Is "genuine multipartite entanglement" really genuine?

TL;DR

This paper investigates the distinction between genuine multipartite entanglement and other forms of quantum correlations, demonstrating that a state can be multipartite-entangled without being genuinely entangled, highlighting the complexity of quantum correlations in multi-party systems.

Contribution

The study provides a detailed analysis of multipartite entanglement in continuous-variable systems, emphasizing the importance of considering various entanglement categories to accurately characterize quantum states.

Findings

The six-partite state is multipartite-entangled but not genuinely entangled.

Considering combinations of modes clarifies the nature of quantum correlations.

Experimental covariance matrix confirms the theoretical analysis.

Abstract

The existence of non-local quantum correlations is certainly the most important specific property of the quantum world. However, it is a challenging task to distinguish correlations of classical origin from genuine quantum correlations, especially when the system involves more than two parties, for which different partitions must be simultaneously considered. In the case of mixed states, intermediate levels of correlations must be introduced, coined by the name inseparability. In this work, we revisit in more detail such a concept in the context of continuous-variable quantum optics. We consider a six-partite quantum state that we have effectively generated by the parametric downconversion of a femtosecond frequency comb, the full 12 x 12 covariance matrix of which has been experimentally determined. We show that, though this state does not exhibit "genuine entanglement", it is undoubtedly multipartite-entangled. The consideration of not only the entanglement of individual mode-decompositions but also of combinations of those solves the puzzle and exemplifies the importance of studying different categories of multipartite entanglement.