Geometric genuine N-partite entanglement measure for arbitrary dimensions

TL;DR

This paper introduces a new geometric measure for genuine multipartite entanglement applicable to systems of arbitrary dimensions, providing a way to quantify and compare entanglement in complex quantum states.

Contribution

The authors develop a novel GME measure based on the volume of a concurrence polygon, applicable to multipartite systems of any dimension, and demonstrate its effectiveness through examples.

Findings

GHZ state is more entangled than W state according to the measure

The measure effectively characterizes genuine multipartite entanglement

Applicable to arbitrary-dimensional quantum systems

Abstract

We present proper genuine multipartite entanglement (GME) measures for arbitrary multipartite and dimensional systems. By using the volume of concurrence regular polygonal pyramid we first derive the GME measure of four-partite quantum systems. From our measure it is verified that the GHZ state is more entangled than the W state. Then we study the GME measure for multipartite quantum states in arbitrary dimensions. A well defined GME measure is constructed based on the volume of the concurrence regular polygonal pyramid. Detailed example shows that our measure can characterize better the genuine multipartite entanglements.