  Nowadays, the classical Internet has mainly envisioned as the underlying
communication infrastructure of the Quantum Internet, aimed at providing
services such as signaling and coordination messages. However, the interplay
between classical and Quantum Internet is complex and its understanding is
pivotal for an effective design of the Quantum Internet protocol stack. The aim
of the paper is to shed the light on this interplay, by highlighting that such
an interplay is indeed bidirectional rather than unidirectional. And the
Quantum Internet exhibits the potential of supporting and even enhancing
classical Internet functionalities.
