A central limit theorem for partial transposes of multipartite Wishart matrices

TL;DR

This paper proves a central limit theorem for partial transposes of multipartite Wishart matrices, extending asymptotic freeness results from bipartite to multipartite cases in quantum information theory.

Contribution

It generalizes asymptotic freeness of partial transposes to multipartite matrices and establishes a central limit theorem in this context.

Findings

Almost sure asymptotic freeness for multipartite partial transposes

Central limit theorem for partial transposes of Wishart matrices

Extension of bipartite results to multipartite setting

Abstract

The partial transposition from quantum information theory provides a new source to distill the so-called asymptotic freeness without the assumption of classical independence between random matrices. Indeed, a recent paper [MP19] established asymptotic freeness between partial transposes in the bipartite situation. In this paper, we prove almost sure asymptotic freeness in the general multipartite situation and establish a central limit theorem for the partial transposes.