A closed time-like curve is a theoretically allowed spacetime trajectory that forms a loop — the end being the same point in space and time as the start. As if this doesn't seem weird enough, give quantum computers access to systems that are trapped in such a curve and things start to get even wilder.
The key point is that by intertwining the past and the future of a quantum system, closed time-like curves induce a nonlinear quantum evolution. And — as has now been experimentally simulated by Martin Ringbauer and colleagues — this non-linearity may be capable of overriding some of the most basic assumptions of quantum mechanics, including the ideal case of perfect discrimination of non-orthogonal states.
As table-top wormholes are not (yet) available, the experiment simulated a single photon locked in a closed time-like curve by ensuring that its initial and final states were exactly the same. A second photon, interacting with the first, was then shown to undergo the predicted nonlinear dynamics — effectively constituting one of the first examples of how relativistic phenomena could influence quantum physics.
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Levi, F. Back from the future. Nature Phys 10, 547 (2014). https://doi.org/10.1038/nphys3068