Abstract: Condensed matter physics has been driven by the discovery of novel phases of matter, such as topological materials. Most recently, advances in the controllability of quantum simulators and computers have enabled both a vast new landscape of non-equilibrium phases of matter and fault tolerant quantum memories. I will first show how conditional mutual information (CMI) serves as an essential quantity in characterizing these phases of open quantum systems and their transitions. Remarkably, these insights have led to new diagnostics for both quantum error correction thresholds as well as machine learnability of quantum and classical systems. In particular, I will demonstrate how some phases of open systems are not learnable via neural networks and how CMI can quantify unlearnability in such systems and potentially real-world data.