Center-of-mass interpretation for bipartite purity analysis of $N$-party entanglement

TL;DR

This paper introduces a geometric, center-of-mass analogy to analyze and visualize the entanglement structure of pure multiparty quantum systems, especially for N qubits, revealing new inequality restrictions.

Contribution

It presents a novel graphical interpretation of multiparty entanglement using a centroid analogy, extending bipartite purity analysis to N-party systems with arbitrary state dimensions.

Findings

Graphical description of multiparty entanglement

Inequality restrictions on entanglement structure

Application to N qubits and arbitrary state dimensions

Abstract

We provide a graphical description of the entanglement of pure-state multiparty systems based on an analogy between a bipartite purity analysis and the centroid of a collection of point masses. This description applies to quantum systems with $N$ parties, each with an arbitrary number of (discrete) states. The case of $N$ qubits is highlighted for simplicity. This geometric description illustrates some of the restrictions in the form of inequalities that apply to entanglement in multiparty systems.