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:0908.3679 · Applied Physics B

Separability criteria and entanglement witnesses for symmetric quantum states

Géza Tóth, Otfried Gühne

Published Dec 10, 2009• 44 citations
arXivHTMLPDF
DOI
10.1007/s00340-009-3839-7

Related papers

Entanglement witness criteria of strong-k-separability for multipartite quantum states

Siqing Yan, Jinchuan Hou

Quantum Information Processing•Jun 11, 2018•1 citation

Concrete Representation and Separability Criteria for Symmetric Quantum State

Chang’e Li, Yuan-Hong Tao, Jun Ping Zhang +2 more

International Journal of Theoretical Physics•May 16, 2014•1 citation

Entanglement criteria and full separability of multi-qubit quantum states

Otfried Gühne

arXiv:1009.3782•Physics Letters A•Nov 14, 2010•40 citations

Quantum entanglement estimation via symmetric-measurement-based positive maps

Jiaxin Li, Hongmei Yao, Shao-Ming Fei +2 more

We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, and the lower bounds of concurrence. We show by detailed examples that our separability criteria, entanglement witnesses, and lower bounds can detect and estimate the quantum entanglement better than existing related results.

arXiv:2405.11741•Physical Review A•May 15, 2024•11 citations

Precise detection of multipartite entanglement in four-qubit Greenberger–Horne–Zeilinger diagonal states

Xiao-Yu Chen, Li-Zhen Jiang, Zhu-An Xu

We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.

arXiv:1808.00368•Frontiers of Physics•Sep 12, 2018•16 citations

Separability criteria and entanglement witnesses from mutually unbiased equiangular tight frames

Alexey E. Rastegin

Abstract Methods of quantum information processing often appear in terms of specially selected states. For example, mutually unbiased bases (MUBs) and symmetric informationally complete measurements are widely applied. Finite frames have found use in many areas including quantum information. Due to its specific inner structure, a single equiangular tight frame (ETF) allows one to formulate criteria to detect non-classical correlations. This study aims to approach entanglement detection with the use of mutually unbiased ETFs. Such frames are an interesting generalization of widely recognized MUBs. It still uses rank-one operators, but the number of outcomes can exceed the dimensionality. Several approaches are considered including separability criteria and entanglement witnesses. Separability criteria for multipartite systems are finally obtained.

Communications in Theoretical Physics•Sep 24, 2025•4 citations
We propose a method of constructing the separability criteria for multipartite quantum states on the basis of entanglement witnesses. The entanglement witnesses are obtained by finding the maximal expectation values of Hermitian operators and then optimizing over all possible Hermitian operators. We derive a set of tripartite separability criteria for the four-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal states. The derived criterion set contains four criteria that are necessary and sufficient for the tripartite separability of the highly symmetric four-qubit GHZ diagonal states; the criteria completely account for the numerically obtained boundaries of the tripartite separable state set. One of the criteria is just the tripartite separability criterion of the four-qubit generalized Werner states.
Abstract Methods of quantum information processing often appear in terms of specially selected states. For example, mutually unbiased bases (MUBs) and symmetric informationally complete measurements are widely applied. Finite frames have found use in many areas including quantum information. Due to its specific inner structure, a single equiangular tight frame (ETF) allows one to formulate criteria to detect non-classical correlations. This study aims to approach entanglement detection with the use of mutually unbiased ETFs. Such frames are an interesting generalization of widely recognized MUBs. It still uses rank-one operators, but the number of outcomes can exceed the dimensionality. Several approaches are considered including separability criteria and entanglement witnesses. Separability criteria for multipartite systems are finally obtained.