Characterizing entanglement with geometric entanglement witnesses

Abstract

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.

19 pages, 4 figures, some typos and notational errors corrected. To be published in J. Phys. A: Math. Theor

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Cited by in corpus (8)

• Entanglement detection
• Entanglement witnesses: construction, analysis and classification
• Geometry of the generalized Bloch sphere for qutrits
• Entanglement witnesses and geometry of entanglement of two--qutrit states
• Parametrizations of density matrices
• Building separable approximations for quantum states via neural networks
• A general dichotomization procedure to provide qudits entanglement criteria
• Universal entanglement detection with geometrically optimal witnesses