High-dimensional quantum communication complexity beyond strategies based on Bell's theorem

TL;DR

This paper demonstrates that high-dimensional quantum communication surpasses Bell-based strategies in communication complexity tasks, with experimental validation up to ten dimensions, revealing advantages tied to specific measurement types.

Contribution

It shows the superiority of high-dimensional quantum communication over Bell-based strategies in CCPs and experimentally verifies these advantages up to ten dimensions.

Findings

Increasing dimension enhances quantum communication advantage.

High-dimensional quantum communication surpasses Bell-based strategies.

Non-rank-one measurements are crucial for observed advantages.

Abstract

Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission and measurement of a single quantum system; in other words quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realise such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the post-quantum Bell correlations obeying only locality in the macroscopic limit. Surprisingly, we find that the advantages are tied to the use of measurements that are not rank-one projective. We provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.