The structure of multidimensional entanglement in multipartite systems

TL;DR

This paper investigates the complex structure of multidimensional entanglement in multipartite quantum systems, providing criteria for characterization and a framework for efficient detection and quantification across various system sizes and dimensions.

Contribution

It introduces necessary and sufficient conditions for tripartite systems and develops a multi-level witness framework applicable to any number of parties and dimensions.

Findings

Derived criteria for tripartite entanglement characterization

Established necessary conditions for multipartite entanglement

Created a scalable framework for entanglement detection

Abstract

We explore the structure of multipartite quantum systems which are entangled in multiple degrees of freedom. We find necessary and sufficient conditions for the characterization of tripartite systems and necessary conditions for any number number of parties. Furthermore we develop a framework of multi-level witnesses for efficient discrimination and quantification of multidimensional entanglement that is applicable for an arbitrary number of systems and dimensions.