Geodesic
Formula for unbiased bases
Kybernetika, Tome 46 (2010) no. 6, pp. 1122-1137

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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.
Classification : 81R05, 81R10, 81R15, 81R50
Keywords: mutually unbiased bases; Weyl pairs; phase states; Lie algebras 
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     author = {Kibler, Maurice R.},
     title = {Formula for unbiased bases},
     journal = {Kybernetika},
     pages = {1122--1137},
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2010},
     mrnumber = {2797432},
     zbl = {1209.81049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_6_a15/}
}
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Kibler, Maurice R. Formula for unbiased bases. Kybernetika, Tome 46 (2010) no. 6, pp. 1122-1137. http://geodesic.mathdoc.fr/item/KYB_2010__46_6_a15/