Tangles of superpositions and the convex-roof extension

Abstract

We discuss aspects of the convex-roof extension of multipartite entanglement measures, that is, $SL(2,\CC)$ invariant tangles. We highlight two key concepts that contain valuable information about the tangle of a density matrix: the {\em zero-polytope} is a convex set of density matrices with vanishing tangle whereas the {\em convex characteristic curve} readily provides a non-trivial lower bound for the convex roof and serves as a tool for constructing the convex roof outside the zero-polytope. Both concepts are derived from the tangle for superpositions of the eigenstates of the density matrix. We illustrate their application by considering examples of density matrices for two-qubit and three-qubit states of rank 2, thereby pointing out both the power and the limitations of the concepts.

arXiv comment7 pages, 5 figures, revtex4

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Cited by in corpus (39)

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• A new parameterized entanglement monotone
• Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• Geometry of entanglement in the Bloch sphere
• Rescaling multipartite entanglement measures for mixed states
• Entanglement in a class of multiqubit mixed states without multipartite tangles
• Practical method to obtain a lower bound to the three-tangle
• Estimating multipartite entanglement measures
• Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
• Invariant-based entanglement monotones as expectation values and their experimental detection
• Three-tangle for high-rank mixed states
• Quantifying genuine tripartite entanglement by reshaping the state
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