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

Chinese Physics B

Entanglement polygon inequalities for a class of mixed states

Xian 现 Shi 石

Published Nov 1, 2024• 0 citations
Publisher

Abstract

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
10.1088/1674-1056/ad8eb0

Related papers

Entanglement Polygon Inequalities for A Class of Mixed States

Xian Shi

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.

arXiv:2407.03972•Jul 4, 2024•0 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

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 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 monogamy and polygamy relations for a superposition of the generalized W -class state and vacuum

Le-Min Lai, Shao-Ming Fei, Zhi-Xi Wang

Abstract Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized W -class state and vacuum in terms of the Tsallis- q entanglement and the Rényi- α entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.

arXiv:2109.11272•Journal of Physics A Mathematical and Theoretical•Sep 7, 2021•6 citations

Polygamy relations of multipartite entanglement beyond qubits

Zhi-Xiang Jin, Shao-Ming Fei

Abstract We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the th power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the th ( ) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.

arXiv:1903.11350•Journal of Physics A Mathematical and Theoretical•Mar 12, 2019•5 citations
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.
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 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.
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.
Abstract Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized W -class state and vacuum in terms of the Tsallis- q entanglement and the Rényi- α entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions.
Abstract We investigate the polygamy relations related to the concurrence of assistance for any multipartite pure states. General polygamy inequalities given by the th power of concurrence of assistance is first presented for multipartite pure states in arbitrary-dimensional quantum systems. We further show that the general polygamy inequalities can even be improved to be tighter inequalities under certain conditions on the assisted entanglement of bipartite subsystems. Based on the improved polygamy relations, lower bound for distribution of bipartite entanglement is provided in a multipartite system. Moreover, the th ( ) power of polygamy inequalities are obtained for the entanglement of assistance as a by-product, which are shown to be tighter than the existing ones. A detailed example is presented.