对于区分共轭隐藏子群，相当好的测量是尽可能好的
For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets
摘要：
最近，Bacon，Childs和van Dam证明了当隐子群是从n个对合中均匀选取时，“相当好的测度”（PGM）对于二面体群D_n上的隐子群问题是最优的.我们证明了，对于任何群和任何子群H，在隐子群是H的一致随机共轭的情况下，PGM是最优单寄存器实验。我们继续表明，当H与其父组形成一个Gel'fand对时，PGM是任何数量寄存器的最佳测量。在这两种情况下，我们都限制了最佳测量成功的概率。这推广了二面体群的情况，并包括许多其他感兴趣的例子。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
