A Block-Sensitivity Lower Bound for Quantum Testing Hamming Distance

Marcos Villagra

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arXiv · 1705.09710

A Block-Sensitivity Lower Bound for Quantum Testing Hamming Distance

Marcos Villagra

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Abstract

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 $\Omega( \sqrt{n/g})$ 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.

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Marcos Villagra. 2017-05-26. A Block-Sensitivity Lower Bound for Quantum Testing Hamming Distance. https://arxiv.org/abs/1705.09710

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