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 $F_θ\lesssim N^2/Δ^2$ , where $Δ$ is the spectral gap, and the dynamical Heisenberg limit $F_θ\lesssim N^2 τ^2$ , 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.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 $F_θ\lesssim N^2/Δ^2$, where $Δ$ is the spectral gap, and the dynamical Heisenberg limit $F_θ\lesssim N^2 τ^2$, 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.

quant-pharXiv:2610.03653Oct 5, 20260 citations

The one-dimensional XXZ model with long-range interactions

Lindberg Lima Gonçalves, André P. Vieira, Lucas Pinheiro Coutinho

arXiv:cond-mat/0008230Journal of Magnetism and Magnetic MaterialsMay 1, 20011 citation

Long-range bipartite entanglement in XXZ spin chains with exponential and power-law long-range interactions

Na Li, Yang Zhao, Wen-Long Ma +2 more

Long-range bipartite entanglement (LBE) and its distribution properties are studied in XXZ spin chains with exponential and power-law long-range interactions (ELRIs and PLRIs). LBE quantified by two-qubit concurrence decays exponentially along with two-site distance in the infinite chain with ELRIs in the thermodynamic limit, and the long-range behavior of two-spin entanglement can detect the quantum phase transition and identify different quantum phases away from the critical point. Moreover, a fine-grained LBE distribution relation is obtained for the infinite XXZ spin chain. On the other hand, in the finite XXZ spin chain with conventional PLRIs, the long-range concurrence decays algebraically and the total one is no longer monotonic along with the chain length. The total LBE distribution property can exhibit a piecewise function, which has a close relationship with the decaying mode and strength of PLRIs. These LBE relations can be regarded as the generalization of Koashi-Bu\ifmmode \check{z}\else \v{z}\fi{}ek-Imoto bound for the prototypical long-range XXZ model, having potential applications in quantum information processing.Long-range bipartite entanglement (LBE) and its distribution properties are studied in XXZ spin chains with exponential and power-law long-range interactions (ELRIs and PLRIs). LBE quantified by two-qubit concurrence decays exponentially along with two-site distance in the infinite chain with ELRIs in the thermodynamic limit, and the long-range behavior of two-spin entanglement can detect the quantum phase transition and identify different quantum phases away from the critical point. Moreover, a fine-grained LBE distribution relation is obtained for the infinite XXZ spin chain. On the other hand, in the finite XXZ spin chain with conventional PLRIs, the long-range concurrence decays algebraically and the total one is no longer monotonic along with the chain length. The total LBE distribution property can exhibit a piecewise function, which has a close relationship with the decaying mode and strength of PLRIs. These LBE relations can be regarded as the generalization of Koashi-Bu\ifmmode \check{z}\else \v{z}\fi{}ek-Imoto bound for the prototypical long-range XXZ model, having potential applications in quantum information processing.

arXiv:2503.09169Physical review. B./Physical review. BSep 22, 20250 citations

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\lesssim N^2/Δ^2

, where

Δ

is the spectral gap, and the dynamical Heisenberg limit

F_θ\lesssim 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.