Comment on "Entanglement transformation between two-qubit mixed states by LOCC" [Phys. Lett. A 373 (2009) 3610]

TL;DR

This paper critiques a previous work on entanglement transformation between two-qubit mixed states, highlighting an incomplete proof and emphasizing that a generalization of Nielsen's theorem for mixed states remains unresolved.

Contribution

It identifies gaps in the proof of a key theorem in entanglement transformation, clarifying that the problem is still open for mixed states.

Findings

The proof of Theorem 2.6 in the referenced paper is incomplete.

The generalization of Nielsen's theorem to mixed states is still an open problem.

The paper clarifies the limitations of previous results on entanglement transformation.

Abstract

The paper [Phys. Lett. A 373 (2009) 3610] by D.-C. Li analyzes the transformation between two-qubit mixed states by local operations and classical communication. We show that the proof of the main theorem, Theorem 2.6 in [Phys. Lett. A 373 (2009) 3610] is not complete. Therefore the generalization of Nielsen's theorem to mixed states still remains an open problem.