A note on the asymptotics of random density matrices

TL;DR

This paper investigates the asymptotic spectral properties of large random density matrices, revealing their eigenvalue distribution and entropy production rate, extending previous results in random matrix theory.

Contribution

It generalizes existing results on the spectral distribution and entropy of random density matrices, providing new insights into their asymptotic behavior.

Findings

Eigenvalue distribution matches Wishart matrices asymptotically

Largest eigenvalue's distribution aligns with Wishart matrices

Entropy production rate scales logarithmically

Abstract

We show in this note that the asymptotic spectral distribution, location and distribution of the largest eigenvalue of a large class of random density matrices coincide with that of Wishart-type random matrices using proper scaling. As an application, we show that the asymptotic entropy production rate is logarithmic. These results are generalizations of those of Nechita, and Sommers and \. Zyczkowski.