Reaching the Limits of Ground-State Metrology with Many-Body Probes

Reaching the Limits of Ground-State Metrology with Many-Body Probes

Seminar author:Víctor Izquierdo

Event date and time:02/05/2026 02:30:pm

Event location:GIQ Seminar Room

Event contact:

The fundamental limits of ground state metrology have been recently established as Fθ ⩽ N^2/∆^2, where Fθ is the Quantum Fisher Information, N is the number of particles, and ∆ is the spectral gap. This bound defines the maximum achievable precision for estimating an unknown Hamiltonian parameter θ using the ground-state of a general N -body Hamiltonian. In this talk, we will discuss the saturability of this bound by realistic many-body probes, as well as the associated preparation/sensing time. We focus on two distinct classes: short-range critical systems and all-to-all interacting models. First, for critical probes, we derive a universal condition on the critical exponents necessary to saturate the static ground-state bound—a condition satisfied, for instance, by the XXZ model. We also argue that the bound can be saturated by gapped long-range interacting systems. We then address the sensing time τ , in particular the possibility to reach Heisenberg scaling (Fθ ∼ N^2τ^2) for optimised adiabatic protocols. We demonstrate that all-to-all interacting systems can effectively reach both the ground-state and Heisenberg bounds, and discuss the possibility of reaching it in the short-range XXZ model. Our results are supported by analytical and numerical calculations for four paradigmatic systems: the 1D Ising model, the XXZ chain, the two-axis twisting Hamiltonian, and the two-mode Bose-Hubbard model.