Entropy Decay Estimates For Collective Noise Models

TL;DR

This paper develops a framework to estimate entropy decay and spectral gaps in collective quantum noise models, particularly Dicke's model, aiding understanding of their convergence to equilibrium.

Contribution

It introduces a general approach combining representation theory and entropy estimates to analyze spectral gaps and mixing conditions in collective noise models.

Findings

Established spectral gap estimates for Dicke's model

Identified conditions for unique equilibrium states

Provided a methodology applicable to broader collective noise models

Abstract

One of the challenges in quantum information science is to control open quantum systems with a large number of qubits. An important aspect of many-body systems is the emergence of collective phenomena. One collective noise model is an open atomic system in an electromagnetic environment. This model was considered by Dicke in the 50's Dicke. In this paper, we study the entropic decay in Dicke's model and other related collective noise models. Specifically, we develop a general framework to estimate the spectral gap and modified logarithmic Sobolev constant of these collective noise models. In addition, we study the necessary mixing conditions a general Dicke's model must satisfy in order to have a unique equilibrium state. The combination of representation theory and entropy estimates could be a guideline to study more general collective noise models.