Exponential Separation between Quantum Communication and Logarithm of Approximate Rank
Abstract
Chattopadhyay, Mande and Sherif (ECCC 2018) recently exhibited a total Boolean function, the sink function, that has polynomial approximate rank and polynomial randomized communication complexity. This gives an exponential separation between randomized communication complexity and logarithm of the approximate rank, refuting the log-approximate-rank conjecture. We show that even the quantum communication complexity of the sink function is polynomial, thus also refuting the quantum log-approximate-rank conjecture. Our lower bound is based on the fooling distribution method introduced by Rao and Sinha (ECCC 2015) for the classical case and extended by Anshu, Touchette, Yao and Yu (STOC 2017) for the quantum case. We also give a new proof of the classical lower bound using the fooling distribution method.
Cite
@article{arxiv.1811.10090,
title = {Exponential Separation between Quantum Communication and Logarithm of Approximate Rank},
author = {Makrand Sinha and Ronald de Wolf},
journal= {arXiv preprint arXiv:1811.10090},
year = {2018}
}
Comments
The same lower bound has been obtained independently and simultaneously by Anurag Anshu, Naresh Goud Boddu and Dave Touchette