  The predictions that quantum theory makes about the outcomes of measurements
are generally probabilistic. This has raised the question whether quantum
theory can be considered complete, or whether there could exist alternative
theories that provide improved predictions. Here we review recent work that
considers arbitrary alternative theories, constrained only by the requirement
that they are compatible with a notion of "free choice" (defined with respect
to a natural causal order). It is shown that quantum theory is "maximally
informative", i.e., there is no other compatible theory that gives improved
predictions. Furthermore, any alternative maximally informative theory is
necessarily equivalent to quantum theory. This means that the state a system
has in such a theory is in one-to-one correspondence with its
quantum-mechanical state (the wave function). In this sense, quantum theory is
complete.
