Separability from Spectrum for Qubit-Qudit States
The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states with the property that is separable for all unitary matrices U. This problem has been solved when the local dimensions m and n satisfy m = 2 and n ≤ 3. We solve all remaining qubit–qudit cases (i.e., when m = 2 and n ≥ 4 is arbitrary). In all of these cases we show that a state is separable from spectrum if and only if has positive partial transpose for all unitary matrices U. This equivalence is in stark contrast with the usual separability problem, where a state having positive partial transpose is a strictly weaker property than it being separable.
- Nathaniel Johnston
- Official publication from Physical Review A
- Preprint from arXiv:1309.2006 [quant-ph]
- Local preprint [pdf]
- Slideshow presentation (short version) [pdf]
- Slideshow presentation (long version) [PowerPoint .ppt]
- N. Johnston. Separability from spectrum for qubit–qudit states. Physical Review A, 88:062330, 2013.
- Is absolute separability determined by the partial transpose? – a paper that considers the same problem in systems with arbitrary local dimensions