  The D-CTC condition is a condition originally proposed by David Deutsch as a
condition on states of a quantum communication network that contains "backward
time-steps" in some of its branches. It has been argued that this is an
analogue for quantum processes in the presence of closed timelike curves
(CTCs). The unusual properties of states of quantum communication networks that
fulfill the D-CTC condition have been discussed extensively in recent
literature. In this work, the D-CTC condition is investigated in the framework
of quantum field theory in the local, operator-algebraic approach due to Haag
and Kastler. It is shown that the D-CTC condition cannot be fulfilled in states
which are analytic for the energy, or satisfy the Reeh-Schlieder property, for
a certain class of processes and initial conditions. On the other hand, if a
quantum field theory admits sufficiently many uncorrelated states across
acausally related spacetime regions (as implied by the split property), then
the D-CTC condition can always be fulfilled approximately to arbitrary
precision. As this result pertains to quantum field theory on globally
hyperbolic spacetimes where CTCs are absent, one may conclude that interpreting
the D-CTC condition as characteristic for quantum processes in the presence of
CTCs could be misleading, and should be regarded with caution. Furthermore, a
construction of the quantized massless Klein-Gordon field on the Politzer
spacetime, often viewed as spacetime analogue for quantum communication
networks with backward time-steps, is proposed in this work.
