| Title:
|
Formula for unbiased bases (English) |
| Author:
|
Kibler, Maurice R. |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
6 |
| Year:
|
2010 |
| Pages:
|
1122-1137 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present paper deals with mutually unbiased bases for systems of qudits in $d$ dimensions. Such bases are of considerable interest in quantum information. A formula for deriving a complete set of $1+p$ mutually unbiased bases is given for $d=p$ where $p$ is a prime integer. The formula follows from a nonstandard approach to the representation theory of the group $SU(2)$. A particular case of the formula is derived from the introduction of a phase operator associated with a generalized oscillator algebra. The case when $d = p^e$ ($e \geq 2$), corresponding to the power of a prime integer, is briefly examined. Finally, complete sets of mutually unbiased bases are analysed through a Lie algebraic approach. (English) |
| Keyword:
|
mutually unbiased bases |
| Keyword:
|
Weyl pairs |
| Keyword:
|
phase states |
| Keyword:
|
Lie algebras |
| MSC:
|
81R05 |
| MSC:
|
81R10 |
| MSC:
|
81R15 |
| MSC:
|
81R50 |
| idZBL:
|
Zbl 1209.81049 |
| idMR:
|
MR2797432 |
| . |
| Date available:
|
2011-04-12T12:57:35Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141471 |
| . |
| Reference:
|
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