For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets

@article{Moore2007ForDC,
  title={For distinguishing conjugate hidden subgroups, the pretty good measurement is as good as it gets},
  author={Cristopher Moore and Alexander Russell},
  journal={Quantum Information & Computation},
  year={2007},
  volume={7},
  pages={752-765}
}
Recently Bacon, Childs and van Dam showed that the “pretty good measurement” (PGM) is optimal for the Hidden Subgroup Problem on the dihedral group Dn in the case where the hidden subgroup is chosen uniformly from the n involutions. We show that, for any group and any subgroup H, the PGM is the optimal one-register experiment in the case where the hidden subgroup is a uniformly random conjugate of H. We go on to show that when H forms a Gel’fand pair with its parent group, the PGM is the… CONTINUE READING

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