  Gedanken experiments are important conceptual tools in the quest to reconcile
our classical intuition with quantum mechanics and nowadays are routinely
performed in the laboratory. An important open question is the quantum
behaviour of the controlling devices in such experiments. We propose a
framework to analyse quantum-controlled experiments and illustrate the
implications by discussing a quantum version of Wheeler's delayed-choice
experiment. The introduction of a quantum-controlled device (i.e., quantum
beamsplitter) has several consequences. First, it implies that we can measure
complementary phenomena with a single experimental setup, thus pointing to a
redefinition of complementarity principle. Second, a quantum control allows us
to prove there are no consistent hidden-variable theories in which "particle"
and "wave" are realistic properties. Finally, it shows that a photon can have a
morphing behaviour between "particle" and "wave"; this further supports the
conclusion that "particle" and "wave" are not realistic properties but merely
reflect how we 'look' at the photon. The framework developed here can be
extended to other experiments, particularly to Bell-inequality tests.
