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- Random matrices, free probability and quantum information theory

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13010115

In

quantum information theory, random techniques have proven to be very useful.

For example, many questions related to the problem of the additivity of

entropies of quantum channels rely on fine properties of concentration of

measure.

In

this talk, I will show that very different techniques of random matrix theory

can complement quite efficiently more classical random techniques. I will spend

some time on discussing the Weingarten calculus approach, and the operator norm

approach. Both techniques have been initially used in free probability theory,

and I will give some new applications of these techniques to quantum

information theory.

©2012 Perimeter Institute for Theoretical Physics