  Cross-correlated noise measurements are performed in etched
Al${}_\text{x}$Ga${}_\text{1-x}$As/GaAs based quantum rings in equilibrium at
bath temperature of $T_\text{bath}=4.2\text{ K}$. The measured white noise
exceeds the thermal (Johnson-Nyquist) noise expected from the measured electron
temperature $T_\text{e}$ and the electrical resistance $R$. This excess part of
the white noise decreases as $T_\text{bath}$ increases and vanishes for
$T_\text{bath}\geq 12\text{ K}$. Excess noise is neither observed if one arm of
a quantum ring is depleted of electrons nor in 1D-constrictions that have a
length and width comparable to the quantum rings. A model is presented that
suggests that the excess noise originates from the correlation of noise
sources, mediated by phase-coherent propagation of electrons.
