Universal shot-noise limit for quantum metrology with local Hamiltonians

TL;DR

This paper establishes a universal shot-noise limit for quantum metrology with local Hamiltonians, showing that precision cannot surpass this limit in such systems when starting from separable states, linking quantum sensing to many-body physics.

Contribution

It derives a fundamental bound on quantum Fisher information growth in local Hamiltonian systems and connects it to operator growth, demonstrating the shot-noise limit's universality in these contexts.

Findings

The shot-noise limit cannot be surpassed in locally interacting quantum systems with separable initial states.

The bound applies to ground states of local, gapped Hamiltonians.

Numerical analysis confirms the bound in the long-range Ising model.

Abstract

Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we derive a universal and fundamental bound for the growth of the quantum Fisher information. We apply our bound to the metrological protocol requiring only separable initial states, which can be readily prepared in experiments. By establishing a link between our bound and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems, we prove that the precision cannot surpass the shot noise limit at all times in locally interacting quantum systems. This conclusion also holds for an initial state that is the non-degenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling