dorsal/arxiv
View SchemaElliptical orbits in the Bloch sphere
| Authors | A. Mandilara, J. W. Clark, M. S. Byrd |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503208 |
| URL | https://arxiv.org/abs/quant-ph/0503208 |
| DOI | 10.1088/1464-4266/7/10/011 |
Abstract
As is well known, when an SU(2) operation acts on a two-level system, its Bloch vector rotates without change of magnitude. Considering a system composed of two two-level systems, it is proven that for a class of nonlocal interactions of the two subsystems including \sigma_i\otimes\sigma_j (with i,j \in {x,y,z}) and the Heisenberg interaction, the geometric description of the motion is particularly simple: each of the two Bloch vectors follows an elliptical orbit within the Bloch sphere. The utility of this result is demonstrated in two applications, the first of which bears on quantum control via quantum interfaces. By employing nonunitary control operations, we extend the idea of controllability to a set of points which are not necessarily connected by unitary transformations. The second application shows how the orbit of the coherence vector can be used to assess the entangling power of Heisenberg exchange interaction.
{
"annotation_id": "a1f7e6e0-b085-4b60-afc0-bbd78a7418f3",
"date_created": "2026-03-02T18:02:17.155000Z",
"date_modified": "2026-03-02T18:02:17.155000Z",
"file_hash": "ec2180635a8c2c021da47af2f13b73ac619f85430e5a826d7383a2831a1e8aff",
"private": false,
"record": {
"abstract": "As is well known, when an SU(2) operation acts on a two-level system, its\nBloch vector rotates without change of magnitude. Considering a system composed\nof two two-level systems, it is proven that for a class of nonlocal\ninteractions of the two subsystems including \\sigma_i\\otimes\\sigma_j (with i,j\n\\in {x,y,z}) and the Heisenberg interaction, the geometric description of the\nmotion is particularly simple: each of the two Bloch vectors follows an\nelliptical orbit within the Bloch sphere. The utility of this result is\ndemonstrated in two applications, the first of which bears on quantum control\nvia quantum interfaces. By employing nonunitary control operations, we extend\nthe idea of controllability to a set of points which are not necessarily\nconnected by unitary transformations. The second application shows how the\norbit of the coherence vector can be used to assess the entangling power of\nHeisenberg exchange interaction.",
"arxiv_id": "quant-ph/0503208",
"authors": [
"A. Mandilara",
"J. W. Clark",
"M. S. Byrd"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1464-4266/7/10/011",
"title": "Elliptical orbits in the Bloch sphere",
"url": "https://arxiv.org/abs/quant-ph/0503208"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b5d9f30e-6ef7-4cc9-8696-b1d8d094ecad",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}