dorsal/arxiv
View SchemaAsymptotic Relative Entropy of Entanglement for Orthogonally Invariant States
| Authors | K. Audenaert, B. De Moor, K. G. H. Vollbrecht, R. F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204143 |
| URL | https://arxiv.org/abs/quant-ph/0204143 |
| DOI | 10.1103/PhysRevA.66.032310 |
| Journal | Phys. Rev. A 66, 032310 (2002) |
Abstract
For a special class of bipartite states we calculate explicitly the asymptotic relative entropy of entanglement $E_R^\infty$ with respect to states having a positive partial transpose (PPT). This quantity is an upper bound to distillable entanglement. The states considered are invariant under rotations of the form $O\otimes O$, where $O$ is any orthogonal matrix. We show that in this case $E_R^\infty$ is equal to another upper bound on distillable entanglement, constructed by Rains. To perform these calculations, we have introduced a number of new results that are interesting in their own right: (i) the Rains bound is convex and continuous; (ii) under some weak assumption, the Rains bound is an upper bound to $E_R^\infty$; (iii) for states for which the relative entropy of entanglement $E_R$ is additive, the Rains bound is equal to $E_R$.
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"abstract": "For a special class of bipartite states we calculate explicitly the\nasymptotic relative entropy of entanglement $E_R^\\infty$ with respect to states\nhaving a positive partial transpose (PPT). This quantity is an upper bound to\ndistillable entanglement. The states considered are invariant under rotations\nof the form $O\\otimes O$, where $O$ is any orthogonal matrix. We show that in\nthis case $E_R^\\infty$ is equal to another upper bound on distillable\nentanglement, constructed by Rains. To perform these calculations, we have\nintroduced a number of new results that are interesting in their own right: (i)\nthe Rains bound is convex and continuous; (ii) under some weak assumption, the\nRains bound is an upper bound to $E_R^\\infty$; (iii) for states for which the\nrelative entropy of entanglement $E_R$ is additive, the Rains bound is equal to\n$E_R$.",
"arxiv_id": "quant-ph/0204143",
"authors": [
"K. Audenaert",
"B. De Moor",
"K. G. H. Vollbrecht",
"R. F. Werner"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.032310",
"journal_ref": "Phys. Rev. A 66, 032310 (2002)",
"title": "Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant States",
"url": "https://arxiv.org/abs/quant-ph/0204143"
},
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