Maximal quantum Fisher information for general su(2) parametrization processes

TL;DR

This paper derives the maximum quantum Fisher information for general su(2) unitary processes, revealing its time-dependent behavior and optimizing parameter estimation, especially in magnetic field sensing.

Contribution

It provides an analytical expression for the maximal quantum Fisher information in su(2) processes, including time-dependent Hamiltonians, advancing quantum metrology techniques.

Findings

Maximal quantum Fisher information has quadratic and oscillatory time components.

Optimal driving frequency matches atomic frequency for best estimation.

Application to magnetic field estimation demonstrates practical relevance.

Abstract

Quantum Fisher information is a key concept in the field of quantum metrology, which aims to enhance the parameter accuracy by using quantum resources. In this paper, utilizing a representation of quantum Fisher information for a general unitary parametrization process, we study unitary parametrization processes governed by su(2) dynamics. We obtain the analytical expression for the Hermitian operator of the parametrization and the maximal quantum Fisher information. We find that the maximal quantum Fisher information over the parameter space consists of two parts, one is quadratic in the time and the other oscillates with the time. We apply our result to the estimation of a magnetic field and obtained the maximal quantum Fisher information. We further discuss a driving field with a time-dependent Hamiltonian and find the maximal quantum Fisher information of the driving frequency attains optimum when it is in resonance with the atomic frequency.