Random Matrix Techniques in Quantum Information Theory

As in classical computer science randomized proofs and constructions are ubiquitous in quantum information. Because quantum mechanics is noncommutative the random objects of study are invariably matrices. Quantum information theory therefore provides a rich source of random matrix problems. One of the most important classes of problems in the mathematical aspects of quantum information theory is the study of data transmission through noisy quantum channels. A famous conjecture reduced the calculation of the channel capacity for classical data to the question of the additivity of minimum channel output entropy. The original conjecture was disproved by Hastings in 2008. Additivity questions are but the latest applications of random matrices in quantum information however. Others include benchmarking of experimental quantum computers as well as the design of optimal codes for numerous data transmission and cryptographic problems. The workshop will gather researchers from areas as various as quantum information theory quantum computing random matrix theory asymptotic convex analysis free probability theory and operator algebras. We believe that the recent resolution of the additivity conjecture provides an excellent opportunity to bring together for the first time specialists with widelyarying backgrounds in both physics and mathematics whose work does (or could!) lie at the intersection of quantum information and random matrices. Our goal would be to make a synthesis of the new research trends related to these problems while introducing audience of non-experts and graduate students to some of the most exciting recent multidisciplinary developments at the interface between physics and mathematics.

This workshop was co-sponsored by the Fields Institute.

Speakers:

Andris Ambainis, University of Latvia
Serban Belinschi, University of Saskatchewan
Fernando Brandao, Departamento de Fisica, Universidade Federal de Minas Gerais, Brazil 
Benoit Collins, University of Ottawa
Bergfinnur Durhuus, University of Copenhagen
Alexander Elgart, Virginia Tech
Motohisa Fukuda, UC Davis
Aram Harrow, University of Bristol
Patrick Hayden, McGill University/Perimeter Institute
Marius Junge, University of Illinois
Chris King, Northeastern University
Debbie Leung, University of Waterloo
Ramis Movassagh, Massachusetts Institute of Technology
Ion Nechita, University of Ottawa
Alexandru Nica, University of Waterloo
Clément Pellegrini, Université de Toulouse III
Jérémie Roland, NEC Laboratories America
Mary Beth Ruskai, Tufts University
Stanislaw Szarek, Case Western Reserve University
Lorenza Viola, Darmouth College
Andreas Winter, University of Bristol
Deping Ye, University of Missouri
Karol Zyczkowski, Jagiellonian University & Polish Academy of Science
Ofer Zeitouni, University of Minnesota