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:2607.18643 · Quantum Information Processing

Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems

Xue-Na Zhu, Gui Bao, Zhi-Xiang Jin, Shao-Ming Fei, Tao Li

quant-phSubmitted Jul 21, 2026• Announced Jul 22, 2026• 0 citations
arXivHTMLPDF

Abstract

The monogamy relations characterize the distribution of quantum correlations among the multipartite quantum systems. We study the monogamy relations of the entanglement of assistance in $2\otimes 2\otimes d$ systems. We present explicitly the relations satisfied by the concurrence, the tangle and the concurrence of assistance, which can be used to derive rigorous monogamy relations. Detailed examples are given to illustrate our results.

Journal reference
Quantum Information Processing(2026) 25:258
DOI
10.1007/s11128-026-05288-w
Comments
8pages

Related papers

Finer distribution of quantum correlations among multiqubit systems

Jin, Z., Fei, S.

We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the $\alpha$th ($\alpha\geq 2$) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the $\beta$th ($0\leq \beta\leq2$) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-$q$ entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.

•Jan 1, 2019•12 citations

Complementary monogamy and polygamy properties among multipartite systems

Tao 陶 Li 李, Jing-Yi 静怡 Zhou 周, Qi 琪 Sun 孙 +3 more

Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for γ-th (0 ≤ γ ≤ α, α ≥ 1) power of quantum entanglement based on unified-(q,s) entanglement and polygamy relations for δ-th (δ ≥ β, 0 ≤ β ≤ 1) power of entanglement of assistance based on unified-(q,s) entanglement of assistance, which provides a complement to the previous research in terms of different parameter regions of γ and δ. These results are then applied to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance to get the corresponding monogamy and polygamy inequalities. Moreover, typical examples are presented for illustration.

Chinese Physics B•Dec 20, 2023•0 citations

Entanglement monogamy relations of qubit systems

Xue‐Na Zhu, Shao-Ming Fei

We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the $\ensuremath{\alpha}\text{th}$ power of concurrence and entanglement of formation are presented for $N$-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.

arXiv:1409.1022•Physical Review A•Aug 28, 2014•138 citations

Monogamy and polygamy relations of multiqubit entanglement based on unified entropy*

Zhi‐Xiang Jin, Cong‐Feng Qiao

Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q,s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s) entanglement for α ≥ 1. We also obtain a class of tighter polygamy relations in the β-th (0 ≤ β ≤ 1) power of unified-(q,s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for the α-th (0 ≤ α ≤ 1) and β-th (β ≥ 1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.

Chinese Physics B•Jan 3, 2020•6 citations

Generalized monogamy relations of concurrence for N -qubit systems

Xue‐Na Zhu, Shao-Ming Fei

We present a different kind of monogamous relations based on concurrence and concurrence of assistance. For $N$-qubit systems $AB{C}_{1}...{C}_{N\ensuremath{-}2}$, the monogamy relations satisfied by the concurrence of $N$-qubit pure states under the partition $AB$ and ${C}_{1}...{C}_{N\ensuremath{-}2}$, as well as under the partition $AB{C}_{1}$ and ${C}_{2}...{C}_{N\ensuremath{-}2}$, are established, which gives rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.

arXiv:1512.09211•Physical Review A•Dec 30, 2015•57 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
Monogamy inequalities of entanglement of assistance in 2⊗2⊗d2\otimes 2\otimes d2⊗2⊗d systems
The monogamy relations characterize the distribution of quantum correlations among the multipartite quantum systems. We study the monogamy relations of the entanglement of assistance in 2⊗2⊗d2\otimes 2\otimes d2⊗2⊗d systems. We present explicitly the relations satisfied by the concurrence, the tangle and the concurrence of assistance, which can be used to derive rigorous monogamy relations. Detailed examples are given to illustrate our results.
We study the distribution of quantum correlations characterized by monogamy relations in multipartite systems. By using the Hamming weight of the binary vectors associated with the subsystems, we establish a class of monogamy inequalities for multiqubit entanglement based on the α\alphaαth (α≥2\alpha\geq 2α≥2) power of concurrence, and a class of polygamy inequalities for multiqubit entanglement in terms of the β\betaβth (0≤β≤20\leq \beta\leq20≤β≤2) power of concurrence and concurrence of assistance. Moveover, we give the monogamy and polygamy inequalities for general quantum correlations. Application of these results to quantum correlations like squared convex-roof extended negativity (SCREN), entanglement of formation and Tsallis-qqq entanglement gives rise to either tighter inequalities than the existing ones for some classes of quantum states or less restrictions on the quantum states. Detailed examples are presented.
Monogamy and polygamy relations are essential properties of quantum entanglement, which characterize the distributions of entanglement in multipartite systems. In this paper, we establish the general monogamy relations for γ-th (0 ≤ γ ≤ α, α ≥ 1) power of quantum entanglement based on unified-(q,s) entanglement and polygamy relations for δ-th (δ ≥ β, 0 ≤ β ≤ 1) power of entanglement of assistance based on unified-(q,s) entanglement of assistance, which provides a complement to the previous research in terms of different parameter regions of γ and δ. These results are then applied to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance and Tsallis-q entanglement of assistance to get the corresponding monogamy and polygamy inequalities. Moreover, typical examples are presented for illustration.
We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the $\ensuremath{\alpha}\text{th}$ power of concurrence and entanglement of formation are presented for NNN-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.
Monogamy relation is one of the essential properties of quantum entanglement, which characterizes the distribution of entanglement in a multipartite system. By virtual of the unified-(q,s) entropy, we obtain some novel monogamy and polygamy inequalities in general class of entanglement measures. For the multiqubit system, a class of tighter monogamy relations are established in term of the α-th power of unified-(q,s) entanglement for α ≥ 1. We also obtain a class of tighter polygamy relations in the β-th (0 ≤ β ≤ 1) power of unified-(q,s) entanglement of assistance. Applying these results to specific quantum correlations, e.g., entanglement of formation, Renyi-q entanglement of assistance, and Tsallis-q entanglement of assistance, we obtain the corresponding monogamy and polygamy relations. Typical examples are presented for illustration. Furthermore, the complementary monogamy and polygamy relations are investigated for the α-th (0 ≤ α ≤ 1) and β-th (β ≥ 1) powers of unified entropy, respectively, and the corresponding monogamy and polygamy inequalities are obtained.
We present a different kind of monogamous relations based on concurrence and concurrence of assistance. For NNN-qubit systems $AB{C}_{1}...{C}_{N\ensuremath{-}2}$, the monogamy relations satisfied by the concurrence of NNN-qubit pure states under the partition ABABAB and ${C}_{1}...{C}_{N\ensuremath{-}2}$, as well as under the partition ABC1AB{C}_{1}ABC1​ and ${C}_{2}...{C}_{N\ensuremath{-}2}$, are established, which gives rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.
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.