Physics of Information: a network-theoretic perspective

In a recent, provocative Nature Physics commentary, Albert-László Barabási writes “as the field [Network Theory] enters the spotlight, Physics must assert its engagement if it wants to continue to be present at the table.” And “[Our children] don’t talk quanta -- they dream bits. They don’t see entanglement but recognize with ease nodes and links”. Quantum Information Science has contributed to a deeper understanding of the Wheeler-Deutsch's motto “It from (qu)bit”. Often, today, when we talk quanta, we do talk bits, and if we want to explore the ultimate limits of information processing and transmission we need to deal with Quantum Mechanics. Additionally, we know that the interface between subareas of Quantum Mechanics and Graph Theory is vast – there are conferences on this topic. In the light of these facts, we would like to ask the following question: can the toolbox of Quantum Information Science be concretely useful in the context of Network Theory (and viz.)? The talk is not about a single topic, but it's a collection of short stories highlighting results of my colleagues and I at the interface between these two fields, and their applications in other areas, as, for example, in Biology.