The Interface of Asymptotic
Geometric Analysis and Quantum Information Theory

Guillaume Aubrun
and I wrote a book focused on the interface between
mathematical aspects of Quantum Information Theory and local theory of
Banach spaces, a field which studies the properties of (very)
high-dimensional objects and is also often called Asymptotic Geometric
Analysis.

The book appeared in the Mathematical Surveys and Monographs series
of the American Mathematical Society in the fall of 2017.
If you read Alice and Bob Meet Banach (or even if you did not, but would like to), you may want to
consult the related blog.