TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.3.085
TI  - Quantum parameter estimation with many-body fermionic systems and application to the Hall effect
PY  - 2024/03/25
UR  - https://scipost.org/SciPostPhys.16.3.085
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 3
SP  - 085
A1  - Giraud, Olivier
AU  - Goerbig, Mark-Oliver
AU  - Braun, Daniel
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.3.085,
	title={{Quantum parameter estimation with many-body fermionic systems and application to the Hall effect}},
	author={Olivier Giraud and Mark-Oliver  Goerbig and Daniel Braun},
	journal={SciPost Phys.},
	volume={16},
	pages={085},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.3.085},
	url={https://scipost.org/10.21468/SciPostPhys.16.3.085},
}