Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions
| dc.creator | Gow, Rod | |
| dc.date | 2007-03-12 | |
| dc.date | 2007-04-05 | |
| dc.date.accessioned | 2026-07-07T07:55:01Z | |
| dc.date.available | 2026-07-07T07:55:01Z | |
| dc.description | Let q be a power of 2. We show by representation theory that there exists a q x q unitary matrix of multiplicative order q+1 whose powers generate q+1 pairwise mutually unbiased base in C^q. When q is a power of an odd prime, there is a q x q unitary matrix of multiplicative order q+1 whose first (q+1)/2 powers generate (q+1)/2 pairwise mutually unbiased bases. We also show how the existence of these matrices implies the existence of a special type of orthogonal decomposition with respect to the Killing form of the special linear and symplectic Lie algebras. | |
| dc.description | 9 pages, some earlier questions resolved | |
| dc.identifier | https://arxiv.org/abs/math/0703333 | |
| dc.identifier | http://arxiv.org/abs/math/0703333 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126830 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Physics | |
| dc.subject | 81P15; 81P68, 20C15 | |
| dc.title | Generation of mutually unbiased bases as powers of a unitary matrix in 2-power dimensions | |
| dc.type | text |