dorsal/arxiv
View SchemaSymmetric Informationally Complete Quantum Measurements
| Authors | Joseph M. Renes, Robin Blume-Kohout, A. J. Scott, Carlton M. Caves |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310075 |
| URL | https://arxiv.org/abs/quant-ph/0310075 |
| DOI | 10.1063/1.1737053 |
| Journal | J. Math. Phys. 45, 2171 (2004) |
Abstract
We consider the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal. Such a set is called a ``symmetric, informationally complete'' POVM (SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d. SIC-POVMs are relevant for quantum state tomography, quantum cryptography, and foundational issues in quantum mechanics. We construct SIC-POVMs in dimensions two, three, and four. We further conjecture that a particular kind of group-covariant SIC-POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
{
"annotation_id": "2f7d0bdf-6f5e-4fb5-bc02-bbbe02df9bc2",
"date_created": "2026-03-02T18:02:02.808000Z",
"date_modified": "2026-03-02T18:02:02.808000Z",
"file_hash": "54fa479e4f569e718a1c8e5307d2caeed43263dbf32b67c7ec7d8615cf2a291e",
"private": false,
"record": {
"abstract": "We consider the existence in arbitrary finite dimensions d of a POVM\ncomprised of d^2 rank-one operators all of whose operator inner products are\nequal. Such a set is called a ``symmetric, informationally complete\u0027\u0027 POVM\n(SIC-POVM) and is equivalent to a set of d^2 equiangular lines in C^d.\nSIC-POVMs are relevant for quantum state tomography, quantum cryptography, and\nfoundational issues in quantum mechanics. We construct SIC-POVMs in dimensions\ntwo, three, and four. We further conjecture that a particular kind of\ngroup-covariant SIC-POVM exists in arbitrary dimensions, providing numerical\nresults up to dimension 45 to bolster this claim.",
"arxiv_id": "quant-ph/0310075",
"authors": [
"Joseph M. Renes",
"Robin Blume-Kohout",
"A. J. Scott",
"Carlton M. Caves"
],
"categories": [
"quant-ph",
"cs.IT",
"math.FA",
"math.IT"
],
"doi": "10.1063/1.1737053",
"journal_ref": "J. Math. Phys. 45, 2171 (2004)",
"title": "Symmetric Informationally Complete Quantum Measurements",
"url": "https://arxiv.org/abs/quant-ph/0310075"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "0f4be0c6-fb71-47fa-b94a-d13adea8b3c2",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}