Random matrix techniques in quantum information theory

TL;DR

This review explores recent advances in applying random matrix techniques to quantum information theory, focusing on quantum states and channels, and analyzing properties like entanglement and entropy.

Contribution

It provides an extensive overview of the latest developments and detailed examples in the use of random matrix methods in quantum information research.

Findings

Analysis of entropic properties of random quantum states

Identification of entanglement thresholds in typical states

Insights into the output set and entropy violations of random quantum channels

Abstract

The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is a blend of a rather exhaustive review, combined with more detailed examples -- coming from research projects in which the authors were involved. We focus on two main topics, random quantum states and random quantum channels. We present results related to entropic quantities, entanglement of typical states, entanglement thresholds, the output set of quantum channels, and violations of the minimum output entropy of random channels.