dorsal/arxiv
View SchemaBloch Equations and Completely Positive Maps
| Authors | Sonja Daffer, Krzysztof Wodkiewicz, John K. McIver |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401177 |
| URL | https://arxiv.org/abs/quant-ph/0401177 |
| DOI | 10.1080/09500340408232495 |
| Journal | J. Mod. Optics 51, 1843 (2004) |
Abstract
The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and colored stochastic noise.
{
"annotation_id": "111d8933-2ae6-414f-8497-6d9c36e11a75",
"date_created": "2026-03-02T18:02:06.865000Z",
"date_modified": "2026-03-02T18:02:06.865000Z",
"file_hash": "2c866ab5bd9435d0e3fa17ed2e52e1a96286d4ded0edbe4d462352e35feb726e",
"private": false,
"record": {
"abstract": "The phenomenological dissipation of the Bloch equations is reexamined in the\ncontext of completely positive maps. Such maps occur if the dissipation arises\nfrom a reduction of a unitary evolution of a system coupled to a reservoir. In\nsuch a case the reduced dynamics for the system alone will always yield\ncompletely positive maps of the density operator. We show that, for Markovian\nBloch maps, the requirement of complete positivity imposes some Bloch\ninequalities on the phenomenological damping constants. For non-Markovian Bloch\nmaps some kind of Bloch inequalities involving eigenvalues of the damping basis\ncan be established as well. As an illustration of these general properties we\nuse the depolarizing channel with white and colored stochastic noise.",
"arxiv_id": "quant-ph/0401177",
"authors": [
"Sonja Daffer",
"Krzysztof Wodkiewicz",
"John K. McIver"
],
"categories": [
"quant-ph"
],
"doi": "10.1080/09500340408232495",
"journal_ref": "J. Mod. Optics 51, 1843 (2004)",
"title": "Bloch Equations and Completely Positive Maps",
"url": "https://arxiv.org/abs/quant-ph/0401177"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "d327cd48-4bfc-463c-831a-6cd9409ead65",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}