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:0903.4413 · Physical Review A

Polygamy of distributed entanglement

Francesco Buscemi, Gilad Gour, Jeong San Kim

Published Jul 20, 2009• 61 citations
arXivHTMLPDF

Abstract

While quantum entanglement is known to be monogamous (i.e., shared entanglement is restricted in multipartite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multiqubit systems and several trade-offs between UE and other correlation measures.

DOI
10.1103/physreva.80.012324

Related papers

Monogamy of Quantum Entanglement

Xiao-Lan Zong, Hao-Hao Yin, Wei Song +1 more

Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.

arXiv:2201.00366•Frontiers in Physics•Jun 9, 2022•13 citations

Polygamy of entanglement in multipartite quantum systems

Jeong San Kim

We show that bipartite entanglement distribution (or entanglement of assistance) in multipartite quantum systems is by nature polygamous. We first provide an analytical upper bound for the concurrence of assistance in bipartite quantum systems and derive a polygamy inequality of multipartite entanglement in arbitrary-dimensional quantum systems.

arXiv:0904.3061•Physical Review A•Aug 4, 2009•13 citations

Tighter monogamy and polygamy relations in multiparty quantum systems

Chenxiao Wang, Limin Gao

The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.

quant-pharXiv:2603.12539•Mar 16, 2026•0 citations

Tighter monogamy and polygamy relations in multiparty quantum systems

Chenxiao Wang, Limin Gao

Abstract The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.

Laser Physics Letters•Mar 1, 2026•1 citation

One-way unlocalizable quantum discord

Zhengjun Xi, Heng Fan, Yongming Li

In this paper, we present the concept of the one-way unlocalizable quantum discord and investigate its properties. We provide a polygamy inequality for it in a tripartite pure quantum system of arbitrary dimension. Several tradeoff relations between the one-way unlocalizable quantum discord and other correlations are given. If the von Neumann measurement is made on a part of the system, we give two expressions of the one-way unlocalizable quantum discord in terms of partial distillable entanglement and quantum disturbance. Finally, we also provide a lower bound for bipartite shareability of quantum correlation beyond entanglement in a tripartite system.

arXiv:1201.3979•Physical Review A•May 3, 2012•14 citations

Polygamy of multiparty q -expected quantum entanglement

Jeong San Kim

We characterize the polygamy nature of quantum entanglement in multiparty systems in terms of $q$-expectation value for the full range of $q\ensuremath{\ge}1$. By investigating some properties of generalized quantum correlations in terms of $q$-expectation value and Tsallis $q$-entropy, we establish a class of polygamy inequalities of multiparty quantum entanglement in arbitrary dimensions based on $q$-expected entanglement measure. As Tsallis $q$-entropy is reduced to von Neumann entropy, and $q$-expectation value becomes the ordinary expectation value when $q$ tends to 1, our results encapsulate previous results of polygamy inequalities based on von Neumann entropy as special cases.

arXiv:1909.10346•Physical Review A•Dec 26, 2019•4 citations
While quantum entanglement is known to be monogamous (i.e., shared entanglement is restricted in multipartite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multiqubit systems and several trade-offs between UE and other correlation measures.
Unlike classical correlation, quantum entanglement cannot be freely shared among many parties. This restricted shareability of entanglement among multi-party systems is known as monogamy of entanglement, which is one of the most fundamental properties of entanglement. Here, we summarize recent theoretical progress in the field of monogamy of entanglement. We firstly review the standard CKW-type monogamy inequalities in terms of various entanglement measures. In particular, the squashed entanglement and one-way distillable entanglement are monogamous for arbitrary dimensional systems. We then introduce some generalized version of monogamy inequalities which extend and sharpen the traditional ones. We also consider the dual polygamy inequalities for multi-party systems. Moreover, we present two new definitions to define monogamy of entanglement. Finally, some challenges and future directions for monogamy of entanglement are highlighted.
The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.
Abstract The monogamy and polygamy properties of quantum entanglement characterize fundamental constraints on the distribution of entanglement in multipartite quantum systems. In this paper, we investigate tighter monogamy and polygamy relations for multipartite entanglement. By establishing a new mathematical inequality, we derive a family of improved monogamy and polygamy inequalities for tripartite quantum systems and further extend these results to general multipartite systems. Comparisons with existing results show that the obtained bounds are tighter. Illustrative examples are provided to demonstrate the effectiveness of the proposed relations.
In this paper, we present the concept of the one-way unlocalizable quantum discord and investigate its properties. We provide a polygamy inequality for it in a tripartite pure quantum system of arbitrary dimension. Several tradeoff relations between the one-way unlocalizable quantum discord and other correlations are given. If the von Neumann measurement is made on a part of the system, we give two expressions of the one-way unlocalizable quantum discord in terms of partial distillable entanglement and quantum disturbance. Finally, we also provide a lower bound for bipartite shareability of quantum correlation beyond entanglement in a tripartite system.
We characterize the polygamy nature of quantum entanglement in multiparty systems in terms of qqq-expectation value for the full range of $q\ensuremath{\ge}1$. By investigating some properties of generalized quantum correlations in terms of qqq-expectation value and Tsallis qqq-entropy, we establish a class of polygamy inequalities of multiparty quantum entanglement in arbitrary dimensions based on qqq-expected entanglement measure. As Tsallis qqq-entropy is reduced to von Neumann entropy, and qqq-expectation value becomes the ordinary expectation value when qqq tends to 1, our results encapsulate previous results of polygamy inequalities based on von Neumann entropy as special cases.