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

Quantum Information Processing

Concurrence vectors of multipartite states based on coefficient matrices

Yi Huang, Daowen Qiu

Published May 19, 2011• 7 citations
Publisher
DOI
10.1007/s11128-011-0247-9

Related papers

Concurrence of Rank-two Multipartite Quantum States

Joonwoo Bae

한국광학회지•Jan 1, 2018•1 citation

Multipartite concurrence of W-class states based on sub-partite quantum systems

Wei Chen, Yanmin Yang, Shao-Ming Fei +2 more

arXiv:2212.07806•Quantum Information Processing•Sep 8, 2023•0 citations

A multipartite entanglement measure based on coefficient matrices

Chao Zhao, Guowu Yang, William N. N. Hung +1 more

Quantum Information Processing•May 15, 2015•12 citations

M-Flip Concurrence in the Framework of Multipartite Spin Coherent States

A. Chafik, K. Berrada, Hichem Eleuch +1 more

Journal of Computational and Theoretical Nanoscience•Aug 22, 2014•0 citations

Mathematical framework for describing multipartite entanglement in terms of rows or columns of coefficient matrices

Yi Huang, Huapeng Yu, Fang Miao +2 more

In this paper, we develop a mathematical framework for describing entanglement quantitatively and qualitatively for multipartite qudit states in terms of rows or columns of coefficient matrices. More specifically, we propose an entanglement measure and separability criteria based on rows or columns of coefficient matrices. This entanglement measure has an explicit mathematical expression by means of exterior products of all pairs of rows or columns in coefficient matrices. It is introduced via our result that the [Formula: see text]-concurrence coincides with the entanglement measure based on two-by-two minors of coefficient matrices. Depending on our entanglement measure, we obtain the separability criteria and maximal entanglement criteria in terms of rows or columns of coefficient matrices. Our conclusions show that just like every two-by-two minor in a coefficient matrix of a multipartite pure state, every pair of rows or columns can also exhibit its entanglement properties, and thus can be viewed as its smallest entanglement contribution unit too. The great merit of our entanglement measure and separability criteria is two-fold. First, they are very practical and convenient for computation compared to other methods. Second, they have clear geometric interpretations.

International Journal of Quantum Information•Dec 13, 2021•2 citations

Concurrence vectors in arbitrary multipartite quantum systems

Seyed Javad Akhtarshenas

For a given pure state of a multipartite system, the concurrence vector is defined by employing the defining representation of generators of the corresponding rotation groups. The norm of a concurrence vector is considered as a measure of entanglement. For the multipartite pure state, the concurrence vector is regarded as the direct sum of concurrence subvectors in the sense that each subvector is associated with a pair of particles. It is proposed to use the norm of each subvector as the contribution of the corresponding pair in entanglement of the system.

arXiv:quant-ph/0311166•Journal of Physics A Mathematical and General•Jul 13, 2005•84 citations
In this paper, we develop a mathematical framework for describing entanglement quantitatively and qualitatively for multipartite qudit states in terms of rows or columns of coefficient matrices. More specifically, we propose an entanglement measure and separability criteria based on rows or columns of coefficient matrices. This entanglement measure has an explicit mathematical expression by means of exterior products of all pairs of rows or columns in coefficient matrices. It is introduced via our result that the [Formula: see text]-concurrence coincides with the entanglement measure based on two-by-two minors of coefficient matrices. Depending on our entanglement measure, we obtain the separability criteria and maximal entanglement criteria in terms of rows or columns of coefficient matrices. Our conclusions show that just like every two-by-two minor in a coefficient matrix of a multipartite pure state, every pair of rows or columns can also exhibit its entanglement properties, and thus can be viewed as its smallest entanglement contribution unit too. The great merit of our entanglement measure and separability criteria is two-fold. First, they are very practical and convenient for computation compared to other methods. Second, they have clear geometric interpretations.
For a given pure state of a multipartite system, the concurrence vector is defined by employing the defining representation of generators of the corresponding rotation groups. The norm of a concurrence vector is considered as a measure of entanglement. For the multipartite pure state, the concurrence vector is regarded as the direct sum of concurrence subvectors in the sense that each subvector is associated with a pair of particles. It is proposed to use the norm of each subvector as the contribution of the corresponding pair in entanglement of the system.