dorsal/arxiv
View SchemaSome families of density matrices for which separability is easily tested
| Authors | Samuel L. Braunstein, Sibasish Ghosh, Toufik Mansour, Simone Severini, Richard C. Wilson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508020 |
| URL | https://arxiv.org/abs/quant-ph/0508020 |
| DOI | 10.1103/PhysRevA.73.012320 |
| Journal | Phys. Rev. A 73, 012320 (2006) |
Abstract
We reconsider density matrices of graphs as defined in [quant-ph/0406165]. The density matrix of a graph is the combinatorial laplacian of the graph normalized to have unit trace. We describe a simple combinatorial condition (the "degree condition") to test separability of density matrices of graphs. The condition is directly related to the PPT-criterion. We prove that the degree condition is necessary for separability and we conjecture that it is also sufficient. We prove special cases of the conjecture involving nearest point graphs and perfect matchings. We observe that the degree condition appears to have value beyond density matrices of graphs. In fact, we point out that circulant density matrices and other matrices constructed from groups always satisfy the condition and indeed are separable with respect to any split. The paper isolates a number of problems and delineates further generalizations.
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"abstract": "We reconsider density matrices of graphs as defined in [quant-ph/0406165].\nThe density matrix of a graph is the combinatorial laplacian of the graph\nnormalized to have unit trace. We describe a simple combinatorial condition\n(the \"degree condition\") to test separability of density matrices of graphs.\nThe condition is directly related to the PPT-criterion. We prove that the\ndegree condition is necessary for separability and we conjecture that it is\nalso sufficient. We prove special cases of the conjecture involving nearest\npoint graphs and perfect matchings. We observe that the degree condition\nappears to have value beyond density matrices of graphs. In fact, we point out\nthat circulant density matrices and other matrices constructed from groups\nalways satisfy the condition and indeed are separable with respect to any\nsplit. The paper isolates a number of problems and delineates further\ngeneralizations.",
"arxiv_id": "quant-ph/0508020",
"authors": [
"Samuel L. Braunstein",
"Sibasish Ghosh",
"Toufik Mansour",
"Simone Severini",
"Richard C. Wilson"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.73.012320",
"journal_ref": "Phys. Rev. A 73, 012320 (2006)",
"title": "Some families of density matrices for which separability is easily tested",
"url": "https://arxiv.org/abs/quant-ph/0508020"
},
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