# Comment on "Optimal convex approximations of quantum states"

## TL;DR

This paper provides complete analytical solutions for the optimal convex approximation of qubit states, correcting and supplementing previous incomplete results in the literature.

## Contribution

It offers new, comprehensive analytical solutions for approximating qubit states, addressing gaps in prior work.

## Key findings

- Corrected previous analytical solutions for qubit state approximation
- Provided complete formulas for optimal convex mixing
- Enhanced understanding of quantum state approximation methods

## Abstract

In a recent paper, M. F. Sacchi [Phys. Rev. A 96, 042325 (2017)] addressed the general problem of approximating an unavailable quantum state by the convex mixing of different available states. For the case of qubit mixed states, we show that the analytical solutions in some cases are invalid. In this Comment, we present complete analytical solutions for the optimal convex approximation. Our solutions can be viewed as correcting and supplementing the results in the aforementioned paper.