Аннотация:
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.)
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