Entanglement and Purity in Open Systems: A Breakdown of the Lindblad Approach

TL;DR

This paper critically evaluates the Lindblad master equation's ability to accurately describe short-time entanglement and purity dynamics in open quantum systems, revealing significant limitations compared to microscopic models.

Contribution

It demonstrates the shortcomings of the Lindblad approach in capturing entanglement growth and purity decay, especially under strong dissipation, and discusses improvements and inconsistencies.

Findings

Lindblad predicts linear purity decay, unlike quadratic decay in microscopic models.

Entanglement can be suppressed entirely when dissipation exceeds interaction strength.

Time-dependent Lindbladians improve some predictions but introduce inconsistencies.

Abstract

We examine the effectiveness of Lindblad master equation in capturing the short-time dynamics of entanglement and purity in open quantum systems. Focusing on two interacting two-level systems interacting with a larger environment, we compare the Lindbladian approach to a full microscopic treatment. While the latter shows entanglement growth and a quadratic decay of purity, the Lindbladian method predicts a linear purity decay and can entirely suppress entanglement when the dissipative coupling exceeds the interaction strength. Introducing a time-dependent Lindbladian improves some predictions but causes inconsistencies in other observables. Our results highlight the limitations of effective models and the need for caution when applying them to describe subtle quantum behaviors.