Explore a physics lecture examining how tensor networks and process trees can capture long-range temporal correlations in quantum systems. Delve into the study of zero-temperature quantum phases characterized by internal entanglement structure and the distinction between short-range and long-range shared information. Learn how process trees accommodate quantum power-law correlations in time, enable efficient computation of multi-time correlation functions, and can be applied to both empirical data and first-principles construction. Understand the practical applications in open quantum systems simulation and quantum computer benchmarking, while considering the theoretical implications for temporal renormalization and temporal quantum phase concepts. Discover how these mathematical tools advance our understanding of non-Markovian processes and temporal correlations generated through system-environment interactions.