  We use techniques of quantum information theory to analyze the quantum causal
histories approach to quantum gravity. We show that while it is consistent to
introduce closed timelike curves (CTCs), they cannot generically carry
independent degrees of freedom. Moreover, if the effective dynamics of the
chronology-respecting part of the system is linear, it should be completely
decoupled from the CTCs. In the absence of a CTC not all causal structures
admit the introduction of quantum mechanics. It is possible for those and only
for those causal structures that can be represented as quantum computational
networks. The dynamics of the subsystems should not be unitary or even
completely positive. However, we show that other commonly maid assumptions
ensure the complete positivity of the reduced dynamics.
