Constructions of mutually unbiased bases Academic Article uri icon

abstract

  • 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 d 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.

published proceedings

  • FINITE FIELDS AND APPLICATIONS

altmetric score

  • 3

author list (cited authors)

  • Klappenecker, A., & Rotteler, M.

citation count

  • 175

complete list of authors

  • Klappenecker, A||Rotteler, M

editor list (cited editors)

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

publication date

  • December 2004