Two orthonormal bases B and B′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |〈b|b′〉|2 = 1/d holds for all b ∈ B and b′ ∈ B′. The size of any set containing painvise mutually unbiased bases of ℂd cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of this fact based on the estimation of exponential sums. We discuss conjectures and open problems concerning the maximal number of mutually unbiased bases for arbitrary dimensions. © Springer-Verlag Berlin Heidelberg 2004.
CITATION STYLE
Klappenecker, A., & Rötteler, M. (2004). Constructions of mutually unbiased bases. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2948, 137–144. https://doi.org/10.1007/978-3-540-24633-6_10
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