A new exponential separation between quantum and classical one-way communication complexity
Quantum Physics
2012-08-02 v3 Computational Complexity
Abstract
We present a new example of a partial boolean function whose one-way quantum communication complexity is exponentially lower than its one-way classical communication complexity. The problem is a natural generalisation of the previously studied Subgroup Membership problem: Alice receives a bit string x, Bob receives a permutation matrix M, and their task is to determine whether Mx=x or Mx is far from x. The proof uses Fourier analysis and an inequality of Kahn, Kalai and Linial.
Cite
@article{arxiv.1007.3587,
title = {A new exponential separation between quantum and classical one-way communication complexity},
author = {Ashley Montanaro},
journal= {arXiv preprint arXiv:1007.3587},
year = {2012}
}
Comments
19 pages; v3: improved results and some bug fixes