Genuine Multipartite Entanglement Measure Based on $\alpha$-concurrence

TL;DR

This paper introduces a new family of genuine multipartite entanglement measures based on the geometric mean of bipartite $oldsymbol{ extalpha}$-concurrences, providing analytical results and distinguishing capabilities for different GME states.

Contribution

It proposes a novel GME measure G$oldsymbol{ extalpha}$C based on $oldsymbol{ extalpha}$-concurrence, with analytical results for GHZ and W states, and demonstrates its effectiveness in distinguishing GME states.

Findings

G$oldsymbol{ extalpha}$C is continuous for pure states

GHZ states are more genuinely entangled than W states according to G$oldsymbol{ extalpha}$C

G$oldsymbol{ extalpha}$C can distinguish GME states that other measures cannot

Abstract

Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite $\alpha$-concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement (GME) measures G$\alpha$C with one parameter $\alpha$ for arbitrary multipartite states. We show that the G$\alpha$C is of continuity for any multipartite pure states. By utilizing the related symmetry, analytical results of G$\alpha$C are derived for any $n$-qubit GHZ states and W states, which show that the GHZ states are more genuinely entangled than the W states. With explicit examples, we demonstrate that the G$\alpha$C can distinguish different GME states that other GME measures fail to. These results justify the potential applications of G$\alpha$C in characterizing genuine multipartite entanglements.