Topologically Robust Quantum Network Nonlocality

TL;DR

This paper demonstrates that quantum network nonlocality remains observable even when the network structure is only partially known, highlighting its topological robustness and potential for secure quantum applications.

Contribution

It introduces a framework showing quantum nonlocality persists with limited network knowledge, and provides examples of nonlocal distributions in simple network configurations.

Findings

Quantum nonlocality can be demonstrated with partial network knowledge.

Nonlocality is robust in large ring networks with minimal structural information.

Applications like randomness certification are feasible under these conditions.

Abstract

We discuss quantum network Bell nonlocality in a setting where the network structure is not fully known. More concretely, an honest user may trust their local network topology, but not the structure of the rest of the network, involving distant (and potentially dishonest) parties. We demonstrate that quantum network nonlocality can still be demonstrated in such a setting, hence exhibiting topological robustness. Specifically, we present quantum distributions obtained from a simple network that cannot be reproduced by classical models, even when the latter are based on more powerful networks. In particular, we show that in a large ring network, the knowledge of only a small part of the network structure (involving only 2 or 3 neighbouring parties) is enough to guarantee nonlocality over the entire network. This shows that quantum network nonlocality can be extremely robust to changes in the network topology. Moreover, we demonstrate that applications of quantum nonlocality, such as the black-box certification of randomness and entanglement, are also possible in such a setting.