The limitations of nice mutually unbiased bases

@article{Aschbacher2004TheLO,
  title={The limitations of nice mutually unbiased bases},
  author={Michael Aschbacher and Andrew M. Childs and Pawe l Wocjan},
  journal={Journal of Algebraic Combinatorics},
  year={2004},
  volume={25},
  pages={111-123}
}
Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show 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. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian… 
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References

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TLDR
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