dorsal/arxiv
View SchemaClass of PPT bound entangled states associated to almost any set of pure entangled states
| Authors | M. Piani, C. Mora |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0607061 |
| URL | https://arxiv.org/abs/quant-ph/0607061 |
| DOI | 10.1103/PhysRevA.75.012305 |
| Journal | Phys. Rev. A 75, 012305 (2007) |
Abstract
We analyze a class of entangled states for bipartite $d \otimes d$ systems, with $d$ non-prime. The entanglement of such states is revealed by the construction of canonically associated entanglement witnesses. The structure of the states is very simple and similar to the one of isotropic states: they are a mixture of a separable and a pure entangled state whose supports are orthogonal. Despite such simple structure, in an opportune interval of the mixing parameter their entanglement is not revealed by partial transposition nor by the realignment criterion, i.e. by any permutational criterion in the bipartite setting. In the range in which the states are Positive under Partial Transposition (PPT), they are not distillable; on the other hand, the states in the considered class are provably distillable as soon as they are Nonpositive under Partial Transposition (NPT). The states are associated to any set of more than two pure states. The analysis is extended to the multipartite setting. By an opportune selection of the set of multipartite pure states, it is possible to construct mixed states which are PPT with respect to any choice of bipartite cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we show that every $k$-positive but not completely positive map is associated to a family of nondecomposable maps.
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"abstract": "We analyze a class of entangled states for bipartite $d \\otimes d$ systems,\nwith $d$ non-prime. The entanglement of such states is revealed by the\nconstruction of canonically associated entanglement witnesses. The structure of\nthe states is very simple and similar to the one of isotropic states: they are\na mixture of a separable and a pure entangled state whose supports are\northogonal. Despite such simple structure, in an opportune interval of the\nmixing parameter their entanglement is not revealed by partial transposition\nnor by the realignment criterion, i.e. by any permutational criterion in the\nbipartite setting. In the range in which the states are Positive under Partial\nTransposition (PPT), they are not distillable; on the other hand, the states in\nthe considered class are provably distillable as soon as they are Nonpositive\nunder Partial Transposition (NPT). The states are associated to any set of more\nthan two pure states. The analysis is extended to the multipartite setting. By\nan opportune selection of the set of multipartite pure states, it is possible\nto construct mixed states which are PPT with respect to any choice of bipartite\ncuts and nevertheless exhibit genuine multipartite entanglement. Finally, we\nshow that every $k$-positive but not completely positive map is associated to a\nfamily of nondecomposable maps.",
"arxiv_id": "quant-ph/0607061",
"authors": [
"M. Piani",
"C. Mora"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.012305",
"journal_ref": "Phys. Rev. A 75, 012305 (2007)",
"title": "Class of PPT bound entangled states associated to almost any set of pure entangled states",
"url": "https://arxiv.org/abs/quant-ph/0607061"
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