Towards higher-order quantum mechanics (Eric Milner's Graduate Scholarship Lecture) - Eric Milner

The axioms of quantum mechanics provide a mathematical framework for defining quantum systems, states, and operations. These definitions are consistent in that quantum operations map quantum states to other quantum states. Interestingly, an agent can manipulate a quantum operation and transform it into another quantum operation. Therefore, we can define quantum super-operations as maps from quantum operations to quantum operations. We refer to quantum operations as first-order operations, and super-operations as second-order operations. Similarly, we can recursively define operations of order n as maps from operations of order n-1 to operations of order n-1. In this talk, I will introduce quantum mechanics and the mathematical framework used to describe quantum systems, states, and operations. Then, I will present how type theory aids in investigating higher-order quantum operations and their properties.