dorsal/arxiv
View SchemaDissipative "Groups" and the Bloch Ball
| Authors | Allan I. Solomon, Sonia G. Schirmer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211027 |
| URL | https://arxiv.org/abs/quant-ph/0211027 |
| Journal | Group 24: Physical and Mathematical Aspects of Symmetry, Institute of Physics Conference Series 173, p. 485 (2003) |
Abstract
We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball.
{
"annotation_id": "8dfc293f-d3d6-44db-af7f-948cdb14cb86",
"date_created": "2026-03-02T18:01:55.732000Z",
"date_modified": "2026-03-02T18:01:55.732000Z",
"file_hash": "3c844e80639691972ad121cb285292da06d9ee4c43e12ecaf5bdbfc2d2ed4cf9",
"private": false,
"record": {
"abstract": "We show that a quantum control procedure on a two-level system including\ndissipation gives rise to a semi-group corresponding to the Lie algebra\nsemi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the\naction of this semi-group on a 3-vector as it moves inside the Bloch sphere, in\nthe Bloch ball.",
"arxiv_id": "quant-ph/0211027",
"authors": [
"Allan I. Solomon",
"Sonia G. Schirmer"
],
"categories": [
"quant-ph"
],
"journal_ref": "Group 24: Physical and Mathematical Aspects of Symmetry, Institute\n of Physics Conference Series 173, p. 485 (2003)",
"title": "Dissipative \"Groups\" and the Bloch Ball",
"url": "https://arxiv.org/abs/quant-ph/0211027"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "796932cf-ac46-4929-879f-aea85f6f486d",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}