dorsal/arxiv
View SchemaOn PSI-complete and PSIR-complete measurements
| Authors | J. Finkelstein |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407078 |
| URL | https://arxiv.org/abs/quant-ph/0407078 |
| DOI | 10.1103/PhysRevA.70.052107 |
| Journal | Phys. Rev. A 70, 052107 (2004). |
Abstract
I construct a POVM which has 2d rank-one elements and which is informationally complete for generic pure states in d dimensions, thus confirming a conjecture made by Flammia, Silberfarb, and Caves (quant-ph/0404137). I show that if a rank-one POVM is required to be informationally complete for all pure states in d dimensions, it must have at least 3d-2 elements. I also show that, in a POVM which is informationally complete for all pure states in d dimensions, for any vector there must be at least 2d-1 POVM elements which do not annihilate that vector.
{
"annotation_id": "862b7a35-e427-49fd-a12b-3065ec5f6dea",
"date_created": "2026-03-02T18:02:10.296000Z",
"date_modified": "2026-03-02T18:02:10.296000Z",
"file_hash": "b67166bd8a233631a4967a0c6f7064b588ac15cd9f8bfe51c67eced50d50395a",
"private": false,
"record": {
"abstract": "I construct a POVM which has 2d rank-one elements and which is\ninformationally complete for generic pure states in d dimensions, thus\nconfirming a conjecture made by Flammia, Silberfarb, and Caves\n(quant-ph/0404137). I show that if a rank-one POVM is required to be\ninformationally complete for all pure states in d dimensions, it must have at\nleast 3d-2 elements. I also show that, in a POVM which is informationally\ncomplete for all pure states in d dimensions, for any vector there must be at\nleast 2d-1 POVM elements which do not annihilate that vector.",
"arxiv_id": "quant-ph/0407078",
"authors": [
"J. Finkelstein"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.70.052107",
"journal_ref": "Phys. Rev. A 70, 052107 (2004).",
"title": "On PSI-complete and PSIR-complete measurements",
"url": "https://arxiv.org/abs/quant-ph/0407078"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "94e778c9-cc6b-43fa-b611-ecdae432964a",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}