Random repeated quantum interactions and random invariant states

TL;DR

This paper studies a generalized model of repeated quantum interactions with randomness in unitaries or states, analyzing the asymptotic behavior of the system and introducing a new ensemble of random density matrices.

Contribution

It introduces a comprehensive framework for random repeated quantum interactions, analyzing convergence to invariant states and defining the asymptotic induced ensemble.

Findings

Convergence of the system's state to a unique invariant state.

Spectral analysis guarantees the existence of invariant states.

Introduction of the asymptotic induced ensemble of random density matrices.

Abstract

We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in detail. One is provided by considering Haar-distributed unitaries to describe each interaction between $\mathcal{H}$ and $\mathcal{K}_n$. The other involves random quantum states describing each copy $\mathcal{K}_n$. In the limit of a large number of interactions, we present convergence results for the asymptotic state of $\mathcal{H}$. This is achieved by studying spectral properties of (random) quantum channels which guarantee the existence of unique invariant states. Finally this allows to introduce a new physically motivated ensemble of random density matrices called the \emph{asymptotic induced ensemble}.