Gaussianization and eigenvalue statistics for random quantum channels (III)

TL;DR

This paper applies advanced calculus to derive exact moments of random quantum channels with pure input states, analyzing a complex random matrix model to understand its eigenvalue behavior and entropy in quantum information theory.

Contribution

It introduces a novel application of Gaussianization methods to compute moments of quantum channels and studies a unique random matrix model with dual eigenvalue scalings.

Findings

Derived exact formulas for moments of quantum channels with pure states.

Analyzed the asymptotic eigenvalue behavior of a complex random matrix model.

Provided an asymptotic expansion for the von Neumann entropy of the model.

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.