  We study the generation of quantum correlations between two excitonic quantum
dot qubits due to their interaction with the same phonon environment. Such
generation results from the fact that during the pure dephasing process at
finite temperatures, each exciton becomes entangled with the phonon
environment. We find that for a wide range of temperatures quantum correlations
are created due to the interaction. The temperature-dependence of the amount of
correlations created displays a trade-off type behaviour; for small
temperatures the phonon-induced distrubance of the qubit states is too small to
lead to a distinct change of the two-qubit state, hence, the amount of created
correlations is small, while for large temperatures the pure dephasing is not
accompanied by the creation of entanglement between the qubits and the
environment, so the environment cannot mediate qubit-qubit quantum
correlations.
