General belief among physicists is that quantum effects are not applicable within the black hole but I feel that the spinning black hole in general and the dyonic black hole in particular may be capable of processing the quantum information. The study of dyonic black hole has been sucessfully carried out in our paper entitled, " Gravitating Dyouns and Dyonic Black Holes in SU(2) and SU(5) Theories" published in International Journal Of Theoretical PPhysics Vol. 47 (2008) pp 2605-2618.
Following the work of Stefan Haking, that says Black holes are not completely black, we also found some such results. As per our theory some information manages to escape from Black Holes. Thus it may possible that Black Holes can process Quantum information. But until we do the mathematics, we cant conclude anything.