PIRSA:13010115

Random matrices, free probability and quantum information theory

APA

Collins, B. (2013). Random matrices, free probability and quantum information theory. Perimeter Institute. https://pirsa.org/13010115

MLA

Collins, Benoit. Random matrices, free probability and quantum information theory. Perimeter Institute, Jan. 31, 2013, https://pirsa.org/13010115

BibTex

          @misc{ pirsa_13010115,
            doi = {10.48660/13010115},
            url = {https://pirsa.org/13010115},
            author = {Collins, Benoit},
            keywords = {Quantum Information},
            language = {en},
            title = {Random matrices, free probability and quantum information theory},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {jan},
            note = {PIRSA:13010115 see, \url{https://pirsa.org}}
          }
          

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.