dorsal/arxiv
View SchemaPhysical realizations of quantum operations
| Authors | F. Buscemi, G. M. D'Ariano, M. F. Sacchi |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305180 |
| URL | https://arxiv.org/abs/quant-ph/0305180 |
| DOI | 10.1103/PhysRevA.68.042113 |
| Journal | Phys. Rev. A 68, 042113 (2003) |
Abstract
Quantum operations (QO) describe any state change allowed in quantum mechanics, such as the evolution of an open system or the state change due to a measurement. We address the problem of which unitary transformations and which observables can be used to achieve a QO with generally different input and output Hilbert spaces. We classify all unitary extensions of a QO, and give explicit realizations in terms of free-evolution direct-sum dilations and interacting tensor-product dilations. In terms of Hilbert space dimensionality the free-evolution dilations minimize the physical resources needed to realize the QO, and for this case we provide bounds for the dimension of the ancilla space versus the rank of the QO. The interacting dilations, on the other hand, correspond to the customary ancilla-system interaction realization, and for these we derive a majorization relation which selects the allowed unitary interactions between system and ancilla.
{
"annotation_id": "fff26c4c-94e8-4fea-b8c2-1490d783644a",
"date_created": "2026-03-02T18:02:00.141000Z",
"date_modified": "2026-03-02T18:02:00.141000Z",
"file_hash": "7c7f56d1682ee1e69faa05858648ecce2f270ac9cf332b916e1982aa7e25cde9",
"private": false,
"record": {
"abstract": "Quantum operations (QO) describe any state change allowed in quantum\nmechanics, such as the evolution of an open system or the state change due to a\nmeasurement. We address the problem of which unitary transformations and which\nobservables can be used to achieve a QO with generally different input and\noutput Hilbert spaces. We classify all unitary extensions of a QO, and give\nexplicit realizations in terms of free-evolution direct-sum dilations and\ninteracting tensor-product dilations. In terms of Hilbert space dimensionality\nthe free-evolution dilations minimize the physical resources needed to realize\nthe QO, and for this case we provide bounds for the dimension of the ancilla\nspace versus the rank of the QO. The interacting dilations, on the other hand,\ncorrespond to the customary ancilla-system interaction realization, and for\nthese we derive a majorization relation which selects the allowed unitary\ninteractions between system and ancilla.",
"arxiv_id": "quant-ph/0305180",
"authors": [
"F. Buscemi",
"G. M. D\u0027Ariano",
"M. F. Sacchi"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.68.042113",
"journal_ref": "Phys. Rev. A 68, 042113 (2003)",
"title": "Physical realizations of quantum operations",
"url": "https://arxiv.org/abs/quant-ph/0305180"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ae7a8f13-2664-4948-ba1b-05cf40e58e05",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}