So we're all in superpositions and get our role when we're investigated or see our action took effectAwwww but quantum mafia is cool!
Everyone starts out with a probability of being every role in the game and submits all actions. slowly the game resolves itself and we figure out who we were when we started!
The problem is what happens when all the cops are in superpositions...
It would be fun though with entangled roles where one person suddenly knows their role because someone else died or was investigated. I have no idea how the scum team world work though, maybe 50% know they have a chance if being part of it and slowly find out?