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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
Submission summary
| Authors (as registered SciPost users): | Olivier Giraud |
| Submission information | |
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| Preprint Link: | scipost_202304_00007v2 (pdf) |
| Date accepted: | Feb. 21, 2024 |
| Date submitted: | Jan. 3, 2024, 11:42 a.m. |
| Submitted by: | Olivier Giraud |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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
List of changes
Published as SciPost Phys. 16, 085 (2024)
Reports on this Submission
Report
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.