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

Abstract

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.

Several typos were corrected

References in corpus (5)

• Aspects of generic entanglement
• Moments and Cumulants of Polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability
• Asymptotics of random density matrices
• Random quantum channels II: Entanglement of random subspaces, Renyi entropy estimates and additivity problems
• Gaussianization and eigenvalue statistics for random quantum channels (III)

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