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Open Quantum Systems Decoherence Entanglement Theory Quantum Correlations

Separability from Spectrum for Qubit-Qudit States

arXiv
Authors: Nathaniel Johnston

Year

2013

Paper ID

32836

Status

Preprint

Abstract Read

~2 min

Abstract Words

116

Citations

N/A

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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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1309.2006 [2] arXiv https://arxiv.org/abs/1309.2006 [3] Publisher https://arxiv.org/abs/1309.2006

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