Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2101.02260 · Physical Review Letters

Triangle Measure of Tripartite Entanglement

Songbo Xie, Joseph H. Eberly

Published Jul 23, 2021• 114 citations
arXivHTMLPDF

Abstract

Although genuine multipartite entanglement has already been generated and verified by experiments, most of the existing measures cannot detect genuine entanglement faithfully. In this work, by exploiting for the first time a previously overlooked constraint for the distribution of entanglement in three-qubit systems, we reveal a new genuine tripartite entanglement measure, which is related to the area of a so-called concurrence triangle. It is compared with other existing measures and is found superior to previous attempts for different reasons. A specific example is illustrated to show that two tripartite entanglement measures can be inequivalent due to the high dimensionality of the Hilbert space. The properties of the triangle measure make it a candidate in potential quantum tasks and available to be used in any multiparty entanglement problems.

DOI
10.1103/physrevlett.127.040403

Related papers

Multi-Photonic Entanglement, A Geometric Approach

Songbo Xie, Joseph H. Eberly

A new genuine tripartite entanglement measure is revealed, interpreted as the area of a so-called concurrence triangle. The new measure is found superior to previous attempts. Specific examples are illustrated.

Frontiers in Optics•Jan 1, 2021•0 citations

Genuine multipartite entanglement measure

Yu Jing Guo, Yanping Jia, Xinping Li +1 more

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 ⩽ 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.

arXiv:2108.03638•Journal of Physics A Mathematical and Theoretical•Feb 17, 2022•41 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.

arXiv:2212.07067•Results in Physics•Dec 6, 2022•28 citations

Tripartite entanglement measure under local operations and classical communication

Xiaozhen Ge, Lijun Liu, Shuming Cheng

Multipartite entanglement is an indispensable resource in quantum communication and computation; however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system [Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show that the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC monotonicity of the three-tangle and find that the bipartite concurrence and the squared concurrence can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalized to the multipartite system. Our results shed light on the study of genuine entanglement and also reveal the complex structure of multipartite systems.

arXiv:2210.06700•Physical Review A•Mar 7, 2023•25 citations

Genuine multipartite entanglement measure based on triangle structure

Yu Chen Guo, Yanping Jia, Xinping Li +1 more

Quantifying genuine entanglement is a crucial task in quantum information theory. Very recently, a genuine three-qubit entanglement measure induced by the area of concurrence triangle was proposed in [Phys. Rev. Lett., 127, 040403]. In this work, we show that this scenario is also valid for any other entanglement measure and system with any dimension. Moreover, in light of the triangle structure, we give genuine entanglement measures for any four-partite system via the complete tripartie entanglement measure and the triangle measure respectively.

•Aug 8, 2021•0 citations

Multipartite entanglement and geometry

Songbo Xie, Joseph H. Eberly

Genuine multipartite entanglement is crucial for quantum information and quantum technologies but quantifying it has been a long-standing challenge. Most existing measures do not meet a “genuine” requirement, making them unsuitable for many applications. Here, we present a surprising triangle measure for tripartite entanglement, and introduce the extension to four-qubit systems. We discuss potential avenues for further generalizations along this geometric path. This indicates that our work may pave the way for further advancements.

Photonics for Quantum (PfQ)•Jul 19, 2023•2 citations
Although genuine multipartite entanglement has already been generated and verified by experiments, most of the existing measures cannot detect genuine entanglement faithfully. In this work, by exploiting for the first time a previously overlooked constraint for the distribution of entanglement in three-qubit systems, we reveal a new genuine tripartite entanglement measure, which is related to the area of a so-called concurrence triangle. It is compared with other existing measures and is found superior to previous attempts for different reasons. A specific example is illustrated to show that two tripartite entanglement measures can be inequivalent due to the high dimensionality of the Hilbert space. The properties of the triangle measure make it a candidate in potential quantum tasks and available to be used in any multiparty entanglement problems.
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 ⩽ 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.
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.
Multipartite entanglement is an indispensable resource in quantum communication and computation; however, it is a challenging task to faithfully quantify this global property of multipartite quantum systems. In this work we study the concurrence fill, which admits a geometric interpretation to measure genuine tripartite entanglement for the three-qubit system [Xie and Eberly, Phys. Rev. Lett. 127, 040403 (2021)]. First, we use the well-known three-tangle and bipartite concurrence to reformulate this quantifier for all pure states. We then construct an explicit example to conclusively show that the concurrence fill can be increased under local operations and classical communication (LOCC) on average, implying it is not an entanglement monotone. Moreover, we give a simple proof of the LOCC monotonicity of the three-tangle and find that the bipartite concurrence and the squared concurrence can have distinct performances under the same LOCC. Finally, we propose a reliable monotone to quantify genuine tripartite entanglement, which can also be easily generalized to the multipartite system. Our results shed light on the study of genuine entanglement and also reveal the complex structure of multipartite systems.
Quantifying genuine entanglement is a crucial task in quantum information theory. Very recently, a genuine three-qubit entanglement measure induced by the area of concurrence triangle was proposed in [Phys. Rev. Lett., 127, 040403]. In this work, we show that this scenario is also valid for any other entanglement measure and system with any dimension. Moreover, in light of the triangle structure, we give genuine entanglement measures for any four-partite system via the complete tripartie entanglement measure and the triangle measure respectively.
Genuine multipartite entanglement is crucial for quantum information and quantum technologies but quantifying it has been a long-standing challenge. Most existing measures do not meet a “genuine” requirement, making them unsuitable for many applications. Here, we present a surprising triangle measure for tripartite entanglement, and introduce the extension to four-qubit systems. We discuss potential avenues for further generalizations along this geometric path. This indicates that our work may pave the way for further advancements.