Multiparty Quantum Communication Complexity

TL;DR

This paper demonstrates quantum entanglement can significantly reduce communication complexity in multiparty scenarios, providing the first known separations beyond constant differences for specific functions.

Contribution

It constructs functions showing exponential separation in communication complexity with and without quantum entanglement in multiparty models.

Findings

Quantum entanglement reduces communication complexity for the constructed functions.

One-round quantum protocol achieves lower communication than classical protocols.

The results establish the first non-constant separation in multiparty communication complexity.

Abstract

Quantum entanglement cannot be used to achieve direct communication between remote parties, but it can reduce the communication needed for some problems. Let each of k parties hold some partial input data to some fixed k-variable function f. The communication complexity of f is the minimum number of classical bits required to be broadcasted for every party to know the value of f on their inputs. We construct a function G such that for the one-round communication model and three parties, G can be computed with n+1 bits of communication when the parties share prior entanglement. We then show that without entangled particles, the one-round communication complexity of G is (3/2)n + 1. Next we generalize this function to a function F. We show that if the parties share prior quantum entanglement, then the communication complexity of F is exactly k. We also show that if no entangled particles are provided, then the communication complexity of F is roughly k*log(k). These two results prove for the first time communication complexity separations better than a constant number of bits.