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

Photonics for Quantum (PfQ)

Multipartite entanglement and geometry

Songbo Xie, Joseph H. Eberly

Published Jul 19, 2023• 2 citations
Publisher

Abstract

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.

DOI
10.1117/12.2675453

Related papers

Multipartite Entanglement: A Journey through Geometry

Songbo Xie, Daniel Younis, Yuhan Mei +1 more

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:2304.03281•Entropy•Feb 29, 2024•16 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

Triangle Measure of Tripartite Entanglement

Songbo Xie, Joseph H. Eberly

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.

arXiv:2101.02260•Physical Review Letters•Jul 23, 2021•114 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

Genuine multipartite entanglement measures based on multi-party teleportation capability

Minjin Choi, Eunok Bae, Soojoon Lee

Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for N-qubit systems, where [Formula: see text], and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.

arXiv:2211.15986•Scientific Reports•Sep 11, 2023•10 citations

Polygon Inequality-Based Genuine Entanglement Measures

Sumit Chilkoti, Mrittunjoy Guha Majumdar

Genuine multipartite entanglement (GME) represents the strongest form of quantum correlation, where all parties of a system across each bipartition are inseparably linked. This resource is crucial for advanced quantum protocols, including multi-party cryptography and distributed quantum computing, yet its quantification remains a significant theoretical challenge. This review surveys a rapidly evolving geometric paradigm that translates this challenge into a problem of polygon inequalities. By representing marginal bipartite entanglements as side lengths, the distribution of entanglement in a multipartite state must satisfy geometric closure conditions akin to forming a polygon. These polygon-based constraints provide a unifying framework for detecting and quantifying GME, offering an intuitive bridge between bipartite entanglement measures and global multipartite structure. We chart the development of this approach from its monogamy-based origins to modern formulations using concurrence triangles, wedge products, and entropy-based polygons. Recent advances have established rigorous conditions for these geometric quantities to serve as faithful, operationally meaningful entanglement measures, while also extending the framework to mixed states and higher-dimensional systems. Despite progress, key challenges persist in ensuring universal monotonicity and experimental robustness. By synthesizing these geometric insights, this review highlights how polygon inequalities are reshaping the quantification of complex quantum correlations and providing novel diagnostic tools for the next generation of quantum technologies.

•Mar 14, 2026•0 citations
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.
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.
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.
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.
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.
Quantifying entanglement is vital to understand entanglement as a resource in quantum information processing, and many entanglement measures have been suggested for this purpose. When mathematically defining an entanglement measure, we should consider the distinguishability between entangled and separable states, the invariance under local transformation, the monotonicity under local operations and classical communication, and the convexity. These are reasonable requirements but may be insufficient, in particular when taking into account the usefulness of quantum states in multi-party quantum information processing. Therefore, if we want to investigate multipartite entanglement as a resource, then it can be necessary to consider the usefulness of quantum states in multi-party quantum information processing when we define a multipartite entanglement measure. In this paper, we define new multipartite entanglement measures for three-qubit systems based on the three-party teleportation capability, and show that these entanglement measures satisfy the requirements for being genuine multipartite entanglement measures. We also generalize our entanglement measures for N-qubit systems, where [Formula: see text], and discuss that these quantities may be good candidates to measure genuine multipartite entanglement.
Genuine multipartite entanglement (GME) represents the strongest form of quantum correlation, where all parties of a system across each bipartition are inseparably linked. This resource is crucial for advanced quantum protocols, including multi-party cryptography and distributed quantum computing, yet its quantification remains a significant theoretical challenge. This review surveys a rapidly evolving geometric paradigm that translates this challenge into a problem of polygon inequalities. By representing marginal bipartite entanglements as side lengths, the distribution of entanglement in a multipartite state must satisfy geometric closure conditions akin to forming a polygon. These polygon-based constraints provide a unifying framework for detecting and quantifying GME, offering an intuitive bridge between bipartite entanglement measures and global multipartite structure. We chart the development of this approach from its monogamy-based origins to modern formulations using concurrence triangles, wedge products, and entropy-based polygons. Recent advances have established rigorous conditions for these geometric quantities to serve as faithful, operationally meaningful entanglement measures, while also extending the framework to mixed states and higher-dimensional systems. Despite progress, key challenges persist in ensuring universal monotonicity and experimental robustness. By synthesizing these geometric insights, this review highlights how polygon inequalities are reshaping the quantification of complex quantum correlations and providing novel diagnostic tools for the next generation of quantum technologies.