Many-body $k$-local ground states as probes for unitary quantum metrology

TL;DR

This paper investigates how many-body ground states of $k$-local Hamiltonians can be used for quantum metrology, revealing they can achieve Heisenberg scaling despite limited correlator access, and explores the tradeoff between Hamiltonian gap and Fisher information.

Contribution

It demonstrates that ground states of $k$-local Hamiltonians can attain Heisenberg-limited sensitivity and analyzes the relationship between Hamiltonian gap and quantum Fisher information.

Findings

Random symmetric ground states exhibit Heisenberg scaling.

Tradeoff identified between Hamiltonian gap and Fisher information.

Ground states can be effective probes despite limited correlator access.

Abstract

Multipartite quantum states saturating the Heisenberg limit of sensitivity typically require full-body correlators to be prepared. On the other hand, experimentally practical Hamiltonians often involve few-body correlators only. Here, we study the metrological performances under this constraint, using tools derived from the quantum Fisher information. Our work applies to any encoding generator, also including a dependence on the parameter. We find that typical random symmetric ground states of $k$-body permutation-invariant Hamiltonians exhibit Heisenberg scaling. Finally, we establish a tradeoff between the Hamiltonian's gap, which quantifies preparation hardness, and the quantum Fisher information of the corresponding ground state.