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:1102.5402 · Communications in Theoretical Physics

Three-Tangle for High-Rank Mixed States

Shu-Juan He, Xiaohong Wang, Shao-Ming Fei, Hongxiang Sun, Qiaoyan Wen

Published Feb 1, 2011• 16 citations
arXivHTMLPDF

Abstract

A family of rank-n (n = 5,6,7,8) three-qubit mixed states are constructed. The explicit expressions for the three-tangle and optimal decompositions for all these states are given. The CKW relations for these states are also discussed.
DOI
10.1088/0253-6102/55/2/12

Related papers

Three-Tangle for High-Rank Mixed States

何淑娟, 王晓红, 费少明 +1 more

rank-n 的一个家庭(n = 5,6,7,8 ) three-qubit 混合了状态被构造。为为所有这些状态的三混乱、最佳的分解的明确的表情被给。为这些状态的 CKW 关系也被讨论。

理论物理通讯：英文版•Jan 1, 2011•0 citations

Three-tangle for mixtures of generalized GHZ and generalized W states

C Eltschka, A Osterloh, J Siewert +1 more

We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized Greenberger–Horne–Zeilinger (GHZ) state, a |000⟩+ b |111⟩, and a generalized W state, c |001⟩+ d |010⟩+ f |100⟩. Using the methods introduced by Lohmayer et al (2006 Phys. Rev. Lett. 97 260502), we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case, we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state.

arXiv:0711.4477•New Journal of Physics•Apr 10, 2008•83 citations

Three-tangle for rank-three mixed states: Mixture of Greenberger-Horne-Zeilinger, W , and flipped- W states

Eylee Jung, Mi-Ra Hwang, DaeKil Park +1 more

Three-tangle for a rank-3 mixture composed of Greenberger-Horne-Zeilinger, $W$, and flipped-$W$ states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere ${S}^{8}$ of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.

arXiv:0810.5403•Physical Review A•Feb 11, 2009•48 citations

Three-tangle for mixtures of generalized GHZ and generalized W states

Christopher Eltschka, Andreas Osterloh, Jens Siewert +1 more

We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized Greenberger-Horne-Zeilinger (GHZ) state, a vertical bar 000 > + b vertical bar 111 >, and a generalized W state, c vertical bar 001 > + d vertical bar 010 > + f vertical bar 100 >. Using the methods introduced by Lohmayer et al (2006 Phys. Rev. Lett. 97 260502), we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case, we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state.

•Jan 1, 2008•44 citations

Entangled multi-qubit states without higher-tangle

Heng Fan, Yong-Cheng Ou, Vwani Roychowdhury

We analyze mixed multi-qubit states composed of a W class state and a product state with all qubit in |0>. We find the optimal pure state decomposition and convex roofs for higher-tangle with bipartite partition between one qubit and the rest qubits for those mixed states. The optimality of the decomposition is ensured by the Coffman-Kundu-Wootters (CKW) inequality which describes the monogamy of quantum entanglement. The generalized monogamy inequality is found to be true for W class states with arbitrary partitions between one qubit and multi-qubit.

arXiv:0707.1578•Jul 11, 2007•3 citations

Entangled Three-Qubit States without Concurrence and Three-Tangle

Robert Lohmayer, Andreas Osterloh, Jens Siewert +1 more

We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this "monogamy" can be lifted for mixed states by virtue of vanishing tangle measures.

arXiv:quant-ph/0606071•Physical Review Letters•Dec 29, 2006•187 citations
We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized Greenberger–Horne–Zeilinger (GHZ) state, a |000⟩+ b |111⟩, and a generalized W state, c |001⟩+ d |010⟩+ f |100⟩. Using the methods introduced by Lohmayer et al (2006 Phys. Rev. Lett. 97 260502), we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case, we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state.
Three-tangle for a rank-3 mixture composed of Greenberger-Horne-Zeilinger, WWW, and flipped-WWW states is analytically calculated. The optimal decompositions in the full range of parameter space are constructed by making use of the convex-roof extension. We also provide an analytical technique, which determines whether or not an arbitrary rank-3 state has vanishing three-tangle. This technique is developed by making use of the Bloch sphere S8{S}^{8}S8 of the qutrit system. The Coffman-Kundu-Wootters inequality is discussed by computing one-tangle and concurrences. It is shown that the one-tangle is always larger than the sum of squared concurrences and three-tangle. The physical implication of three-tangle is briefly discussed.
We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized Greenberger-Horne-Zeilinger (GHZ) state, a vertical bar 000 > + b vertical bar 111 >, and a generalized W state, c vertical bar 001 > + d vertical bar 010 > + f vertical bar 100 >. Using the methods introduced by Lohmayer et al (2006 Phys. Rev. Lett. 97 260502), we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case, we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state.
We analyze mixed multi-qubit states composed of a W class state and a product state with all qubit in |0>. We find the optimal pure state decomposition and convex roofs for higher-tangle with bipartite partition between one qubit and the rest qubits for those mixed states. The optimality of the decomposition is ensured by the Coffman-Kundu-Wootters (CKW) inequality which describes the monogamy of quantum entanglement. The generalized monogamy inequality is found to be true for W class states with arbitrary partitions between one qubit and multi-qubit.
We provide a complete analysis of mixed three-qubit states composed of a Greenberger-Horne-Zeilinger state and a W state orthogonal to the former. We present optimal decompositions and convex roofs for the three-tangle. Further, we provide an analytical method to decide whether or not an arbitrary rank-2 state of three qubits has vanishing three-tangle. These results highlight intriguing differences compared to the properties of two-qubit mixed states, and may serve as a quantitative reference for future studies of entanglement in multipartite mixed states. By studying the Coffman-Kundu-Wootters inequality we find that, while the amounts of inequivalent entanglement types strictly add up for pure states, this "monogamy" can be lifted for mixed states by virtue of vanishing tangle measures.