Mathematical methods of quantum information theory, Lecture 3

In 2017 Reinhard Werner gave a series of lectures on the mathematical methods of quantum information theory at the Leibniz Universität Hannover. These lectures were recorded and I have the pleasure of hosting these videos on my youtube channel. Over the coming weeks I'll be posting these lectures here.

The prerequisites for these lectures are a standard course on quantum mechanics and some familiarity with mathematical analysis, e.g., Hilbert space, operators, etc., although these topics are reviewed in the first lectures.

Lecture notes and exercises will not be distributed.

In this third lecture, composition, tensor product, channels, Heisenberg picture, Schrödinger picture, complete positivity, channel examples: unitary, depolarizing, von Neumann measurement were discussed.

[ArthurParzygnat]

Thanks for the videos! I'm confused about the depolarizing channel. It's actually not linear (plug in rho=0). However, it is affine. How does one define complete positivity for affine maps? In particular, how is the tensor product defined?