Semi-device-independent certification of the number of measurements

We develop a method for semi-device-independent certification of the number of measurements. We achieve this by testing whether Bob's steering equivalent observables can be simulated by $k$ measurements, which we do by testing whether they are $k$-compatible with separable joint observable. This test can be performed with the aid of hierarchy of semidefinite programs, and whenever it fails one can conclude that Alice must have access to at least ($k+1$)-incompatible measurements.