Comment on "Local Copying of $d\times d$-dimensional Partially Entangled Pure States"

TL;DR

This paper critiques a recent result on LOCC cloning of partially entangled states, pointing out a key error and providing an example to challenge the original conclusions.

Contribution

It identifies a flaw in previous work on LOCC cloning conditions and offers a counterexample to clarify the correct understanding.

Findings

The original condition is based on an incorrect assumption.

A counterexample demonstrates the flaw in the previous result.

Clarifies the limitations of LOCC cloning for partially entangled states.

Abstract

Recently, Li. \emph{et. al.} [Int. J. Theor. Phys., 48, 2777 (2009)] derived a necessary and sufficient condition for LOCC cloning of a set of bipartite orthogonal partially but equally entangled state. We demonstrates that, the result is based on a wrong observation regarding a set of non-maximally entangled states with equal entanglement. We also provide a simple example in favor of our comment.