  Closed timelike curves are among the most controversial features of modern
physics. As legitimate solutions to Einstein's field equations, they allow for
time travel, which instinctively seems paradoxical. However, in the quantum
regime these paradoxes can be resolved leaving closed timelike curves
consistent with relativity. The study of these systems therefore provides
valuable insight into non-linearities and the emergence of causal structures in
quantum mechanics-essential for any formulation of a quantum theory of gravity.
Here we experimentally simulate the non-linear behaviour of a qubit interacting
unitarily with an older version of itself, addressing some of the fascinating
effects that arise in systems traversing a closed timelike curve. These include
perfect discrimination of non-orthogonal states and, most intriguingly, the
ability to distinguish nominally equivalent ways of preparing pure quantum
states. Finally, we examine the dependence of these effects on the initial
qubit state, the form of the unitary interaction, and the influence of
decoherence.
