  The design of the Quantum Internet protocol stack is at its infancy and
early-stage conceptualization. And different heterogeneous proposals are
currently available in the literature. The underlying assumption of the
existing proposals is that they implicitly mimic classical Internet Protocol
design principles: "A name indicates what we seek. An address indicates where
it is. A route indicates how to get there''. Hence the network nodes are
labeled with classical addresses, constituted by classical bits, and these
labels aim at reflecting the node location within the network topology. In this
paper, we argue that this twofold assumption of classical and location-aware
addressing constitutes a restricting design option, which prevents to scale the
quantumness to the network functionalities, beyond simple information
encoding/decoding. On the contrary, by embracing quantumness within the node
addresses, quantum principles and phenomena could be exploited for enabling a
quantum native functioning of the entire communication network. This will
unleash the ultimate vision and capabilities of the Quantum Internet.
