Quantum metrology with unitary parametrization processes

TL;DR

This paper introduces a new way to represent quantum Fisher information for unitary processes, linking it to a Hermitian operator H, simplifying calculations and enabling analysis of optimal states and multiparameter scenarios.

Contribution

It presents an alternative Hermitian operator-based representation of quantum Fisher information for unitary processes, enhancing understanding and calculation methods in quantum metrology.

Findings

Derived explicit expression of H for collective spin systems.

Identified optimal states for maximum quantum Fisher information.

Provided analytical formulas for specific initial states.

Abstract

Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Furthermore, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation in the last.