Identifying classical and quantum causal relations with transfer entropy

In the realm of physics, causality remains an enigmatic and debated concept. Though numerous measures of causality have been proposed, including Causal Influence, Liam’s causality, Pearl’s average causal effect, Granger’s causality, and Transfer entropy , a unified consensus on its characterization and quantification has yet to be reached. This thesis focuses on transfer entropy, a model-free metric introduced by Thomas Schreiber, with widespread applications across many disciplines. Notably, transfer entropy has been used in fields like neuroscience, finance, and the study of complex systems. Our aim is to provide a comprehensive understanding of transfer entropy and explore its application to quantum circuits. We investigate how transfer entropy behaves when data originates from quantum processes, focusing particularly on spin measurements, different initial states, and different channels. To achieve this, we developed a program that can simulate classical and quantum measures of two interacting observables and calculate the transfer entropy from the obtained time series. For the quantum case, we derive an analytical formula for transfer entropy in our specific setup, enabling us to study its properties and calculate its value without relying on simulation.