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

Karol Gietka,Friederike Metz,Tim Keller,Jing Li

doi:10.22331/q-2021-07-01-489

Karol Gietka, Friederike Metz + Show 2 more

Open Access

https://doi.org/10.22331/q-2021-07-01-489

Copy DOI

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.

Highlights

Quantum metrology [1] is concerned with harnessing quantum resources following from the quantum-mechanical framework to increase the sensitivity of unknown parameter estimation beyond the standard quantum limit [2]
We have shown that the Heisenberg limit (HL) achievable in regular quantum metrology poses an upper bound for the attainable quantum Fisher information (QFI) in critical quantum metrology when the preparation of the critical ground state is taken into account as well
As reaching the HL requires different states than instantaneous eigenstates of a critical system, optimal regular quantum metrology is always superior to critical quantum metrology given the same amount of time resources

Summary

Introduction

Quantum metrology [1] is concerned with harnessing quantum resources following from the quantum-mechanical framework (in particular, quantum entanglement) to increase the sensitivity of unknown parameter estimation beyond the standard quantum limit [2]. Highly non-classical states are highly sensitive to decoherence and noise [8, 9] which often renders quantum-enhanced measurements as proof-of-principle experiments To counteract these effects, one can resort to quantum enhanced measurements without entanglement [10] or critical quantum metrology associated with quantum phase transitions which received much attention in the recent years [11,12,13,14,15,16,17,18,19,20,21]

Objectives

Discussion

Conclusion