Discrete Phase-Space Structures and Mutually Unbiased Bases

  • A. B. Klimov
  • J. L. Romero
  • G. Björk
  • L. L. Sánchez-Soto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4547)


We propose a unifying phase-space approach to the construction of mutually unbiased bases for an n-qubit system. It is based on an explicit classification of the geometrical structures compatible with the notion of unbiasedness. These consist of bundles of discrete curves intersecting only at the origin and satisfying certain additional conditions. The effect of local transformations is also studied.


Mutually unbiased bases quantum state estimation Galois fields Abelian curves 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • A. B. Klimov
    • 1
  • J. L. Romero
    • 1
  • G. Björk
    • 2
  • L. L. Sánchez-Soto
    • 3
  1. 1.Departamento de Física, Universidad de Guadalajara, Revolución 1500, 44420 Guadalajara, JaliscoMexico
  2. 2.School of Information and Communication Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 KistaSweden
  3. 3.Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 MadridSpain

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