Testing dimension and non-classicality in communication networks

TL;DR

This paper develops a framework for testing the dimension and non-classicality of mediating systems in communication networks, demonstrating quantum systems' advantages over classical ones and improving noise tolerance in network protocols.

Contribution

It introduces a general, device-independent framework for testing system dimension and non-classicality in networks, applicable to both classical and quantum systems.

Findings

Quantum systems outperform classical systems at fixed dimension.

Transformation devices enhance noise tolerance significantly.

Classical simulation of quantum systems is dimensionally costly.

Abstract

We consider networks featuring preparation, transformation, and measurement devices, in which devices exchange communication via mediating physical systems. We investigate the problem of testing the dimension of the mediating systems in the device-independent scenario, that is, based on observable data alone. A general framework for tackling this problem is presented, considering both classical and quantum systems. These methods can then also be used to certify the non-classicality of the mediating systems, given an upper bound on their dimension. Several case studies are reported, which illustrate the relevance of the framework. These examples also show that, for fixed dimension, quantum systems largely outperform classical ones. Moreover, the use of a transformation device considerably improves noise tolerance when compared to simple prepare-and-measure networks. These results suggest that the classical simulation of quantum systems becomes costly in terms of dimension, even for simple networks.