dorsal/arxiv
View SchemaAnother dual formulation of the separability problem
| Authors | D. Salgado, J. L. Sanchez-Gomez, M. Ferrero |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509124 |
| URL | https://arxiv.org/abs/quant-ph/0509124 |
Abstract
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several inmediate consequences are analyzed: (i) a sufficient criterion for separability for bipartite quantum systems, (ii) a complete solution to the separability problem for pure states also of bipartite systems independent of the classical Schmidt decomposition method and (iii) a natural generalization of these results to multipartite systems.
{
"annotation_id": "5e60b3b9-5ba4-4410-89a3-29a2b4e33cff",
"date_created": "2026-03-02T18:02:20.470000Z",
"date_modified": "2026-03-02T18:02:20.470000Z",
"file_hash": "aec3de3f32521f7732c2358b6fa6b78b7377ff82c374232181cf96bb1241d6e6",
"private": false,
"record": {
"abstract": "We show how the separability problem is dual to that of decomposing any given\nmatrix into a conic combination of rank-one partial isometries, thus offering a\nduality approach different to the positive maps characterization problem.\nSeveral inmediate consequences are analyzed: (i) a sufficient criterion for\nseparability for bipartite quantum systems, (ii) a complete solution to the\nseparability problem for pure states also of bipartite systems independent of\nthe classical Schmidt decomposition method and (iii) a natural generalization\nof these results to multipartite systems.",
"arxiv_id": "quant-ph/0509124",
"authors": [
"D. Salgado",
"J. L. Sanchez-Gomez",
"M. Ferrero"
],
"categories": [
"quant-ph"
],
"title": "Another dual formulation of the separability problem",
"url": "https://arxiv.org/abs/quant-ph/0509124"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8bb44013-9063-4eaf-b63f-a0e5e407bd46",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}