  We discuss some seemingly paradoxical yet valid effects of quantum physics in
information processing. Firstly, we argue that the act of ``doing nothing'' on
part of an entangled quantum system is a highly non-trivial operation and that
it is the essential ingredient underlying the computational speedup in the
known quantum algorithms. Secondly, we show that the watched pot effect of
quantum measurement theory gives the following novel computational possibility:
suppose that we have a quantum computer with an on/off switch, programmed ready
to solve a decision problem. Then (in certain circumstances) the mere fact that
the computer would have given the answer if it were run, is enough for us to
learn the answer, even though the computer is in fact not run.
