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:2407.03972

Entanglement Polygon Inequalities for A Class of Mixed States

Xian Shi

Published Jul 4, 2024• 0 citations
arXivHTMLPDF

Abstract

The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density matrices of generalized W-class states in multipartite higher dimensional systems. First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement, then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement. At last, we get an inequality for the mixed states, which can be regarded as a relation for bipartite entanglement.

DOI
10.48550/arxiv.2407.03972

Related papers

Entanglement polygon inequalities for a class of mixed states

Xian 现 Shi 石

Abstract The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density matrices of generalized W-class states in multipartite higher dimensional systems. First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement, then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement. At last, we get an inequality for the mixed states, which can be regarded as a relation for bipartite entanglement.

Chinese Physics B•Nov 1, 2024•0 citations

Entanglement polygon inequality in qudit systems

Xue Yang, Yan‐Han Yang, Ming‐Xing Luo

Entanglement is an important resource for quantum communication tasks. Most results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We first derive an entanglement polygon inequality for the $q$ concurrence, which manifests the relationship among all the ``one-to-group'' marginal entanglements in any multipartite qudit system. This implies lower and upper bounds for the marginal entanglement of any three-qudit system. We further extend our study to general entanglement distribution inequalities for high-dimensional entanglement in terms of the unified-$(r,s)$ entropy entanglement, including Tsallis entropy, R\'enyi entropy, and von Neumann entropy entanglement as special cases. These results provide insights into characterizing bipartite high-dimensional entanglement in quantum information processing.

arXiv:2205.08801•Physical Review A•Jun 2, 2022•21 citations

Tighter monogamy and polygamy relations based on the generalized W-class states

LI Bo, XIE Bing, ZHANG ZhanJun

Entanglement monogamy and polygamy are indispensable features of multipartite quantum systems that describe the entanglement distribution characteristics in these systems. Under the arbitrary partition of superposition of generalized W-class and vacuum states, we investigate a class of monogamy and polygamy inequality based on Tsallis-q and Rényi-q entropy entanglements. We show with concrete examples that parameter selection reduces these inequalities to some existing inequalities; that is, the existing inequalities can be considered a special case of this new class of inequality. Otherwise, these inequalities are tighter than existing ones and are finer representations of entanglement distributions in tripartite and multipartite quantum systems. The inequality of monogamy and polygamy established in this paper has wider applicability.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Oct 31, 2023•0 citations

Tighter Constraints of Multiqubit Entanglement*

Long-Mei 龙妹 Yang 杨, Bin 斌 Chen 陈, Shao-Ming 少明 Fei 费 +1 more

Abstract Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-q entanglement, and Rényi-α entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.

arXiv:1906.03571•Communications in Theoretical Physics•May 1, 2019•30 citations

Tighter constraints of multiqubit entanglement

Yang, L., Chen, B., Fei, S. +1 more

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-$q$ entanglement and R\'{e}nyi-$\alpha$ entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.

•Jan 1, 2019•14 citations

Optimized monogamy and polygamy inequalities for multipartite qubit entanglement*

Jiabin Zhang, Zhi‐Xiang Jin, Shao-Ming Fei +1 more

We investigate the monogamy and polygamy inequalities of arbitrary multipartite quantum states, and provide new classes of monogamy and polygamy inequalities of multiqubit entanglement in terms o f concurrence, entanglement of formation, negativity, and Tsallis- q entanglement, respectively. We show that these new monogamy and polygamy inequality relations are tighter than the existing ones with detailed examples.

Chinese Physics B•Mar 24, 2021•0 citations
The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density matrices of generalized W-class states in multipartite higher dimensional systems. First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement, then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement. At last, we get an inequality for the mixed states, which can be regarded as a relation for bipartite entanglement.
Abstract The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density matrices of generalized W-class states in multipartite higher dimensional systems. First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement, then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement. At last, we get an inequality for the mixed states, which can be regarded as a relation for bipartite entanglement.
Entanglement is an important resource for quantum communication tasks. Most results are focused on qubit entanglement. Our goal in this work is to characterize the multipartite high-dimensional entanglement. We first derive an entanglement polygon inequality for the qqq concurrence, which manifests the relationship among all the ``one-to-group'' marginal entanglements in any multipartite qudit system. This implies lower and upper bounds for the marginal entanglement of any three-qudit system. We further extend our study to general entanglement distribution inequalities for high-dimensional entanglement in terms of the unified-(r,s)(r,s)(r,s) entropy entanglement, including Tsallis entropy, R\'enyi entropy, and von Neumann entropy entanglement as special cases. These results provide insights into characterizing bipartite high-dimensional entanglement in quantum information processing.
Entanglement monogamy and polygamy are indispensable features of multipartite quantum systems that describe the entanglement distribution characteristics in these systems. Under the arbitrary partition of superposition of generalized W-class and vacuum states, we investigate a class of monogamy and polygamy inequality based on Tsallis-q and Rényi-q entropy entanglements. We show with concrete examples that parameter selection reduces these inequalities to some existing inequalities; that is, the existing inequalities can be considered a special case of this new class of inequality. Otherwise, these inequalities are tighter than existing ones and are finer representations of entanglement distributions in tripartite and multipartite quantum systems. The inequality of monogamy and polygamy established in this paper has wider applicability.
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We provide classes of monogamy and polygamy inequalities of multiqubit entanglement in terms of concurrence, entanglement of formation, negativity, Tsallis-qqq entanglement and R\'{e}nyi-α\alphaα entanglement, respectively. We show that these inequalities are tighter than the existing ones for some classes of quantum states.