Constructions of Mutually Unbiased Bases Academic Article uri icon


  • 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.

author list (cited authors)

  • Klappenecker, A., & Rötteler, M.

citation count

  • 136

editor list (cited editors)

  • Mullen, G. L., Poli, A., & Stichtenoth, H.

publication date

  • January 2004