2013/09/08 by Nathaniel Johnston · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.88.062330
published as Phys. Rev. A 88, 062330 (2013) · 5 pages
arxiv created 2013/09/08 · arxiv updated 2014/01/17
The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states ρ with the property that U^*ρU 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 U^*ρU 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.