Adiabatic critical quantum metrology cannot reach the Heisenberg limit even when shortcuts to adiabaticity are applied

TL;DR

This paper demonstrates that adiabatic critical quantum metrology, even with shortcuts to adiabaticity, cannot reach the Heisenberg limit of precision, making regular quantum metrology more effective.

Contribution

It proves the fundamental limit of adiabatic critical quantum metrology and shows shortcuts to adiabaticity do not improve its precision beyond this limit.

Findings

Adiabatic critical quantum metrology cannot attain the Heisenberg limit.

Shortcuts to adiabaticity do not enable surpassing the Heisenberg limit.

Regular quantum metrology remains superior under optimal conditions.

Abstract

We show that the quantum Fisher information attained in an adiabatic approach to critical quantum metrology cannot lead to the Heisenberg limit of precision and therefore regular quantum metrology under optimal settings is always superior. Furthermore, we argue that even though shortcuts to adiabaticity can arbitrarily decrease the time of preparing critical ground states, they cannot be used to achieve or overcome the Heisenberg limit for quantum parameter estimation in adiabatic critical quantum metrology. As case studies, we explore the application of counter-diabatic driving to the Landau-Zener model and the quantum Rabi model.