Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication

TL;DR

This paper demonstrates that quantum superposition of communication directions can exponentially reduce communication complexity in distributed tasks, surpassing classical and one-way quantum protocols.

Contribution

It introduces a tripartite communication task showing exponential advantage using quantum superposition of communication directions, a novel resource in quantum communication complexity.

Findings

Exponential communication savings with quantum superposition

Advantage persists with bounded error protocols

Surpasses classical and one-way quantum communication methods

Abstract

In communication complexity, a number of distant parties have the task of calculating a distributed function of their inputs, while minimizing the amount of communication between them. It is known that with quantum resources, such as entanglement and quantum channels, one can obtain significant reductions in the communication complexity of some tasks. In this work, we study the role of the quantum superposition of the direction of communication as a resource for communication complexity. We present a tripartite communication task for which such a superposition allows for an exponential saving in communication, compared to one-way quantum (or classical) communication; the advantage also holds when we allow for protocols with bounded error probability.