Quantum versus Randomized Communication Complexity, with Efficient Players

TL;DR

This paper demonstrates a significant separation between quantum and classical communication complexity using efficient quantum protocols with small circuit implementations, highlighting the potential advantages of quantum communication.

Contribution

It introduces an explicit partial Boolean function that exhibits an exponential gap in communication complexity between quantum and classical models with efficient quantum parties.

Findings

Quantum protocols can compute the function with small quantum circuits.

Classical randomized protocols require exponentially more communication.

Efficient quantum protocols match the strongest known quantum-classical separation.

Abstract

We study a new type of separation between quantum and classical communication complexity which is obtained using quantum protocols where all parties are efficient, in the sense that they can be implemented by small quantum circuits with oracle access to their inputs. More precisely, we give an explicit partial Boolean function that can be computed in the quantum-simultaneous-with-entanglement model of communication, however, every interactive randomized protocol is of exponentially larger cost. Furthermore, all the parties in the quantum protocol can be implemented by quantum circuits of small size with blackbox access to the inputs. Our result qualitatively matches the strongest known separation between quantum and classical communication complexity and is obtained using a quantum protocol where all parties are efficient.