Exponential Separation of Quantum and Classical Non-Interactive Multi-Party Communication Complexity

TL;DR

This paper demonstrates the first exponential separation between quantum and classical multi-party communication complexity in non-interactive settings, highlighting quantum advantages for specific relational problems.

Contribution

It introduces a relational communication problem with an exponential quantum-classical complexity gap in non-interactive multi-party models.

Findings

Quantum protocols solve the problem with O(log n) cost.

Classical protocols require n^{c/k^2} cost, which is superpolynomial.

Separation is exponential for constant k.

Abstract

We give the first exponential separation between quantum and classical multi-party communication complexity in the (non-interactive) one-way and simultaneous message passing settings. For every k, we demonstrate a relational communication problem between k parties that can be solved exactly by a quantum simultaneous message passing protocol of cost O(log n) and requires protocols of cost n^{c/k^2}, where c>0 is a constant, in the classical non-interactive one-way message passing model with shared randomness and bounded error. Thus our separation of corresponding communication classes is superpolynomial as long as k=o(\sqrt{\log n / \log\log n}) and exponential for k=O(1).