  We compare the asymmetry-induced exchange splitting delta_1 of the
bright-exciton ground-state doublet in self-assembled (In,Ga)As/GaAs quantum
dots, determined by Faraday rotation, with its homogeneous linewidth gamma,
obtained from the radiative decay in time-resolved photoluminescence.
Post-growth thermal annealing of the dot structures leads to a considerable
increase of the homogeneous linewidth, while a strong reduction of the exchange
splitting is simultaneously observed. The annealing can be tailored such that
delta_1 and gamma become comparable, whereupon the carriers are still well
confined. This opens the possibility to observe polarization entangled photon
pairs through the biexciton decay cascade.
