dorsal/arxiv
View SchemaGeometrical aspects of entanglement
| Authors | Jon Magne Leinaas, Jan Myrheim, Eirik Ovrum |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605079 |
| URL | https://arxiv.org/abs/quant-ph/0605079 |
| DOI | 10.1103/PhysRevA.74.012313 |
Abstract
We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a ``relativistic'' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and non-unitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability, and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.
{
"annotation_id": "d287a806-6d95-4b57-b8ca-4221032bffd6",
"date_created": "2026-03-02T18:02:26.594000Z",
"date_modified": "2026-03-02T18:02:26.594000Z",
"file_hash": "fade884bd1ea0cd3be69b0a9a7045139a145d09ea7feb374f5a29f07ffbbc159",
"private": false,
"record": {
"abstract": "We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm\ndefining the metric on the set of density matrices. We focus first on the\nsimplest case of two two-level systems and show that a ``relativistic\u0027\u0027\nformulation leads to a complete analysis of the question of separability. Our\napproach is based on Schmidt decomposition of density matrices for a composite\nsystem and non-unitary transformations to a standard form. The positivity of\nthe density matrices is crucial for the method to work. A similar approach\nworks to some extent in higher dimensions, but is a less powerful tool. We\nfurther present a numerical method for examining separability, and illustrate\nthe method by a numerical study of bound entanglement in a composite system of\ntwo three-level systems.",
"arxiv_id": "quant-ph/0605079",
"authors": [
"Jon Magne Leinaas",
"Jan Myrheim",
"Eirik Ovrum"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.012313",
"title": "Geometrical aspects of entanglement",
"url": "https://arxiv.org/abs/quant-ph/0605079"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8a56a173-5c43-44d6-a2ae-060c3ae21a55",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}