Gaussianization and eigenvalue statistics for Random quantum channels (III)

Details Gaussianization and eigenvalue statistics for Random quantum channels (III) Gaussianization and eigenvalue statistics for Random quantum channels (III)

2009-10-09

arxiv.org/abs/0910.1768v2

Ann. Appl. Probab. Volume 21, Number 3 (2011), 1136-1179

Physics

Quantum Physics

34 pages and 14 figures

Scientific paper

10.1214/10-AAP722

In this paper, we present applications of the calculus developed in \cite{collins-nechita-1}, and obtain an exact formula for the moments of random quantum channels whose input is a pure state thanks to gaussianization methods. Our main application is an in-depth study of the random matrix model introduced by Hayden and Winter and used recently by Brandao, Horodecki, Fukuda and King to refine the Hastings counterexample to the additivity conjecture in Quantum Information Theory. This model is exotic from the point of view of random matrix theory, as its eigenvalues obey to two different scalings simultaneously. We study its asymptotic behavior and obtain an asymptotic expansion for its von Neumann entropy.

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