Quantum One-Way Communication is Exponentially Stronger Than Classical Communication

TL;DR

This paper proves that quantum one-way communication can exponentially outperform classical communication, establishing the first such separation with only a single round of quantum communication.

Contribution

It demonstrates that the exponential separation between quantum and classical communication complexity can be achieved with a one-round quantum protocol, resolving an open problem.

Findings

Quantum one-way protocols are exponentially more efficient than classical ones.

The paper confirms that a single round of quantum communication suffices for exponential separation.

It extends Raz's two-round protocol to a one-round setting.

Abstract

In STOC 1999, Raz presented a (partial) function for which there is a quantum protocol communicating only $O(\log n)$ qubits, but for which any classical (randomized, bounded-error) protocol requires $\poly(n)$ bits of communication. That quantum protocol requires two rounds of communication. Ever since Raz's paper it was open whether the same exponential separation can be achieved with a quantum protocol that uses only one round of communication. Here we settle this question in the affirmative.