dorsal/arxiv
View SchemaThe laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states
| Authors | Samuel L. Braunstein, Sibasish Ghosh, Simone Severini |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406165 |
| URL | https://arxiv.org/abs/quant-ph/0406165 |
| DOI | 10.1007/s00026-006-0289-3 |
| Journal | Annals of Combinatorics, Volume 10, No 3, 2006 |
Abstract
We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graph on four vertices representing entangled states. It turns out that for some of these graphs the value of the concurrence is exactly fractional.
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"abstract": "We study entanglement properties of mixed density matrices obtained from\ncombinatorial Laplacians. This is done by introducing the notion of the density\nmatrix of a graph. We characterize the graphs with pure density matrices and\nshow that the density matrix of a graph can be always written as a uniform\nmixture of pure density matrices of graphs. We consider the von Neumann entropy\nof these matrices and we characterize the graphs for which the minimum and\nmaximum values are attained. We then discuss the problem of separability by\npointing out that separability of density matrices of graphs does not always\ndepend on the labelling of the vertices. We consider graphs with a tensor\nproduct structure and simple cases for which combinatorial properties are\nlinked to the entanglement of the state. We calculate the concurrence of all\ngraph on four vertices representing entangled states. It turns out that for\nsome of these graphs the value of the concurrence is exactly fractional.",
"arxiv_id": "quant-ph/0406165",
"authors": [
"Samuel L. Braunstein",
"Sibasish Ghosh",
"Simone Severini"
],
"categories": [
"quant-ph",
"math.CO"
],
"doi": "10.1007/s00026-006-0289-3",
"journal_ref": "Annals of Combinatorics, Volume 10, No 3, 2006",
"title": "The laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states",
"url": "https://arxiv.org/abs/quant-ph/0406165"
},
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