  Non-Markovian dynamics is studied for two interacting quibts strongly coupled
to a dissipative bosonic environment. For the first time, we have derived the
non-Markovian quantum state diffusion (QSD) equation for the coupled two-qubit
system without any approximations, and in particular, without the Markov
approximation. As an application and illustration of our derived time-local QSD
equation, we investigate the temporal behavior of quantum coherence dynamics.
In particular, we find a strongly non-Markovian regime where entanglement
generation is significantly modulated by the environmental memory.
Additionally, we studied the residual entanglement in the steady state by
analyzing the steady state solution of the QSD equation. Finally, we have
discussed an approximate QSD equation.
