dorsal/arxiv
View SchemaEquiangular lines, mutually unbiased bases, and spin models
| Authors | Chris Godsil, Aidan Roy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511004 |
| URL | https://arxiv.org/abs/quant-ph/0511004 |
| DOI | 10.1016/j.ejc.2008.01.002 |
| Journal | European Journal of Combinatorics 30 (2009), pp. 246--262 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters (k,n,k,l) we construct sets of n+1 mutually unbiased bases in C^k. We show how to construct these difference sets from commutative semifields and that several known maximal sets of mutually unbiased bases can be obtained in this way, resolving a conjecture about the monomiality of maximal sets. We also relate mutually unbiased bases to spin models.
{
"annotation_id": "e661da22-5576-4da3-b58c-dde7b0cba2ec",
"date_created": "2026-03-02T18:02:20.237000Z",
"date_modified": "2026-03-02T18:02:20.237000Z",
"file_hash": "144e119f4d3c1aa850b15200728efe56eb05a3331d5ee460ba42eb1f5f88e42f",
"private": false,
"record": {
"abstract": "We use difference sets to construct interesting sets of lines in complex\nspace. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in\nC^k when k-1 is a prime power. Using semiregular relative difference sets with\nparameters (k,n,k,l) we construct sets of n+1 mutually unbiased bases in C^k.\nWe show how to construct these difference sets from commutative semifields and\nthat several known maximal sets of mutually unbiased bases can be obtained in\nthis way, resolving a conjecture about the monomiality of maximal sets. We also\nrelate mutually unbiased bases to spin models.",
"arxiv_id": "quant-ph/0511004",
"authors": [
"Chris Godsil",
"Aidan Roy"
],
"categories": [
"quant-ph",
"math.CO"
],
"doi": "10.1016/j.ejc.2008.01.002",
"journal_ref": "European Journal of Combinatorics 30 (2009), pp. 246--262",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Equiangular lines, mutually unbiased bases, and spin models",
"url": "https://arxiv.org/abs/quant-ph/0511004"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "44b32f13-9f4e-47b8-af0b-ea822b236da5",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}