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

Geometric multipartite entanglement measures

Gerardo A. Paz-Silva, John Henry Reina

arXiv:quant-ph/0603102Physics Letters AJan 9, 20074 citations

Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure

Yinfei Li, Jiangwei Shang

In this paper, 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 potential application of our measure for tasks involving genuine multipartite entanglement.In this paper, 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 potential application of our measure for tasks involving genuine multipartite entanglement.

arXiv:2112.10509Physical Review ResearchApr 20, 202242 citations

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

Peiyuan Teng

arXiv:1609.02076Quantum Information ProcessingJun 12, 201712 citations

Concurrence triangle induced genuine multipartite entanglement measure

Zhi‐Xiang Jin, Yuan-Hong Tao, Yaoting Gui +3 more

We study the quantification of genuine multipartite entanglement (GME) for general multipartite states. A set of inequalities satisfied by the entanglement of N-partite pure states is derived by exploiting the restrictions on entanglement distributions, showing that the bipartite entanglement between each part and its remaining ones cannot exceed the sum of the other partners with their remaining ones. Then a series of triangles, named concurrence triangles, are established corresponding to these inequalities. Proper genuine multipartite entanglement measures are thus constructed by using the geometric mean area of these concurrence triangles, which are non-increasing under local operation and classical communication. The GME measures classify which parts are separable or entangled with the rest ones for non genuine entangled pure states. The GME measures for mixed states are given via the convex roof construction, and a witness to detect the GME of multipartite mixed states is presented by an approach based on state purifications. Detailed examples are given to illustrate the effectiveness of our GME measures.We study the quantification of genuine multipartite entanglement (GME) for general multipartite states. A set of inequalities satisfied by the entanglement of N-partite pure states is derived by exploiting the restrictions on entanglement distributions, showing that the bipartite entanglement between each part and its remaining ones cannot exceed the sum of the other partners with their remaining ones. Then a series of triangles, named concurrence triangles, are established corresponding to these inequalities. Proper genuine multipartite entanglement measures are thus constructed by using the geometric mean area of these concurrence triangles, which are non-increasing under local operation and classical communication. The GME measures classify which parts are separable or entangled with the rest ones for non genuine entangled pure states. The GME measures for mixed states are given via the convex roof construction, and a witness to detect the GME of multipartite mixed states is presented by an approach based on state purifications. Detailed examples are given to illustrate the effectiveness of our GME measures.

arXiv:2212.07067Results in PhysicsDec 6, 202228 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.

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 potential application of our measure for tasks involving genuine multipartite entanglement.