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Quantum parameter estimation with many-body fermionic systems and application to the Hall effect

by Olivier Giraud, Mark-Oliver Goerbig, Daniel Braun

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Submission summary

Authors (as registered SciPost users): Olivier Giraud
Submission information
Preprint Link: scipost_202304_00007v2  (pdf)
Date accepted: 2024-02-21
Date submitted: 2024-01-03 11:42
Submitted by: Giraud, Olivier
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We calculate the quantum Fisher information for a generic many-body fermionic system in a pure state depending on a parameter. We discuss the situations where the parameter is imprinted in the basis states, in the state coefficients, or both. In the case where the parameter dependence of coefficients results from a Hamiltonian evolution, we derive a particularly simple expression for the quantum Fisher information. We apply our findings to the quantum Hall effect, and evaluate the quantum Fisher information associated with the optimal measurement of the magnetic field for a system in the ground state of the effective Hamiltonian. The occupation of electron states with high momentum enforced by the Pauli principle leads to a super-Heisenberg scaling of the sensitivity with a power law that depends on the geometry of the sensor.

Author comments upon resubmission

We thank both Referees for their careful assessment of our work. We modified the manuscript to take into account all of the Referee's observations. This has given us the opportunity to be more precise on various aspects our our work and to enrich the paper with results closer to experimental preoccupations.

List of changes

Changes are highlighted in red in the new version of the manuscript

Published as SciPost Phys. 16, 085 (2024)

Reports on this Submission

Anonymous Report 2 on 2024-2-17 (Invited Report)


The author's response to the referee's comments, quite unusually, is contained in highlighted parts of the modified text. Those modifications, however, satisfactorily address all my previous comments.

The article gives a detailed and comprehensive analysis of the theoretical bounds on the accuracy of 2DEG as a magnetic field sensor. In my view, this fulfills the acceptance criteria for SciPost Physics, and with the last round of modifications the paper is ready for publication.

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Anonymous Report 1 on 2024-2-6 (Invited Report)


In the red-marked resubmitted manuscript I have seen most of my previously asked questions answered. However, I would have appreciated if the authors would have written a proper response since this would have facilitated my second review. Nevertheless, I now support publication of this manuscript in SciPost Physics.

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