  In general relativity, closed timelike curves can break causality with
remarkable and unsettling consequences. At the classical level, they induce
causal paradoxes disturbing enough to motivate conjectures that explicitly
prevent their existence. At the quantum level, resolving such paradoxes induce
radical benefits - from cloning unknown quantum states to solving problems
intractable to quantum computers. Instinctively, one expects these benefits to
vanish if causality is respected. Here we show that in harnessing entanglement,
we can efficiently solve NP-complete problems and clone arbitrary quantum
states - even when all time-travelling systems are completely isolated from the
past. Thus, the many defining benefits of closed timelike curves can still be
harnessed, even when causality is preserved. Our results unveil the subtle
interplay between entanglement and general relativity, and significantly
improve the potential of probing the radical effects that may exist at the
interface between relativity and quantum theory.

Quantum Physics;General Relativity and Quantum Cosmology