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:0901.4729 · Annals of Physics

Entanglement witnesses and geometry of entanglement of two-qutrit states

Reinhold A. Bertlmann, Philipp Krammer

Published Feb 13, 2009• 61 citations
arXivHTMLPDF
DOI
10.1016/j.aop.2009.01.008

Related papers

Two-qutrit entanglement witnesses and Gell-Mann matrices

M. A. Jafarizadeh, Y. Akbari, Naghi Behzadi

arXiv:0802.0270•The European Physical Journal D•Mar 13, 2008•11 citations

The geometry of bipartite qutrits including bound entanglement

Bernhard Baumgartner, Beatrix C. Hiesmayr, Heide Narnhofer

arXiv:0705.1403•Physics Letters A•Nov 20, 2007•76 citations

Entanglement and the geometry of two qubits

J.E. Avron, O. Kenneth

arXiv:0807.0212•Annals of Physics•Aug 18, 2008•32 citations

Geometry of Entanglement Witnesses for Two Qutrits

Dariusz Chruściński, Filip Wudarski

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 × 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parametrized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement witnesses parametrized by improper rotations from the orthogonal group O(2).

arXiv:1105.4821•Open Systems & Information Dynamics•Dec 1, 2011•18 citations

Characterizing entanglement with geometric entanglement witnesses

Philipp Krammer

We show how to detect entangled, bound entangled and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert–Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the 'magic simplex', i.e. the set of Bell-state mixtures of arbitrary dimension.

arXiv:0807.4830•Journal of Physics A Mathematical and Theoretical•Jan 15, 2009•13 citations

Geometry and Entanglement of Super-Qubit Quantum States

Oktay K. Pashaev, Aygül Koçak

arXiv:2410.04361•Springer proceedings in mathematics & statistics•Jan 1, 2025•0 citations
We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 × 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parametrized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement witnesses parametrized by improper rotations from the orthogonal group O(2).
We show how to detect entangled, bound entangled and separable bipartite quantum states of arbitrary dimension and mixedness using geometric entanglement witnesses. These witnesses are constructed using properties of the Hilbert–Schmidt geometry and can be shifted along parameterized lines. The involved conditions are simplified using Bloch decompositions of operators and states. As an example we determine the three different types of states for a family of two-qutrit states that is part of the 'magic simplex', i.e. the set of Bell-state mixtures of arbitrary dimension.