Rethinking Causality in Quantum Mechanics

Causality is central to understanding the mechanisms of nature: some event "e;A"e; is the cause of another event "e;B"e;. Surprisingly, causality does not follow this simple rule in quantum physics: due to to quantum superposition we might be led to believe that "e;A causes B"e; and that "e;B causes A"e;. This idea is not only important to the foundations of physics but also leads to practical advantages: a quantum circuit with such indefinite causality performs computationally better than one with definite causality. This thesis provides one of the first comprehensive introductions to quantum causality, and presents a number of advances. It provides an extension and generalization of a framework that enables us to study causality within quantum mechanics, thereby setting the stage for the rest of the work. This comprises: mathematical tools to define causality in terms of probabilities; computational tools to prove indefinite causality in an experiment; means to experimentally test particular causal structures; and finally an algorithm that detects the exact causal structure in an quantum experiment.