Nonclassicality in Quantum Communication Networks*

Quantum communication networks are rapidly being developed and applied, however, there is still much to understand about the operational advantages that quantum networks actually provide. In this work, we introduce nonclassicality as a quantifier of quantum advantage, which generalizes standard Bell nonlocality to signaling systems. To this end, we apply a black-box framework for characterizing communication networks in terms of their communication resources and causal structure. We devise operational tests that quantify a network's performance against a given task. We derive a connection between a class of operational tests and the network's ability to simulate a given behavior. Finally, we apply our nonclassicality framework to demonstrate explicit quantum advantages across a wide range of quantum network topologies and resource configurations. To obtain our main results, we develop a resource-theoretic quantum circuit model for simulating general communication networks assisted by quantum resources. Using quantum hardware-compatible variational optimization techniques, we optimize these simulations over the set of free operations. We first demonstrate in bipartite signaling systems that quantum communication, entanglement-assisted classical communication, and entanglement-assisted quantum communication resources can all demonstrate explicit advantages over classical communication resources. We then extend our techniques to showcase quantum advantages in multiaccess networks, broadcast networks, and multipoint communication networks. Overall, the described operational tests can be used to help certify and verify resources in quantum networks. We also identify distributed computing advantages where quantum resources are able to perform distributed computational tasks with greater success than classical resources. Finally, our work demonstrates a class of variational quantum networking protocols that can automatically establish protocols such as dense-coding or key distribution on uncharacterized network devices where the quality of the protocol is characterized operationally by the simulation error.