A random matrix theory of decoherence

TL;DR

This paper employs random matrix theory to model how a quantum system loses coherence due to interactions with a chaotic environment, providing analytical and numerical insights into the average density matrix and purity.

Contribution

It introduces a novel approach using random matrix ensembles to analyze decoherence, contrasting with previous focus on average measures like purity and entropy.

Findings

Analytic expressions for average density matrix and purity in linear response.

Agreement between different approaches in large environment limit.

Numerical analysis of two-qubit decoherence dynamics.

Abstract

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence, and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.