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

Journal of Physics A Mathematical and Theoretical

Comment on ‘Monogamy of multi-qubit entanglement using Rényi entropy’

Long-Bao Yu, Lihua Zhang, Junlong Zhao, Yong-Sheng Tang

Published Nov 27, 2017• 0 citations
Publisher

Abstract

Abstract In an article in 2010, Kim et al introduced the definition of Rényi- α entanglement for bipartite quantum states and established an analytic formula of Rényi- α entanglement for arbitrary two-qubit states with α ⩾ 1 . They also derived a monogamy of entanglement in multi-qubit systems in terms of Rényi- α entanglement for α ⩾ 2 Kim et al (2010 J. Phys. A: Math. Theor . 43 445305). We find the proofs of theorems 2 and 3 contain some errors and we also present an improved derivation to overcome this flaw. The alternative derivation shows that the main conclusions remain valid despite the invalidity of the proofs.

DOI
10.1088/1751-8121/aa9d04

Related papers

Monogamy of multi-qubit entanglement using Rényi entropy

Jeong San Kim, Barry C. Sanders

We introduce a class of bipartite entanglement measures based on Rényi-α entropy, namely Rényi-α entanglement with an analytic formula in two-qubit systems for α ⩾ 1. We also show that multi-qubit entanglement has a monogamy inequality in terms of Rényi-α entanglement for all α ⩾ 2.

arXiv:0911.5180•Journal of Physics A Mathematical and Theoretical•Oct 18, 2010•117 citations

Tighter Rényi- α entropy entanglement monogamy and polygamy relations of qubit systems

Wen Zhou, Zhong‐Xi Shen, Dong-Ping Xuan +2 more

Abstract The monogamy and polygamy relations characterize the distributions of quantum entanglement in multipartite systems. We investigate the monogamy relations related to the Rényi- α entanglement (R α E) and polygamy relations related to the R α E of assistance (R α EoA). We present new entanglement monogamy relations satisfied by the η -th ( η ≥ 2) power of R α E for α ≥ 2, and by the γ -th ( γ ≥ 4) power of R α E for 7 − 1 2 ≤ α < 2 , respectively. Moreover, we present polygamy relations satisfied by the t th power of R α EoA with 7 − 1 2 ≤ α < 13 − 1 2 for 0 ≤ t ≤ 1. We also give relationships among the residual entanglements of R α E and R α EoA, and the three tangle based on our general monogamy relations.

Communications in Theoretical Physics•Feb 27, 2026•0 citations

Comment on “Unification of multiqubit polygamy inequalities”

Wei Song, Junlong Zhao, Long-Bao Yu +1 more

Recently, Kim established a unified view of polygamy of multiqubit entanglement [Phys. Rev. A 85, 032335 (2012)]. In order to prove their main results, Kim first proposed an important property which is illustrated in Lemma 2. We point out that his proofs of Lemma 2 are flawed because of some errors in his derivations. Furthermore, we present an improved method to prove the original results.

Physical Review A•May 4, 2017•2 citations

General monogamy relation of multiqubit systems in terms of squared Rényi- α entanglement

Wei Song, Yan-Kui Bai, Mou Yang +2 more

We prove that the squared R\'enyi-$\ensuremath{\alpha}$ entanglement ($\mathrm{SR}\ensuremath{\alpha}\mathrm{E}$), which is the generalization of entanglement of formation, obeys a general monogamy inequality in an arbitrary $N$-qubit mixed state. Furthermore, for a class of R\'enyi-$\ensuremath{\alpha}$ entanglement, we prove that the monogamy relations of the $\mathrm{SR}\ensuremath{\alpha}\mathrm{E}$ have a hierarchical structure when the $N$-qubit system is divided into $k$ parties. As a by-product, the analytical relation between the R\'enyi-$\ensuremath{\alpha}$ entanglement and the squared concurrence is derived for bipartite $2\ensuremath{\bigotimes}d$ systems. Based on the monogamy properties of $\mathrm{SR}\ensuremath{\alpha}\mathrm{E}$, we can construct the corresponding multipartite entanglement indicators, which still work well even when the indicators based on the squared concurrence and EOF lose their efficacy. In addition, the monogamy property of the $\ensuremath{\mu}\mathrm{th}$ power of R\'enyi-$\ensuremath{\alpha}$ entanglement is analyzed.

