  We study for a composite quantum system with a quantum Turing architecture
the temporal non-locality of quantum mechanics by using the temporal Bell
inequality, which will be derived for a discretized network dynamics by
identifying the subsystem indices with (discrete) parameter time. However, the
direct ``observation'' of the quantum system will lead to no violation of the
temporal Bell inequality and to consistent histories of any subsystem. Its
violation can be demonstrated, though, for a delayed-choice measurement.
