Random matrices, free probability and quantum information theory



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Recording Details

Speaker(s): 
Scientific Areas: 
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PIRSA Number: 
13010115

Abstract

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.