arXiv:1512.02711•Physical Review A•Feb 3, 2016•60 citations

Tighter monogamy relations of multiqubit entanglement in terms of Rényi- α entanglement

Li-Min Gao, Feng-Li Yan, Ting Gao

Abstract We explore the existence of monogamy relations in terms of Rényi- α entanglement. By using the power of the Rényi- α entanglement, we establish a class of tight monogamy relations of multiqubit entanglement with larger lower bounds than the existing monogamy relations for α ≥ 2, the power η > 1, and 2 > α ≥ 7 − 1 2 , the power η > 2, respectively.

arXiv:1905.02952•Communications in Theoretical Physics•Jul 15, 2020•10 citations

Tighter constraints of multiqubit entanglement in terms of Rényi-α entropy*

Meng-Li Guo, Bo Li, Zhi-Xi Wang +1 more

Quantum entanglement plays essential roles in quantum information processing. The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems. We present a class of monogamy inequalities related to the μ-th power of the entanglement measure based on Rényi-α entropy, as well as polygamy relations in terms of the μ-th power of Rényi-α entanglement of assistance. These monogamy and polygamy relations are shown to be tighter than the existing ones.

arXiv:2006.08853•Chinese Physics B•Apr 29, 2020•8 citations
Abstract In an article in 2010, Kim et al introduced the definition of Rényi- α entanglement for bipartite quantum states and established an analytic formula of Rényi- α entanglement for arbitrary two-qubit states with α ⩾ 1 . They also derived a monogamy of entanglement in multi-qubit systems in terms of Rényi- α entanglement for α ⩾ 2 Kim et al (2010 J. Phys. A: Math. Theor . 43 445305). We find the proofs of theorems 2 and 3 contain some errors and we also present an improved derivation to overcome this flaw. The alternative derivation shows that the main conclusions remain valid despite the invalidity of the proofs.
Abstract The monogamy and polygamy relations characterize the distributions of quantum entanglement in multipartite systems. We investigate the monogamy relations related to the Rényi- α entanglement (R α E) and polygamy relations related to the R α E of assistance (R α EoA). We present new entanglement monogamy relations satisfied by the η -th ( η ≥ 2) power of R α E for α ≥ 2, and by the γ -th ( γ ≥ 4) power of R α E for 7 − 1 2 ≤ α < 2 , respectively. Moreover, we present polygamy relations satisfied by the t th power of R α EoA with 7 − 1 2 ≤ α < 13 − 1 2 for 0 ≤ t ≤ 1. We also give relationships among the residual entanglements of R α E and R α EoA, and the three tangle based on our general monogamy relations.
We prove that the squared R\'enyi-$\ensuremath{\alpha}$ entanglement ($\mathrm{SR}\ensuremath{\alpha}\mathrm{E}$), which is the generalization of entanglement of formation, obeys a general monogamy inequality in an arbitrary NNN-qubit mixed state. Furthermore, for a class of R\'enyi-$\ensuremath{\alpha}$ entanglement, we prove that the monogamy relations of the $\mathrm{SR}\ensuremath{\alpha}\mathrm{E}$ have a hierarchical structure when the NNN-qubit system is divided into kkk parties. As a by-product, the analytical relation between the R\'enyi-$\ensuremath{\alpha}$ entanglement and the squared concurrence is derived for bipartite $2\ensuremath{\bigotimes}d$ systems. Based on the monogamy properties of $\mathrm{SR}\ensuremath{\alpha}\mathrm{E}$, we can construct the corresponding multipartite entanglement indicators, which still work well even when the indicators based on the squared concurrence and EOF lose their efficacy. In addition, the monogamy property of the $\ensuremath{\mu}\mathrm{th}$ power of R\'enyi-$\ensuremath{\alpha}$ entanglement is analyzed.