Genuine multipartite entanglement measure

TL;DR

This paper introduces a method to construct genuine multipartite entanglement measures from bipartite and k-partite measures, extends the triangle relation to continuous measures, and explores geometric structures in multipartite entanglement.

Contribution

It proposes a new approach to quantify genuine multipartite entanglement using existing bipartite and k-partite measures, and generalizes geometric entanglement relations.

Findings

Triangle relation holds for any continuous entanglement measure and system dimension.

Tetrahedron structure describes four-partite entanglement.

No symmetric geometric structure exists for systems with more than four parties.

Abstract

Quantifying genuine entanglement is a crucial task in quantum information theory.In this work, we give an approach of constituting genuine $m$-partite entanglement measures from any bipartite entanglement and any $k$-partite entanglement measure, $3\leq k<m$. In addition, as a complement to the three-qubit concurrence triangle proposed in [Phys. Rev. Lett., 127, 040403], we show that the triangle relation is also valid for any continuous entanglement measure and system with any dimension. We also discuss the tetrahedron structure for the four-partite system via the triangle relation associated with tripartite and bipartite entanglement respectively. For multipartite system that contains more than four parties, there is no symmetric geometric structure as that of tri- and four-partite cases.