Universal Sensitivity Bound for Thermal Quantum Dynamic Sensing

TL;DR

This paper derives a universal upper bound on the quantum Fisher information for thermal quantum sensors, linking sensitivity limits to non-commutation and temperature, applicable to many-body systems in equilibrium and non-equilibrium states.

Contribution

It unifies equilibrium and non-equilibrium quantum metrology frameworks by establishing a fundamental sensitivity bound for thermal probes based on non-commutation and temperature scaling.

Findings

The quantum Fisher information is bounded by the non-commutation between the transformed local generator and the Hamiltonian.

The upper bound scales quadratically with inverse temperature and evolution time.

The bounds are validated across various many-body models.

Abstract

This work unifies the equilibrium and non-equilibrium frameworks of quantum metrology within the context of many-body systems. We investigate dynamic sensing schemes to derive an upper bound on the quantum Fisher information for probe states in thermal equilibrium with their environment. We establish that the dynamic quantum Fisher information for a thermal probe state is upper bounded by the degree of non-commutation between the transformed local generator and the Hamiltonian for the thermal state. Furthermore, we show that this upper bound scales as the square of the product of the inverse temperature and the evolution time. In the low-temperature limit, we establish an additional upper bound expressed as the seminorm of the commutator divided by the energy gap. We apply this thermal dynamic sensing scheme to various models, demonstrating that the dynamic quantum Fisher information satisfies the established upper bounds.