Quantum Fisher Information With General Quantum Coherence in multi-dimensional quantum systems

TL;DR

This paper investigates the link between quantum Fisher information and a new measure called General Quantum Coherence in multi-dimensional quantum systems, revealing a quadratic relationship that can enhance quantum parameter estimation precision.

Contribution

It introduces General Quantum Coherence (GQC), a novel measure capturing high-dimensional quantum coherence and energy interactions, and establishes its quadratic relation with QFI.

Findings

GQC captures quantum coherence and eigenenergy effects in high-dimensional states.

A quadratic relationship between GQC and QFI is demonstrated.

Results provide guidelines for improving quantum measurement precision.

Abstract

Quantum metrology is a science about quantum measurements and it plays a key role in precision of quantum parameter estimation. Meanwhile, quantum coherence is an important quantum feature and quantum Fisher information (QFI) is an important indicator for precision of quantum parameter estimation. In this paper, we explore the relationship between QFI and quantum coherence in multi-dimensional quantum systems. We introduce a new concept referred to as General Quantum Coherence (GQC), which characterizes the quantum coherence and the eigenenergies of the Hamiltonian in the interaction processes. GQC captures quantum nature of high-dimensional quantum states and addresses shortcomings in coherence measurement. Additionally, we observe a stringent square relationship between GQC and QFI. This finding provides a crucial guideline for improving the precision of parameter estimation.