Discontinuous quantum evolutions in the presence of closed timelike curves

Abstract

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.

v2: Some corrections and clarifications to the "Discontinuities" section. No results or conclusions are changed. v3: Minor changes. v4: Final version published in Phys. Rev. D.

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