Links between geometric functional analysis and quantum information theory

Quantum Information theory (QIT) provides theoretical underpinnings for the project of building a quantum computer, one of the major scientific and technological challenges of the 21st century. Over the last decade it became clear that QIT enjoys very close links to geometric functional analysis, for example to Banach space theory and to the theory of operator spaces.
In this talk we will exemplify these links by showing how the questions about additivity properties of quantum channels, solved by Hayden/Winter and Hastings in 2008 and 2009, can be reformulated (and answered) as instances of Dvoretzky's theorem on almost spherical sections of convex bodies. (Based on joint work with G. Aubrun and E. Werner.)