量子测试汉明距离的块敏感性下界
A Block-Sensitivity Lower Bound for Quantum Testing Hamming Distance
摘要：
Gap-Hamming距离问题是决定长度为$n$的两个字符串之间的汉明距离$h$是大于$a$还是小于$b$的承诺问题，其中间隙$g=|a-b|\geq 1$和$a$和$b$可以取决于$n$。在这篇短文中，我们给出了计算两个长度为$n$的字符串之间的Gap-Hamming距离的量子查询复杂度的$Ω( \sqrt{n/g})$的下界。证明是一个组合参数的基础上块的敏感性和减少从一个阈值函数。
英文摘要：
The Gap-Hamming distance problem is the promise problem of deciding if the Hamming distance $h$ between two strings of length $n$ is greater than $a$ or less than $b$, where the gap $g=|a-b|\geq 1$ and $a$ and $b$ could depend on $n$. In this short note, we give a lower bound of $Ω( \sqrt{n/g})$ on the quantum query complexity of computing the Gap-Hamming distance between two given strings of lenght $n$. The proof is a combinatorial argument based on block sensitivity and a reduction from a threshold function.
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。
