An Operational Framework for Nonclassicality in Quantum Communication Networks

Quantum resources, such as entanglement or quantum communication, offer significant communication advantages in information processing. We develop an operational framework for realizing these communication advantages in resource-constrained quantum networks. The framework computes linear bounds on the input/output probabilities of classical networks with limited communication and globally shared randomness. Since the violation of these classical bounds witnesses nonclassicality, a measurable communication advantage, the framework maximizes the violation of the classical bound using variational quantum optimization methods tailored to the communication network and quantum resources. This operational framework for nonclassicality can be scaled on quantum computers or deployed in the field to optimize noisy quantum networks for communication advantages. Applying this framework, we investigate the nonclassicality of communication networks that are assisted by quantum resources. We find that entanglement between communication-constrained parties is sufficient for nonclassicality to be found, whereas in networks with multiple senders, quantum communication with no entanglement-assistance is sufficient for nonclassicality to be found. As a result, entanglement is necessary for nonclassicality when a single sender broadcasts to multiple receivers.