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

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.