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arXiv · 1309.2006

Separability from Spectrum for Qubit-Qudit States

Nathaniel Johnston
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Abstract

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.

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Nathaniel Johnston. 2013-09-08. Separability from Spectrum for Qubit-Qudit States. https://doi.org/10.1103/physreva.88.062330

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