  We consider Deutsch's computational model of a quantum system evolving in a
spacetime containing closed timelike curves. Although it is known that this
model predicts non-linear and non-unitary evolutions of the system, we
demonstrate that it also gives rise to evolutions which are a discontinuous
function of the input state. These discontinuities persist for the most natural
modifications of Deutsch's approach.

Quantum Physics;General Relativity and Quantum Cosmology;High Energy Physics - Theory