关于量子单向置换的一个注记
A note on quantum one-way permutations
摘要：
我们讨论了量子单向排列的存在性问题。首先，我们证明了对一个给定的量子态，构造一个多项式大小的网络来反映它与对一个置换求逆是等价的。接下来，我们考虑这样一个问题：如果一个状态很难准备，那么操作者对这个状态的反思是否很难构建？通过对Grover算法的重新考察，我们给出了这个问题与单向置换存在性之间的关系。此外，我们比较我们的方法Grover的算法，并讨论我们的结果可能的应用。
英文摘要：
We discuss the question of the existence of quantum one-way permutations. First, we prove the equivalence between inverting a permutation and that of constructing a polynomial size network for reflecting about a given quantum state. Next, we consider the question: if a state is difficult to prepare, is the operator reflecting about that state difficult to construct? By revisiting Grover's algorithm, we present the relationship between this question and the existence of one-way permutations. Moreover, we compare our method to Grover's algorithm and discuss possible applications of our results.
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。
