce a systematic framework to construct nonlocal observables with extensive quantum Fisher information (QFI) density in stabilizer codes. The construction maps stabilizer generators to dual Ising spins whose correlators equal string order parameters, converting hidden nonlocal order into a metrologically accessible observable. Applying this to monitored cluster codes and the toric code, we identify transitions in the QFI scaling from an extensive regime, where long-range string order prevails, to an intensive one driven by competing single-site measurements.