Reaching the Limits of Ground-State Metrology with Many-Body Probes
Abstract
We investigate the physical requirements to reach the ultimate limits of ground-state metrology -- i.e., the estimation of an unknown parameter θ of an N-body Hamiltonian via measurements on its ground state -- using many-body probes featuring either short-range or long-range interactions. We characterize the conditions to saturate two fundamental limits of the quantum Fisher information Fθ: the static ground-state bound Fθ≲ N2/Δ2, where Δ is the spectral gap, and the dynamical Heisenberg limit Fθ≲ N2 τ2, where τ is the total protocol duration. To saturate the static limit, we argue that short-range interacting systems require a spectral gap that closes with N. At second-order quantum critical points this leads to a universal condition on the critical exponents, ν(d+z)=1, which can be approached arbitrarily closely, as we show for the XXZ chain; cat-like ground states at first-order transitions provide an alternative route to static optimality. In contrast, we find that all-to-all interacting models can achieve optimality even in gapped regimes. Furthermore, reaching the dynamical bound is tightly related to the ground-state preparation time; we demonstrate that its optimal, inverse-gap profile can be obtained via local adiabatic protocols. By analyzing paradigmatic systems -- the transverse-field Ising chain, the XXZ chain, a squeezing Hamiltonian, and the two-mode Bose-Hubbard model -- we identify specific many-body probes capable of approaching both limits. Overall, our results provide a theoretical basis for the design of (local) many-body ground-state sensors operating at the ultimate limits of quantum precision.
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BibTeX
@misc{andre2026reaching,
title = {{Reaching the Limits of Ground-State Metrology with Many-Body Probes}},
author = {Erik L. André and Víctor Izquierdo and Ricard Puig and John Calsamiglia and Martí Perarnau-Llobet},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03653},
eprint = {2610.03653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03653},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reaching the Limits of Ground-State Metrology with Many-Body Probes
AU - Erik L. André
AU - Víctor Izquierdo
AU - Ricard Puig
AU - John Calsamiglia
AU - Martí Perarnau-Llobet
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03653
UR - https://arxiv.org/abs/2610.03653
AB - We investigate the physical requirements to reach the ultimate limits of ground-state metrology -- i.e., the estimation of an unknown parameter θ of an N-body Hamiltonian via measurements on its ground state -- using many-body probes featuring either short-range or long-range interactions. We characterize the conditions to saturate two fundamental limits of the quantum Fisher information F_θ: the static ground-state bound F_θ≲ N^2/Δ^2, where Δ is the spectral gap, and the dynamical Heisenberg limit F_θ≲ N^2 τ^2, where τ is the total protocol duration. To saturate the static limit, we argue that short-range interacting systems require a spectral gap that closes with N. At second-order quantum critical points this leads to a universal condition on the critical exponents, ν(d+z)=1, which can be approached arbitrarily closely, as we show for the XXZ chain; cat-like ground states at first-order transitions provide an alternative route to static optimality. In contrast, we find that all-to-all interacting models can achieve optimality even in gapped regimes. Furthermore, reaching the dynamical bound is tightly related to the ground-state preparation time; we demonstrate that its optimal, inverse-gap profile can be obtained via local adiabatic protocols. By analyzing paradigmatic systems -- the transverse-field Ising chain, the XXZ chain, a squeezing Hamiltonian, and the two-mode Bose-Hubbard model -- we identify specific many-body probes capable of approaching both limits. Overall, our results provide a theoretical basis for the design of (local) many-body ground-state sensors operating at the ultimate limits of quantum precision.
ER -