Information-theoretic lower bounds for quantum sorting
Computational Complexity
2019-02-19 v1 Data Structures and Algorithms
Combinatorics
Quantum Physics
Abstract
We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set and are asked to identify a linear extension of using pairwise comparisons. For the standard sorting problem, in which is empty, it is known that the quantum query complexity is not asymptotically smaller than the classical information-theoretic lower bound. We prove that this holds for a wide class of partially ordered sets, thereby improving on a result from Yao (STOC'04).
Cite
@article{arxiv.1902.06473,
title = {Information-theoretic lower bounds for quantum sorting},
author = {Jean Cardinal and Gwenaël Joret and Jérémie Roland},
journal= {arXiv preprint arXiv:1902.06473},
year = {2019}
}