Multipartite Entanglement Detection via Correlation Minor Norm

TL;DR

This paper extends the correlation minor norm (CMN) method to detect and differentiate multipartite entangled states using correlation tensor matricizations, also introducing a measure of global quantum discord.

Contribution

It generalizes the CMN for multipartite systems and demonstrates its effectiveness in entanglement detection and classification, along with analyzing correlations in reduced states.

Findings

CMN can detect multipartite entanglement

Differentiates classes of entangled states

Introduces a measure of global quantum discord

Abstract

Entanglement is a uniquely quantum resource giving rise to many quantum technologies. It is therefore important to detect and characterize entangled states, but this is known to be a challenging task, especially for multipartite mixed states. The correlation minor norm (CMN) was recently suggested as a bipartite entanglement detector employing bounds on the quantum correlation matrix. In this paper we explore generalizations of the CMN to multipartite systems based on matricizations of the correlation tensor. It is shown that the CMN is able to detect and differentiate classes of multipartite entangled states. We further analyze the correlations within the reduced density matrices and show their significance for entanglement detection. Finally, we employ matricizations of the correlation tensor for introducing a measure of global quantum discord.