First, we will look into some basic differences between classical and Quantum zero-error. We will then define the quantum super-activation phenomenon which is exclusive to quantum setup. Then we will proceed to explain the super-duper activation phenomenon which is the strongest form of quantum super-activation.
Hilbert Modules will be introduced as a way of generalizing Hilbert Spaces. The immediate consequences of the definition will be presented, along with a few examples. I will then talk about operators between Hilbert Modules and their properties. If time permits we will also go over the analogue of the Riesz Representation Theorem in the Hilbert Module setting.