Quantum Communication Advantage in TFNP

TL;DR

This paper demonstrates a total search problem where quantum communication significantly outperforms classical methods, showcasing an exponential advantage in the SMP model over classical two-way communication.

Contribution

It introduces a bipartite total search problem with an exponential quantum communication advantage, based on a query complexity problem by Yamakawa and Zhandry.

Findings

Quantum SMP protocol has exponentially smaller communication complexity.

Classical two-way randomized communication complexity has a lower bound.

The problem is a bipartite version of a recent query complexity problem.

Abstract

We exhibit a total search problem with classically verifiable solutions whose communication complexity in the quantum SMP model is exponentially smaller than in the classical two-way randomized model. Our problem is a bipartite version of a query complexity problem recently introduced by Yamakawa and Zhandry (JACM 2024). We prove the classical lower bound using the structure-vs-randomness paradigm for analyzing communication protocols.