Effect of initial system-environment correlations with spin environments

Understanding the dynamics of open quantum systems is a highly important task for the implementation of emerging quantum technologies. To make the problem tractable theoretically, it is common to neglect initial system-environment correlations. However, this assumption is questionable in situations where the system is interacting strongly with the environment. In particular, the system state preparation can then influence the dynamics of the system via the system-environment correlations. To gain insight into the effect of these correlations, we solve an exactly solvable model of a quantum spin interacting with a spin environment both with and without initial correlations for arbitrary system-environment coupling strengths. We show that the effect of the system state preparation may or may not be significant in the strong system-environment coupling regime at low temperatures. We also study the dynamics of the entanglement between two spins interacting with a common spin environment with and without initial system-environment correlations to demonstrate that the correlations can play a significant role in the dynamics of two-qubit systems as well.