  We consider the reversible processes between two one-to-one correlated
measurement outcomes which underly both problem-solving and quantum
nonlocality. In the former case the two outcomes are the setting and the
solution of the problem, in the latter those of measuring a pair of maximally
entangled observables whose subsystems are space separate. We argue that the
quantum description of these processes mathematically describes the correlation
but leaves the causal structure that physically ensures it free, also of
violating the time-symmetry required of the description of a reversible
process. It would therefore be incomplete and could be completed by
time-symmetrizing it. This is done by assuming that the two measurements evenly
contribute to selecting the pair of correlated measurement outcomes.
Time-symmetrization leaves the ordinary quantum description unaltered but shows
that it is the quantum superposition of unobservable time-symmetrization
instances whose causal structure is completely defined. Each instance is a
causal loop: causation goes from the initial to the final measurement outcome
and then back from the final to the initial outcome. In the speedup, all is as
if the problem solver knew in advance half of the information about the
solution she will produce in the future and could use this knowledge to produce
the solution with fewer computation steps. In nonlocality, the measurement on
either subsystem retrocausally and locally changes the state of both subsystems
when the two were not yet spatially separate. This locally causes the
correlation between the two future measurement outcomes.
