Quantum Boundaries in Networks

The field of quantum information has sparked considerable attention, due to both its promising technological applications, and the fact that it is showing to be instrumental to the understanding of the very foundations of our current description of reality. In a nutshell, quantum information studies how the operational capabilities of a physical agent change when in possession of quantum resources, and what useful tasks they can perform/enhance (in particular, but not only, communication tasks). In recent years, both the theoretical efforts and the technological advancements are getting mature to explore quantum information protocols in multipartite settings with several agents and sources, sometimes called quantum networks. This approach has already proved to boost the tools and scope of the field, but it is far from being understood comprehensively. In this project we aim at pushing our knowledge of quantum theory and its operational limits, via the network approach. Concretely, we will consider practical tasks in the areas of metrology, thermodynamics, hardware certification, communication. We will study the extent and limits of these tasks when the parties are arranged in simple networks, that is, networks that are either small or with a simple topology. We will in particular focus on the boundaries among situations in which the parties can act either on: 1) classical systems, 2) quantum systems, or possibly 3) objects featuring post-quantum behaviors. Some of the questions we aim at answering are: - What are the simplest network experiments featuring a quantum advantage? What applications can they have? - In which situations quantum collective effects are useful for sensing, and when is it instead sufficient to use classical metrological probes? - Can we imagine tests for the possible violation of quantum mechanics in multipartite experiments involving e.g., gravity, or many-body systems? As we will be dedicated to testing the limits of quantum theory, we will especially focus on experiments in which subsets of a given network (such as the quantum inputs in some of its nodes) are well characterized, and to what extent this trust can be leveraged in order to certify other (possibly global) properties of the network. These semi-device-independent scenarios are particularly suited to quantum optics platforms and will also enable the development of useful protocols for communication and sensing. Indeed, our research will be fundamentally theoretical, but it has the potential to be verified experimentally with current and near-term technology.