  Self-testing usually refers to the task of taking a given set of observed
correlations that are assumed to arise via a process that is accurately
described by quantum theory, and trying to infer the quantum state and
measurements. In other words it is concerned with the question of whether we
can tell what quantum black-box devices are doing by looking only at their
input-output behaviour and is known to be possible in several cases. Here we
introduce a more general question: is it possible to self-test a theory, and,
in particular, quantum theory? More precisely, we ask whether within a
particular causal structure there are tasks that can only be performed in
theories that have the same correlations as quantum mechanics in any scenario.
We present a candidate task for such a correlation self-test and analyse it in
a range of generalised probabilistic theories (GPTs), showing that none of
these perform better than quantum theory. A generalisation of our results
showing that all non-quantum GPTs are strictly inferior to quantum mechanics
for this task would point to a new way to axiomatise quantum theory, and enable
an experimental test that simultaneously rules out such GPTs.
