The Quantum Internet, a network interconnecting remote quantum devices through quantum links in synergy with classical ones, is envisioned as the final stage of the quantum revolution, opening fundamentally new communications and computing capabilities. But the Quantum Internet is governed by the laws of quantum mechanics. Phenomena with no counterpart in classical networks, such as no-cloning, quantum measurement, entanglement and quantum teleportation, impose new challenging constraints for network design. Specifically, classical network functionalities are based on the assumption that classical information can be safely read and copied. However, this assumption does not hold in the Quantum Internet. As a consequence, its design requires ...