The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems

TL;DR

This paper reviews and extends the entropy vector framework to classify and quantify various forms of multipartite entanglement in high-dimensional quantum systems, including separability and entanglement dimensionality.

Contribution

It introduces new methods to distinguish different entanglement structures and assess entanglement dimensionality using entropy vectors in multipartite systems.

Findings

Extended entropy vector techniques to identify various entanglement types.

Developed criteria for decomposability, $k$-separability, and $k$-partite entanglement.

Provided tools to evaluate entanglement dimensionality.

Abstract

We review and generalize the recently introduced framework of entropy vectors for detecting and quantifying genuine multipartite entanglement in high dimensional multicomponent quantum systems. We show that these ideas can be extended to discriminate among other forms of multipartite entanglement. In particular, we develop methods to test whether density matrices are: decomposable, i.\ e.\ separable with respect to certain given partitions of the subsystems; $k$-separable, i.\ e.\ separable with respect to $k$ partitions of the subsystems; $k$-partite entangled, i.e. there is entanglement among a subset of at least $k$ parties. We also discuss how to asses the dimensionality of entanglement in all these cases.