  We analyze the potential of the $c$-plane InGaN/GaN quantum dots for
polarization entangled photon emission by means of an atomistic many-body
framework. Special attention is paid to the impact of random alloy fluctuations
on the excitonic fine structure and the excitonic binding energy. Our
calculations show that $c$-plane InGaN/GaN quantum dots are ideal candidates
for high temperature entangled photon emission as long as the underlying
$C_{3v}$-symmetry is preserved. However, when assuming random alloy
fluctuations in the dot, our atomistic calculations reveal that while the large
excitonic binding energies are only slightly affected, the $C_{3v}$ symmetry is
basically lost due to the alloy fluctuations. We find that this loss in
symmetry significantly impacts the excitonic fine structure. The observed
changes in fine structure and the accompanied light polarization
characteristics have a detrimental effect for polarization entangled photon
pair emission via the biexciton-exciton cascade. Here, we also discuss possible
alternative schemes that benefit from the large excitonic binding energies, to
enable non-classical light emission from $c$-plane InGaN/GaN quantum dots at
elevated temperatures.
