An Operational Framework for Nonclassicality in Quantum Communication Networks

Abstract: Quantum resources such as entanglement and quantum communication offer significant advantages in distributed information processing. We develop an operational framework for realizing these enhancements in resource-constrained quantum networks. We first compute linear constraints on the input/output probabilities that arise in classical networks with limited communication and globally shared randomness. We then maximize the violation of these classical bounds by applying variational quantum optimization to a parameterized quantum network ansatz that encodes a fixed set of quantum communication resources. A violation of the classical bounds indicates nonclassicality, which means that an explicit communication advantage is realized because extra classical communication is required to simulate the behavior of the quantum network. We demonstrate nonclassicality in many basic point-to-point and multi-point communication networks. In all cases, we find that entanglement-assisted communication, both classical and quantum, leads to nonclassicality. Moreover, networks having multiple senders can exhibit nonclassicality using quantum communication without entanglement-assistance. Finally, we discuss how our approaches can be implemented on quantum networking hardware and used to automatically certify quantum resources and realize communication advantages in noisy quantum networks.