There is no generalization of known formulas for mutually unbiased bases

@article{Archer2003ThereIN,
  title={There is no generalization of known formulas for mutually unbiased bases},
  author={Claude O. Archer},
  journal={Journal of Mathematical Physics},
  year={2003},
  volume={46},
  pages={022106}
}
  • C. Archer
  • Published 26 December 2003
  • Mathematics
  • Journal of Mathematical Physics
In a quantum system having a finite number N of orthogonal states, two orthonormal bases {ai} and {bj} are called mutually unbiased if all inner products ⟨ai∣bj⟩ have the same modulus 1∕N. This concept appears in several quantum information problems. The number of pairwise mutually unbiased bases is at most N+1 and various constructions of such N+1 bases have been found when N is a power of a prime number. We study families of formulas that generalize these constructions to arbitrary dimensions… 
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51 Citations
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Methods Citations
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ON MUTUALLY UNBIASED BASES
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  • Mathematics
    2008 International Symposium on Information Theory and Its Applications
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It is demonstrated that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free parameters which cannot be absorbed by a global unitary operation.
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It is shown that the number of resulting mutually unbiased bases can be at most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon previous approaches.
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References

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