How quantum superposition could unravel the ‘grandfather paradox’

The ‘grandfather paradox’ has long been one of the most popular thought experiments in physics: you travel back in time and murder your grandfather before he’s ever born. If you’ve killed your grandfather, you’ve prevented your own existence, but if you never existed, how could you have committed the murder in the first place? Some physicists have avoided the question by arguing that backwards time travel simply isn’t consistent with the laws of physics, or by asserting a ‘many worlds’ interpretation of the Universe. But could the concept of quantum superposition remove what seems so paradoxical from this tale of time travel and murder once and for all?