  The causal structure of any experiment implies restrictions on the observable
correlations between measurement outcomes, which are different for experiments
exploiting classical, quantum, or post-quantum resources. In the study of Bell
nonlocality, these differences have been explored in great detail for more and
more involved causal structures. Here, we go in the opposite direction and
identify the simplest causal structure which exhibits a separation between
classical, quantum, and post-quantum correlations. It arises in the so-called
Instrumental scenario, known from classical causal models. We derive
inequalities for this scenario and show that they are closely related to
well-known Bell inequalities, such as the Clauser-Horne-Shimony-Holt
inequality, which enables us to easily identify their classical, quantum, and
post-quantum bounds as well as strategies violating the first two. The
relations that we uncover imply that the quantum or post-quantum advantages
witnessed by the violation of our Instrumental inequalities are not
fundamentally different from those witnessed by the violations of standard
inequalities in the usual Bell scenario. However, non-classical tests in the
Instrumental scenario require fewer input choices than their Bell scenario
counterpart, which may have potential implications for device-independent
protocols.
