Coherence-Assisted Entanglement Activation During Open Evolution

TL;DR

This paper derives bounds on system-environment entanglement generated during open quantum evolution, linking it to initial coherence and decoherence, with applications to the spin-boson model.

Contribution

It provides the first quantitative bounds on entanglement creation during pure dephasing interactions for arbitrary initial states.

Findings

Bounds relate entanglement to initial coherence and environmental information

Larger entanglement correlates with increased decoherence

Application to spin-boson model shows entanglement dynamics and non-Markovian effects

Abstract

The fact that in the course of an open evolution there is, in a vast majority of cases, the creation of system-environment entanglement out of the initial coherence, 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 and for arbitrary initial conditions. Our main results are the following bounds on the relative entropy of entanglement $E_r(\sigma_{SE})$ after evolution: $ C_r(\rho_S) - H(\mathcal{I}|\mathcal{M}) \leq E_r(\sigma_{SE}) \leq C_r(\rho_S) - C_r(\sigma_S) + H(\mathcal{I})$, connecting it on one side to the initial relative entropy of coherence, $C_r(\rho_S)$, and information extractable from the environment, $H(\mathcal{I}|\mathcal{M})$, and on the other side to the decoherence strength, $ C_r(\rho_S) - C_r(\sigma_S)$, making quantitatively precise the statement that larger entanglement leads to more decoherence. 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 better understand and quantify the complicated correlations, produced during an open evolution, which will hopefully lead to better and new decoherence mitigation techniques.