# Qubit Entanglement generation by Gaussian non-Markovian dynamics

## TL;DR

This paper investigates how two qubits can become entangled through a shared bosonic bath in non-Markovian dynamics, revealing differences from Markovian behavior and conditions for entanglement generation.

## Contribution

It derives entanglement generation conditions for Gaussian non-Markovian maps and compares them to Markovian cases, highlighting differences in time scales and dependencies.

## Key findings

- Entanglement can be generated more rapidly in non-Markovian regimes.
- Non-Markovian entanglement conditions differ from Markovian ones, especially in the singular coupling limit.
- Entanglement generation conditions are time-independent for non-Markovian Gaussian baths.

## Abstract

We consider two qubits interacting with a common bosonic bath, but not directly between themselves. We derive the (bipartite) entanglement generation conditions for Gaussian non-Markovian dynamical maps and show that they are similar as in the Markovian regime; however, they depend on different physical coefficients and hold on different time scales. Indeed, for small times, in the non-Markovian regime entanglement is possibly generated on a shorter time scale ($\propto t^2$) than in the Markovian one ($\propto t$). Moreover, although the singular coupling limit of non-Markovian dynamics yields Markovian ones, we show that the same limit does not lead from non-Markovian entanglement generation conditions to Markovian ones. Also, the entanglement generation conditions do not depend on the initial time for non-Markovian open dynamics resulting from couplings to bosonic Gaussian baths, while they may depend on time for open dynamics originated by couplings to classical, stochastic Gaussian environments.