  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.

Quantum Physics