Random Quantum Channels I: Graphical Calculus and the Bell State Phenomenon.

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 [7], 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 further work to have new applications to minimal output entropy inequalities. [ABSTRACT FROM AUTHOR]