Multipartite entanglement detection via correlation minor norm

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 bi-partite 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.

Automated summary

Entanglement is a crucial quantum resource for various quantum technologies. Detecting and characterizing entangled states, especially for multipartite mixed states, is challenging. The correlation minor norm (CMN) has been proposed as a bipartite entanglement detector using quantum correlation matrix bounds. This paper explores generalizations of CMN to multipartite systems based on matricizations of the correlation tensor. The CMN is shown to successfully detect and differentiate classes of multipartite entangled states. The correlations within reduced density matrices are also analyzed for entanglement detection. Finally, matricizations of the correlation tensor are used to introduce a measure of global quantum discord.