# Estimation on geometric measure of quantum coherence

## TL;DR

This paper analyzes the geometric measure of quantum coherence, providing bounds and exploring its relation with mixedness, with a focus on maximally coherent mixed states.

## Contribution

It offers tight bounds for the geometric measure of quantum coherence and examines the coherence-mixedness trade-off.

## Key findings

- Bounds are tight for maximally coherent mixed states
- Trade-off relation between coherence and mixedness is established
- Provides analytical tools for quantifying quantum coherence

## Abstract

We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.