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Self-testing usually refers to the task of taking a given set of observedcorrelations that are assumed to arise via a process that is accuratelydescribed by quantum theory, and trying to infer the quantum state andmeasurements. In other words it is concerned with the question of whether wecan tell what quantum black-box devices are doing by looking only at theirinput-output behaviour and is known to be possible in several cases. Here weintroduce a more general question: is it possible to self-test a theory, and,in particular, quantum theory? More precisely, we ask whether within aparticular causal structure there are tasks that can only be performed intheories 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 ina range of generalised probabilistic theories (GPTs), showing that none ofthese perform better than quantum theory. A generalisation of our resultsshowing that all non-quantum GPTs are strictly inferior to quantum mechanicsfor this task would point to a new way to axiomatise quantum theory, and enablean experimental test that simultaneously rules out such GPTs.

Self-testing of physical theories, or, is quantum theory optimal with respect to some information-processing task?