对于判别共轭隐藏子群，优良测量已是最优
量子物理
2007-05-23 v3
摘要
最近Bacon、Childs和van Dam证明了在二面体群D_n上的隐藏子群问题中，当隐藏子群从n个对合中均匀选取时，“优良测量”（PGM）是最优的。我们证明，对于任意群及任意子群H，当隐藏子群是H的均匀随机共轭时，PGM是最优的单寄存器实验。我们进一步证明当H与其父群构成Gel'fand对时，PGM对于任意数量的寄存器都是最优测量。在两种情形下我们都给出了最优测量成功的概率上界。这推广了二面体群的情形，并包含了若干其他引人关注的例子。
引用
@article{arxiv.quant-ph/0501177,
title = {For Distinguishing Conjugate Hidden Subgroups, the Pretty Good Measurement is as Good as it Gets},
author = {Cristopher Moore and Alexander Russell},
journal= {arXiv preprint arXiv:quant-ph/0501177},
year = {2007}
}
备注
proved additional conditions for optimality due to Yuen, Kennedy and Max; also bounded the probability of success in the one-register and multiregister cases