Quantifying coherence in terms of Fisher information

TL;DR

This paper introduces a new coherence measure based on quantum Fisher information, linking coherence directly to parameter estimation accuracy in quantum metrology, with explicit formulas for qubits.

Contribution

It presents a novel coherence measure derived from Fisher information that captures operational meaning in quantum parameter estimation, distinguishing it from traditional measures.

Findings

Coherence measure directly connected to estimation accuracy

Explicit analytic form for qubit states

Clarifies difference between non-unitary and unitary parametrization

Abstract

In quantum metrology, the parameter estimation accuracy is bounded by quantum Fisher information. In this paper, we present coherence measures in terms of (quantum) Fisher information by directly considering the post-selective non-unitary parametrization process. This coherence measure demonstrates the apparent operational meaning by the exact connection between coherence and parameter estimation accuracy. We also discuss the distinction between our coherence measure and the quantum Fisher information subject to unitary parametrization. The analytic coherence measure is given for qubit states.