Quantum and Post-Quantum Phenomena in Networks

In certain experiments, or networks, testing a latent classical common cause explanation of the observed statistics can amount to checking a finite number of Bell inequalities. However, checking for latent quantum common cause explanation is, in general, more intricate and interesting. In this talk I will say that if such a quantum common cause explanation exists, the observed data is quantum, and otherwise it is "post-quantum". I will discuss how a post-quantum explanation in a simple network cannot be detected from statistics alone (in a device-independent manner) thus necessitating a natively quantum framework. I will then go on to discuss how things get more interesting when one composes simple networks.