Exponential Separation of Quantum and Classical One-Way Communication Complexity for a Boolean Function

TL;DR

This paper demonstrates an exponential gap between quantum and classical one-way communication complexities for a specific Boolean function, highlighting fundamental differences in information processing capabilities.

Contribution

It provides the first exponential separation for a Boolean function in one-way communication complexity, extending previous relation-based results and implications for cryptography.

Findings

Quantum communication can be exponentially more efficient than classical

The result applies to the bounded storage cryptographic model

Quantum storage compromises security in certain cryptographic settings

Abstract

We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently by Kerenidis and Raz [KR06]. Our version of the result gives an example in the bounded storage model of cryptography, where the key is secure if the adversary has a certain amount of classical storage, but is completely insecure if he has a similar amount of quantum storage.