The Annals of Applied Probability

Gaussianization and eigenvalue statistics for random quantum channels (III)

Benoît Collins and Ion Nechita

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Abstract

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.

Article information

Source
Ann. Appl. Probab. Volume 21, Number 3 (2011), 1136-1179.

Dates
First available in Project Euclid: 2 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1307020394

Digital Object Identifier
doi:10.1214/10-AAP722

Mathematical Reviews number (MathSciNet)
MR2830615

Zentralblatt MATH identifier
1221.81035

Subjects
Primary: 15A52
Secondary: 94A17: Measures of information, entropy 94A40: Channel models (including quantum)

Keywords
Random matrices Weingarten calculus quantum information theory random quantum channel

Citation

Collins, Benoît; Nechita, Ion. Gaussianization and eigenvalue statistics for random quantum channels (III). Ann. Appl. Probab. 21 (2011), no. 3, 1136--1179. doi:10.1214/10-AAP722. https://projecteuclid.org/euclid.aoap/1307020394


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