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

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

2009-05-14

arxiv.org/abs/0905.2313v2

Communications in Mathematical Physics 297, 2 (2010) 345-370

Physics

Quantum Physics

Several typos were corrected

Scientific paper

10.1007/s00220-010-1012-0

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.

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