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Formula for Unbiased Bases

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 = pe (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.
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Contributor : Dominique Girod <>
Submitted on : Monday, January 10, 2011 - 3:15:04 PM
Last modification on : Wednesday, November 18, 2020 - 4:42:04 PM


  • HAL Id : in2p3-00554244, version 1



M. Kibler. Formula for Unbiased Bases. Kybernetika, Institute of Information Theory and Automation, 2010, 46, pp.1122-1137. ⟨in2p3-00554244⟩



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