Conditions for entanglement transformation between a class of multipartite pure states with generalized Schmidt decompositions

TL;DR

This paper extends Nielsen's criterion for entanglement transformation from bipartite to a specific class of multipartite pure states with generalized Schmidt decompositions, providing a broader understanding of state convertibility.

Contribution

It generalizes the majorization criterion for bipartite states to certain multipartite states with generalized Schmidt decompositions, advancing entanglement theory.

Findings

Extended Nielsen's criterion to multipartite states

Identified conditions for state convertibility in the new class

Provided theoretical framework for multipartite entanglement transformations

Abstract

In this note we generalize Nielsen's marjoization criterion for the convertibility of bipartite pure states [Phys. Rev. Lett \textbf{83}, 436(1999)] to a special class of multipartite pure states which have generalized Schmidt decompositions.