  The properties of quantum information in space-time can be investigated by
studying operational tasks. In one such task, summoning, an unknown quantum
state is supplied at one point, and a call is made at another for it to be
returned at a third. Hayden-May recently proved necessary and sufficient
conditions for guaranteeing successful return of a summoned state for finite
sets of call and return points when there is a guarantee of at most one
summons. We prove necessary and sufficient conditions when there may be several
possible summonses and complying with any one constitutes success. We show
there is a "quantum paradox of choice" in summoning: the extra freedom in
completing the task makes it strictly harder. This intriguing result has
practical applications for distributed quantum computing and cryptography and
also implications for our understanding of relativistic quantum information and
its localization in space-time.
