Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure

TL;DR

This paper introduces a new measure for genuine multipartite entanglement based on the geometric mean of bipartite concurrences, which is simple, symmetric, and effective in distinguishing different entanglement structures.

Contribution

It proposes a novel entanglement measure that is computationally straightforward, maximized by maximally entangled states, and capable of detecting distinctions missed by other measures.

Findings

Maximizes for absolutely maximally entangled states

Distinguishes entanglement orderings from other measures

Detects differences in genuine multipartite entanglement

Abstract

In this work we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the $W$ states. With explicit examples we show that our measure results in distinct entanglement orderings from other measures, and can detect differences in certain types of genuine multipartite entanglement while other measures cannot. These results justify the practical application of our measure for tasks involving genuine multipartite entanglement.