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High-Dimensional Entanglement in States with Positive Partial Transposition. (arXiv:1802.04975v1 [quant-ph])
来源于:arXiv
Genuine high-dimensional entanglement, i.e. the property of having a high
Schmidt number, constitutes a resource in quantum communication, overcoming
limitations of low-dimensional systems. States with a positive partial
transpose (PPT), on the other hand, are generally considered weakly entangled,
as they can never be distilled into pure entangled states. This naturally
raises the question, whether high Schmidt numbers are possible for PPT states.
Volume estimates suggest that optimal, i.e. linear, scaling in local dimension
should be possible, albeit without providing an insight into the possible
slope. We provide the first explicit construction of a family of PPT states
that achieves linear scaling in local dimension and we prove that random PPT
states typically share this feature. Our construction also allows us to answer
a recent question by Chen et al. on the existence of PPT states whose Schmidt
number increases by an arbitrarily large amount upon partial transposition.
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