Invertible condition of quantum Fisher information matrix for a mixed qubit

TL;DR

This paper establishes a condition to determine when two parameters can be simultaneously estimated in a mixed qubit state, advancing the understanding of quantum multiparameter estimation.

Contribution

It introduces a specific condition for the simultaneous estimability of two parameters in mixed qubits, providing a new tool for quantum metrology.

Findings

Derived a condition for simultaneous parameter estimation in mixed qubits

Applied the condition to demonstrate its practical use

Enhanced understanding of quantum Fisher information in mixed states

Abstract

Estimating multiparamter simultaneously as precise as possible is an important goal of quantum metrolo- gy. As a first step to this end, here we give a condition determining whether two arbitrary parameters can be estimated simultaneously for a qubit in the mixed state. An application of this condition is shown.