  We establish for the first time an exact stochastic dynamical equation for an
open quantum systems coupled to correlated noises. We rigorously investigate
the nonequilibrium dynamics of a qubit system under the influence of two
strongly correlated non-Markovian baths by exactly solving the stochastic
Schr\"{o}dinger equation of an open quantum system. We show that the quantum
dynamics of the qubit system is profoundly modulated by the mutual correlation
between baths and the bath memory times through dissipation and fluctuation. We
report a new physical effect on generating large values of the
inner-correlation and entanglement of the distant two qubits arising from the
strong bath correlation for a class of super-radiation states.
