Mathematical methods of quantum information theory, Lecture 10

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 10th lecture, corollaries for the Stinespring dilation Theorem and were discussed.

[caseyjones]

For the question that comes up at 51:42, the error occurs beginning at 49:20. The conditions should be A_ik = 0 for i ≠ k and A_lj = 0 for j ≠ l, because both exceptions (i=k and j=l) correspond to the common summand |k><l|. Thus only the off-diagonal elements are zero.