  The purpose of this paper is to show the unusual behavior of a number of
simple circuits under the effects of post-selection. A useful duality exists
between post-selected ensembles and a consistent picture of acausal physics
embodying the application of Novikov's consistency postulate to the
wave-function of a time machine. A competing view applies this postulate to
density matrices instead, but that lies outside the scope of this paper. To
find out the result of a measurement on a particular circuit, we consider a
weighted distribution of histories between some initial and final time, such
that each individually obeys ordinary quantum mechanics. The weight of a
particular history is given by a joint distribution over the values of a part
of the system dubbed the time machine, at two chosen times. In the dual
post-selection picture the weight is simply the probability for the 'periodic
bit' to satisfy the constraint, plus a small noise part, often assumed
constant, representing the error rate of the time machine's channel. The
emerging bit is one of a Bell pair, its partner kept in reserve to test that
the bit entering the time machine later matches the one which emerged. This is
done by interfering the incoming bit with the reserve member of the pair and
keeping the experimental runs that interfere constructively. Noise can be
effectively simulated by keeping a small proportion of runs that interfere
destructively, or by perturbing the reserve bit to decohere it by a similar
amount. Paradoxes remain but are tractable.
