Formula for unbiased bases

Maurice R. Kibler

Kybernetika (2010)

  • Volume: 46, Issue: 6, page 1122-1137
  • ISSN: 0023-5954

Abstract

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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 S U ( 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 ≥ 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.

How to cite

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Kibler, Maurice R.. "Formula for unbiased bases." Kybernetika 46.6 (2010): 1122-1137. <http://eudml.org/doc/197121>.

@article{Kibler2010,
abstract = {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 $d = p^e$ ($e \ge 2$), 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.},
author = {Kibler, Maurice R.},
journal = {Kybernetika},
keywords = {mutually unbiased bases; Weyl pairs; phase states; Lie algebras; mutually unbiased bases; Weyl pairs; phase states; Lie algebras},
language = {eng},
number = {6},
pages = {1122-1137},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Formula for unbiased bases},
url = {http://eudml.org/doc/197121},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Kibler, Maurice R.
TI - Formula for unbiased bases
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 6
SP - 1122
EP - 1137
AB - 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 $d = p^e$ ($e \ge 2$), 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.
LA - eng
KW - mutually unbiased bases; Weyl pairs; phase states; Lie algebras; mutually unbiased bases; Weyl pairs; phase states; Lie algebras
UR - http://eudml.org/doc/197121
ER -

References

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