# Asymptotic free independence and entry permutations for Gaussian random matrices

## TL;DR

This paper investigates how certain entry permutations, including transpose and others relevant to quantum physics, induce asymptotic freeness in Gaussian random matrices under specific conditions.

## Contribution

It characterizes conditions on entry permutations that lead to asymptotic freeness in Gaussian matrices, extending understanding to permutations used in quantum information.

## Key findings

- Permutations like transpose induce asymptotic freeness.
- Conditions on permutations ensure asymptotic freeness in Gaussian matrices.
- Includes permutations relevant to quantum physics and information theory.

## Abstract

The paper presents conditions on entry permutations that induce asymptotic freeness when acting on Gaussian random matrices. The class of permutations described includes the matrix transpose, as well as entry permutations relevant in Quantum Information Theory and Quantum Physics.