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13th International Conference on Symmetry Methods in Physics (SYMPHYS XIII), Dubna : Russie, Fédération De (2009)
Bases for qudits from a nonstandard approach to SU(2)
Maurice Robert Kibler1

Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for quantum information and quantum computation are constructed from angular momentum theory and su(2) Lie algebraic methods. We report on a formula for deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated application of the formula can be used for generating mutually unbiased bases in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection between mutually unbiased bases and the unitary group SU(d) is briefly discussed in the case d = p^e.
1 :  IPNL - Institut de Physique Nucléaire de Lyon
Physique/Physique Quantique

Physique/Physique mathématique

Mathématiques/Physique mathématique
su(2) and su(d) Lie algebras – angular momentum – mutually unbiased bases – qubits and qudits
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Kibler2_Symphys13_final.pdf(195.7 KB)
Kibler2_Symphys13_final.ps(497.2 KB)