Connectivity structures of quantum entanglement

TL;DR

This paper introduces a novel classification tool for quantum entanglement called the connectivity order, by associating connectivity structures with entangled states and measurement devices, enhancing understanding of quantum correlations.

Contribution

It proposes the connectivity order as a new classification method for quantum entanglement based on connectivity structures linked to states and measurements.

Findings

Defines connectivity order as a new entanglement classification tool

Associates connectivity structures with quantum states and measurement devices

Provides a framework for analyzing quantum entanglement complexity

Abstract

In this paper, after some recalls about connectivity structures and about the formalisms of quantum mechanics, we associate some families of connectivity structures with any entangled quantum state, and with any "measurement device" on such states. This finally allows us to define a new classification tool for quantum entanglement: the connectivity order. --- Dans ce texte, apr\`es des rappels d'une part sur la notion de structure connective et d'autre part sur les formalismes de la m\'ecanique quantique, nous associons certaines familles de structures connectives \`a tout \'etat quantique intriquant un nombre fini quelconque de particules, ainsi qu'\`a tout "dispositif de mesure", portant sur de tels \'etats. Cela nous permet finalement de d\'efinir un nouvel outil de classification de l'intrication quantique : l'ordre connectif.