So much for classical objects and time travel. But what would happen if a quantum particle entered a closed time-like curve? In the early 90s, the physicist David Deutsch showed that not only is this possible but that it can only happen in a way that does not allow superluminal signalling. So quantum mechanics plays havoc with causality but in a way that is consistent with relativity and so prevents grandfather-type paradoxes. Deutsch’s result has extraordinary implications. It implies that closed time-like curves can be used to solve NP-complete problems in polynomial time and to violate Heisenberg’s uncertainty principle.
via https://medium.com/the-physics-arxiv-blog/the-quantum-experiment-that-simulates-a-time-machine–185a7cc9bd11