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arXiv · 1708.05901

The Inverse Eigenvalue Problem for Entanglement Witnesses

Nathaniel Johnston·Everett Patterson
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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.

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Nathaniel Johnston, Everett Patterson. 2017-08-19. The Inverse Eigenvalue Problem for Entanglement Witnesses. https://doi.org/10.1016/j.laa.2018.03.043

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