Unitary Solution to a Quantum Gravity Information Paradox

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.