We consider a toy model of the interaction of a qubit with an exotic
space-time containing a time-like curve. Consistency seems to require that the
global evolution of the qubit be non-unitary. Given that quantum mechanics is
globally unitary, this then is an example of a quantum gravity information
paradox. However, we show that a careful analysis of the problem in the
Heisenberg picture reveals an underlying unitarity, thus resolving the paradox.Comment: 5 page
