Hidden Fisher Information in Many-Body Quantum Sensors
Abstract
Quantum Fisher information (QFI) determines the ultimate precision of a quantum sensor after optimization over all allowed measurements, but it does not quantify how difficult the optimal readout is to implement. We introduce a moment Fisher hierarchy FM(k), which measures the fraction of QFI accessible to collective spin moments up to degree k, together with a readout-complexity scale k90 defined by the minimum degree required to recover 90% of the QFI. Applying this framework to a nonlinear collective-spin sensor, we show that many-body dynamics can preserve large QFI while transferring the optimal readout into high-rank SU(2) tensor sectors inaccessible to low-order collective observables. For system sizes up to N=100, first moments access only ∼ 10−2 of the available QFI, while the degree required to recover 90% of it grows to k90≃ 28. A rank-resolved analysis of the symmetric logarithmic derivative (SLD) under weak damping shows that the nonlinear protocol pushes the optimal readout toward the highest available tensor ranks while strongly depleting its low-rank weight. These results identify nonlinear tangent-space shear as the mechanism behind a finite-size readout-complexity bottleneck in many-body quantum metrology.
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BibTeX
@misc{rahman2026hidden,
title = {{Hidden Fisher Information in Many-Body Quantum Sensors}},
author = {Atta ur Rahman and Muhammad Noman and Samira Elghaayda and Saeed Haddadi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33893},
eprint = {2610.33893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33893},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Hidden Fisher Information in Many-Body Quantum Sensors
AU - Atta ur Rahman
AU - Muhammad Noman
AU - Samira Elghaayda
AU - Saeed Haddadi
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33893
UR - https://arxiv.org/abs/2610.33893
AB - Quantum Fisher information (QFI) determines the ultimate precision of a quantum sensor after optimization over all allowed measurements, but it does not quantify how difficult the optimal readout is to implement. We introduce a moment Fisher hierarchy F_M^(k), which measures the fraction of QFI accessible to collective spin moments up to degree k, together with a readout-complexity scale k_90 defined by the minimum degree required to recover 90% of the QFI. Applying this framework to a nonlinear collective-spin sensor, we show that many-body dynamics can preserve large QFI while transferring the optimal readout into high-rank SU(2) tensor sectors inaccessible to low-order collective observables. For system sizes up to N=100, first moments access only ∼ 10^−2 of the available QFI, while the degree required to recover 90% of it grows to k_90≃ 28. A rank-resolved analysis of the symmetric logarithmic derivative (SLD) under weak damping shows that the nonlinear protocol pushes the optimal readout toward the highest available tensor ranks while strongly depleting its low-rank weight. These results identify nonlinear tangent-space shear as the mechanism behind a finite-size readout-complexity bottleneck in many-body quantum metrology.
ER -