Random quantum channels I: graphical calculus and the Bell state phenomenon

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

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

This paper is the first of a series where we study quantum channels from the random matrix point of view. We develop a graphical tool that allows us to compute the expected moments of the output of a random quantum channel. As an application, we study variations of random matrix models introduced by Hayden \cite{hayden}, and show that their eigenvalues converge almost surely. In particular we obtain for some models sharp improvements on the value of the largest eigenvalue, and this is shown in a further work to have new applications to minimal output entropy inequalities.

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

Domaines: Physique Quantique [quant-ph]; Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]

Benoît Collins, Ion Nechita. Random quantum channels I: graphical calculus and the Bell state phenomenon. 2009. ⟨hal-00384127v1⟩