Quantum contextuality provides communication complexity advantage

TL;DR

This paper demonstrates that quantum contextuality can be harnessed to achieve communication complexity advantages over classical methods, and introduces protocols for quantum key distribution based on this principle.

Contribution

It establishes a link between quantum contextuality and communication complexity advantage, providing new protocols for semi-device-independent quantum key distribution.

Findings

Quantum contextuality enables communication tasks with quantum advantage.

Quantum advantage in these tasks implies contextuality under certain conditions.

The difference in communication complexities grows with the number of inputs.

Abstract

Despite the conceptual importance of contextuality in quantum mechanics, there is a hitherto limited number of applications requiring contextuality but not entanglement. Here, we show that for any quantum state and observables of sufficiently small dimensions producing contextuality, there exists a communication task with quantum advantage. Conversely, any quantum advantage in this task admits a proof of contextuality whenever an additional condition holds. We further show that given any set of observables allowing for quantum state-independent contextuality, there exists a class of communication tasks wherein the difference between classical and quantum communication complexities increases as the number of inputs grows. Finally, we show how to convert each of these communication tasks into a semi-device-independent protocol for quantum key distribution.