Maximally correlated multipartite quantum states

TL;DR

This paper explores quantum states with maximum entanglement and discord across multiple parties, extending bipartite measures to multipartite systems and examining their nonlocality properties, influenced by the underlying number fields.

Contribution

It introduces a novel measure for multipartite quantum discord based on bipartitions and analyzes nonlocality in maximally entangled states across different number fields.

Findings

Maximum entanglement and discord states exist for multipartite systems.

Nonlocality can surpass local states in maximally entangled systems.

The nature of the underlying number field affects nonlocality emergence.

Abstract

We investigate quantum states that posses both maximum entanglement and maximum discord between the pertinent parties. Since entanglement (discord) is defined only for bipartite (two qubit) systems, we shall introduce an appropriate sum over of all bi-partitions as the associated measure. The ensuing definition --not new for entanglement-- is thus extended here to quantum discord. Also, additional dimensions within the parties are considered ({\it qudits}). We also discuss nonlocality (in the form of maximum violation of a Bell inequality) for all multiqubit systems. The emergence of more nonlocal states than local ones, all of them possessing maximum entanglement, will be linked, surprisingly enough, to whether quantum mechanics is defined over the fields of real or complex numbers.