Coherence-Assisted Entanglement Activation During Open Evolution

Abstract: The fact that in the course of an open evolution there is, in a vast majority of cases, a creation of system-environment entanglement out of the initial coherences, has been known for many years. However, how much entanglement can be created under general assumptions has not been analyzed yet. In this work, we investigate system-environment entanglement generation under a broad and important class of interactions known as pure dephasing interactions. Using completely general initial states, we derive a series of bounds on the amount of the created entanglement, connecting it to the initial system coherences as well as to the decohrence strength, making quantitatively precise the statement that larger entanglement leads to more decoherence. Interestingly, we obtain lower bounds, certifying minimal amount of entanglement that can be produced. As an illustration, we apply our results to the spin-boson model, where a qubit interacts with a bosonic bath, showing time evolution of the entanglement and the Markovian/non-Markovian crossover. Our results help to better understand and quantify the complicated correlations, produced during an open evolution, which will hopefully lead to better/new decoherence mitigation techniques.