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.

Authors:

  • Nathaniel Johnston
  • Everett Patterson

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Cite as:

  • N. Johnston and E. Patterson. The inverse eigenvalue problem for entanglement witnesses. E-print: arXiv:1708.05901 [quant-ph], 2017.

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