Lower Bounds on Quantum Metrological Precision

TL;DR

This thesis explores the potential of unpolarized Dicke states for magnetic field sensing, establishes lower bounds on quantum Fisher information using Legendre transforms, and develops a theory for gradient magnetometry to assess spatial magnetic field sensitivity.

Contribution

It introduces tight lower bounds on quantum Fisher information from limited measurements and advances the understanding of gradient magnetometry in quantum metrology.

Findings

Unpolarized Dicke states are highly sensitive to magnetic fields.

Legendre transform-based bounds improve estimation efficiency.

New theory for spatial magnetic field sensitivity in gradient magnetometry.

Abstract

In this thesis, first, we investigate the metrological usefulness of a family of states known as unpolarized Dicke states, which turn to be very sensitive to the magnetic field. Quantum mechanics plays a central role in achieving such a high precision. Second, we investigate possible lower bounds on the quantum Fisher information, a quantity that characterizes the usefulness of a state for quantum metrology, using the theory of Legendre transforms such that we obtain tight lower bounds based on few measurements of the initial quantum state that will be used for metrology. And last but not least, we investigate gradient magnetometry, i.e., we develop a theory to study the sensitivity of some states on the change in space of the magnetic field.