Physics – Quantum Physics
Scientific paper
2005-01-31
Physics
Quantum Physics
proved additional conditions for optimality due to Yuen, Kennedy and Max; also bounded the probability of success in the one-r
Scientific paper
Recently Bacon, Childs and van Dam showed that the ``pretty good measurement'' (PGM) is optimal for the Hidden Subgroup Problem on the dihedral group D_n 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 optimal measurement for any number of registers. In both cases we bound the probability that the optimal measurement succeeds. This generalizes the case of the dihedral group, and includes a number of other examples of interest.
Moore Cristopher
Russell Alexander
No associations
LandOfFree
For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-300522