Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the "genuine" requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems.Genuine multipartite entanglement is crucial for quantum information and related technologies, but quantifying it has been a long-standing challenge. Most proposed measures do not meet the "genuine" requirement, making them unsuitable for many applications. In this work, we propose a journey toward addressing this issue by introducing an unexpected relation between multipartite entanglement and hypervolume of geometric simplices, leading to a tetrahedron measure of quadripartite entanglement. By comparing the entanglement ranking of two highly entangled four-qubit states, we show that the tetrahedron measure relies on the degree of permutation invariance among parties within the quantum system. We demonstrate potential future applications of our measure in the context of quantum information scrambling within many-body systems.

arXiv:2304.03281EntropyFeb 29, 202416 citations

Examining the dimensionality of genuine multipartite entanglement

Christoph Spengler, Marcus Huber, Andreas Gabriel +1 more

arXiv:1106.5664Quantum Information ProcessingFeb 17, 201220 citations

Genuine Multipartite Entanglement Measure Based on $α$ -concurrenceGenuine Multipartite Entanglement Measure Based on $α$-concurrence

Keke Wang, Zhi-Wei Wei, Shao-Ming Fei

Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite $α$ -concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement (GME) measures G $α$ C with one parameter $α$ for arbitrary multipartite states. We show that the G $α$ C is of continuity for any multipartite pure states. By utilizing the related symmetry, analytical results of G $α$ 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 $α$ C can distinguish different GME states that other GME measures fail to. These results justify the potential applications of G $α$ C in characterizing genuine multipartite entanglements.Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite $α$-concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement (GME) measures G$α$C with one parameter $α$ for arbitrary multipartite states. We show that the G$α$C is of continuity for any multipartite pure states. By utilizing the related symmetry, analytical results of G$α$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$α$C can distinguish different GME states that other GME measures fail to. These results justify the potential applications of G$α$C in characterizing genuine multipartite entanglements.

arXiv:2505.05998May 9, 20250 citations

Genuine Multipartite Entanglement Measure Based on

α

-concurrence

Quantifying genuine entanglement is a crucial task in quantum information theory. Based on the geometric mean of bipartite

α

-concurrences among all bipartitions, we present a class of well-defined genuine multipartite entanglement (GME) measures G

α

C with one parameter

α

for arbitrary multipartite states. We show that the G

α

C is of continuity for any multipartite pure states. By utilizing the related symmetry, analytical results of G

α

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

α

C can distinguish different GME states that other GME measures fail to. These results justify the potential applications of G

α

C in characterizing genuine multipartite entanglements.