Adversary Lower Bound for Element Distinctness

TL;DR

This paper constructs an explicit optimal adversary matrix to establish lower bounds for the element distinctness problem when the alphabet size is large.

Contribution

It introduces a new explicit adversary matrix that achieves optimal lower bounds for element distinctness with large alphabets.

Findings

Established a tight lower bound for element distinctness.

Provided an explicit construction of the adversary matrix.

Enhanced understanding of quantum query complexity for this problem.

Abstract

In this note we construct an explicit optimal (negative-weight) adversary matrix for the element distinctness problem, given that the size of the alphabet is sufficiently large.