There is no generalization of known formulas for mutually unbiased bases
| dc.creator | archer, Claude | |
| dc.date | 2003-12-26 | |
| dc.date.accessioned | 2026-07-07T06:08:42Z | |
| dc.date.available | 2026-07-07T06:08:42Z | |
| dc.description | In a quantum system having a finite number $N$ of orthogonal states, two orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most $N+1$ and various constructions of $N+1$ such bases have been found when $N$ is a power of a prime number. We study families of formulas that generalize these constructions to arbitrary dimensions using finite rings.We then prove that there exists a set of $N+1$ mutually unbiased bases described by such formulas, if and only if $N$ is a power of a prime number. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0312204 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0312204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/91718 | |
| dc.subject | Quantum Physics | |
| dc.title | There is no generalization of known formulas for mutually unbiased bases | |
| dc.type | text |