Gaussianization and eigenvalue statistics for Random quantum channels (III)

Benoît Collins (1, 2) , Ion Nechita (1)

1 Department of Mathematics and Statistics [Ottawa]
2 ICJ - Institut Camille Jordan

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.

Mots clés: Random matrices; Weingarten calculus; Quantum information theory; Random quantum channel

Domaines: Physique Quantique [quant-ph]; Probabilités [math.PR]

Benoît Collins, Ion Nechita. Gaussianization and eigenvalue statistics for Random quantum channels (III). 2009. ⟨hal-00424058⟩