SIC POVMs and Clifford groups in prime dimensions

@article{Zhu2010SICPA,
  title={SIC POVMs and Clifford groups in prime dimensions},
  author={Huangjun Zhu},
  journal={Journal of Physics A},
  year={2010},
  volume={43},
  pages={305305}
}
  • Huangjun Zhu
  • Published 18 March 2010
  • Mathematics
  • Journal of Physics A
We show that in prime dimensions not equal to 3, each group covariant symmetric informationally complete positive operator valued measure (SIC POVM) is covariant with respect to a unique Heisenberg–Weyl (HW) group. Moreover, the symmetry group of the SIC POVM is a subgroup of the Clifford group. Hence, two SIC POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension 3, each group… 

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