  Experimental determination of an unknown quantum state usually requires
several incompatible measurements. However, it is also possible to determine
the full quantum state from a single, repeated measurement. For this purpose,
the quantum system whose state is to be determined is first coupled to a second
quantum system (the "assistant") in such a way that part of the information in
the quantum state is transferred to the assistant. The actual measurement is
then performed on the enlarged system including the original system and the
assistant. We discuss in detail the requirements of this procedure and
experimentally implement it on a simple quantum system consisting of nuclear
spins.
