The Inverse Eigenvalue Problem for Entanglement Witnesses
arXiv:1708.05901 · doi:10.1016/j.laa.2018.03.043
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.
arXiv comment24 pages, comments welcome
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- Perturbative expansion of entanglement negativity using patterned matrix calculus
- Bounds on mixed state entanglement
- Sharing EPR steering between sequential pairs of observers
- Nonequivalence between absolute separability and positive partial transposition in the symmetric subspace
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- On the extreme points of sets of absolulely separable and PPT states
- Decomposable Pauli diagonal maps and Tensor Squares of Qubit Maps
- Effective criteria for entanglement witnesses in small dimensions
- The detection power of real entanglement witnesses under local unitary equivalence
- Spectral characterizations of entanglement witnesses
- Quantum Information Approaches to Quantum Gravity