The Inverse Eigenvalue Problem for Entanglement Witnesses

Abstract

We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely solve this problem in the two-qubit case and we derive a large family of new necessary conditions on the spectra in arbitrary dimensions. We also establish a natural duality relationship with the set of absolutely separable states, and we completely characterize witnesses (i.e., separating hyperplanes) of that set when one of the local dimensions is 2.

24 pages, comments welcome

References in corpus (4)

• Entanglement detection
• Geometry of sets of quantum maps: a generic positive map acting on a high-dimensional system is not completely positive
• Spectral properties of entanglement witnesses
• Norms and Cones in the Theory of Quantum Entanglement

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• Quantum Information Approaches to Quantum Gravity