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June 2011 Gaussianization and eigenvalue statistics for random quantum channels (III)
Benoît Collins, Ion Nechita
Ann. Appl. Probab. 21(3): 1136-1179 (June 2011). DOI: 10.1214/10-AAP722


In this paper, we present applications of the calculus developed in Collins and Nechita [Comm. Math. Phys. 297 (2010) 345–370] 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 [Comm. Math. Phys. 284 (2008) 263–280] and used recently by Brandao and Horodecki [Open Syst. Inf. Dyn. 17 (2010) 31–52] and Fukuda and King [J. Math. Phys. 51 (2010) 042201] 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 two different scalings simultaneously. We study its asymptotic behavior and obtain an asymptotic expansion for its von Neumann entropy.


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Benoît Collins. Ion Nechita. "Gaussianization and eigenvalue statistics for random quantum channels (III)." Ann. Appl. Probab. 21 (3) 1136 - 1179, June 2011.


Published: June 2011
First available in Project Euclid: 2 June 2011

zbMATH: 1221.81035
MathSciNet: MR2830615
Digital Object Identifier: 10.1214/10-AAP722

Primary: 15A52
Secondary: 94A17 , 94A40

Keywords: quantum information theory , random matrices , random quantum channel , Weingarten calculus

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.21 • No. 3 • June 2011
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