Schmidt number witnesses and bound entanglement
By Anna Sanpera, D. Bruß, Maciej Lewenstein. 2000
195 citations recorded by the source corpus.
The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. Finally, we present strong evidence that all bound entangled states with positive partial transpose in ${\mathcal{C}}^{3}\ensuremath{\bigotimes}{\mathcal{C}}^{3}$ have Schmidt number 2.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/b837dace56c78408d1726edb04d8b3df14f03c16
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In Artificial Intelligence
In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Entanglement certification from theory to experiment (2018, background): “[144] Anna Sanpera, Dagmar Bruß, and Maciej Lewenstein, “Schmidt-number witnesses and bound entanglement,” Phys.”
- Entanglement detection (2008, background): “11 This follows from the fact that the witnessW = 1/d − |ψ〉〈ψ |, where |ψ〉 is maximally entangled, does not detect NPT states [146], combined with an argument as in Theorem 3 of Ref.”